Method and device for processing cytometric data

Abstract

Methods and devices for processing cytometric data are disclosed. The present disclosure provides a method for processing cytometric data, the method comprising the steps of: dividing a first data matrix into a first plurality of first sub-matrices, encoding each of the first sub-matrices into a corresponding vector representation to obtain the first plurality of vector representations, and aggregating the first plurality of vector representations into a first ensemble representation. The first data matrix is ​​indicative of a first plurality of properties of a first set of cells.

Description

[Technical field]

[0001] (CROSS REFERENCE TO RELATED APPLICATIONS) This application claims the benefit of and priority to U.S. Provisional Patent Application No. 63 / 362,124, filed March 29, 2022, which is incorporated by reference herein in its entirety.

[0002] The present disclosure relates to methods and devices for processing cytometric data, in particular for the classification of hematological malignancies. [Background technology]

[0003] Hematological malignancies are cancers of the blood, bone marrow, and lymph nodes. These hematological malignancies are associated with significant morbidity and mortality, negatively impacting quality of life. Accurate classification of hematological malignancies is necessary to select the appropriate treatment strategy for each new admitted patient. Hematological malignancies arise from and recapitulate to varying degrees the complex and diverse cell lineages and stages of cytogenesis that produce blood cells and other cells that respond to immune stimuli. This leads to different disease characteristics and prognosis. For example, acute lymphoblastic leukemia (ALL) and acute myeloid leukemia (AML) are caused by abnormalities in lymphocytes and myeloid cells, respectively. Acute promyelocytic leukemia (APL) is a subtype of AML, and other types of hematological malignancies such as chronic lymphocytic leukemia (CLL) and a wide variety of lymphomas all have different symptoms and prognosis and require different treatment strategies. Summary of the Invention

[0004] Due to the wide variety of hematological malignancies, rapid and accurate classification is crucial to determine effective disease management and the first steps towards a cure for patients.

[0005] Flow cytometry (FC) generates data from high-throughput streams of individual cells from bone marrow, blood, or lymphoid tissue specimens for high-quality hematological malignancy screening, diagnosis, and monitoring. Antibodies labeled with fluorescent tags allow for the characterization of complex expression of cellular proteins (i.e., antigens) by flow cytometry. Thousands or millions of cells in a specimen sample are evaluated using a panel of antibodies that are differentiated from one another by specific channels that emit different fluorescent tags, generating a large number of data points. The physician or examiner relies on visualization tools to display the fluorescence indicating the expression of pairs of antigens in cell populations in a two-dimensional scatter plot, and then performs a hierarchical gating procedure to identify abnormal cell populations. After the physician or examiner interprets the combination of multiple antibody pairs and fluorescence, the type of hematological malignancy in the patient can be determined by evaluation of morphological findings and other appropriate tests. The manual gating process of FC is laborious and subjective to subjective judgment between physicians. Current tools aid the gating process, and for the most part only provide unsupervised cell population clustering. The goal of these tools is to rapidly identify cell populations that appear to form related clusters, but the ultimate procedure for generating an interpretation remains unchanged.

[0006] Differentiating between types of hematological malignancies is crucial to determine treatment strategies for newly diagnosed patients. Flow cytometry (FC) can be used as a diagnostic indicator by measuring multi-parameter fluorescent markers on thousands of antibody-bound cells, but manual interpretation of large-scale flow cytometry data has long been a time-consuming and complex task for hematologists and laboratory experts. Some embodiments lead to the development of a representation learning algorithm to perform sample-level automatic classification. In this work, we propose a chunking-for-pooling strategy to incorporate large-scale FC data into a supervised deep representation learning procedure for automatic classification of hematological malignancies. The use of a discriminatively trained representation learning strategy and the design of fixed-size chunking and pooling are two of the features of the framework provided in this disclosure. It improves the discriminatory power of FC sample-level embedding (or pooling) while at the same time solving the robustness problem due to the unavoidable use of downsampling in traditional distribution-based approaches to derive FC representations. The framework provided in this disclosure is evaluated on two datasets. Our framework outperforms other baseline methods, achieving an unweighted average recall (UAR) of 92.3% for 4-class recognition on the UPMC dataset and 85.0% for 5-class recognition on the hema.to dataset. We further compared the robustness of our proposed framework with that of traditional downsampling approaches. Analysis of the impact of chunk size and error cases revealed further insights into the characteristics of different hematological malignancies in FC data.

[0007] The present disclosure provides a novel method or device for efficiently processing cytometric data, which can help doctors or examiners to efficiently determine the type of hematological malignancy in patients. Also, the conventional method for processing cytometric data requires too much computing power and memory space. The novel method or device provided in the present disclosure can save computing power, memory space, and power consumption.

[0008] To address the bottleneck of computational power and memory space, random downsampling of cytometric data has been proposed. Such random downsampling may cause undesired variations and may also have the risk of discarding important cells or residual tumor cells. The novel method or device provided in the present disclosure can reduce the undesired variations and the risk of discarding important cells or residual tumor cells.

[0009] The exemplary embodiments disclosed herein aim to solve one or more problems associated with the prior art, as well as to provide additional features that will become readily apparent by reference to the following detailed description in conjunction with the accompanying drawings. According to various embodiments, exemplary systems, methods, devices, and computer program products are disclosed herein. However, it is understood that these embodiments are presented by way of example and not limitation, and it will be apparent to those skilled in the art upon reading this disclosure that various modifications to the disclosed embodiments can be made while remaining within the scope of the present invention.

[0010] An embodiment of the present disclosure provides a method for processing cytometric data, the method including: dividing a first data matrix into a first plurality of first sub-matrices, encoding each of the first sub-matrices into a corresponding vector representation to obtain the first plurality of vector representations, and aggregating the first plurality of vector representations into a first ensemble representation, where the first data matrix is ​​indicative of a first plurality of properties of a first set of cells.

[0011] Another embodiment of the present disclosure provides a device for processing cytometric data, the device including a processor and a memory coupled to the processor. The processor executes computer readable instructions stored in the memory to perform operations including receiving a first data matrix indicative of a first plurality of properties of a first set of cells, dividing, by the processor, the first data matrix into a first plurality of first sub-matrices, encoding, by the processor, each of the first sub-matrices into a corresponding vector representation to obtain the first plurality of vector representations, and aggregating, by the processor, the first plurality of vector representations into a first ensemble representation. [Brief description of the drawings]

[0012] To explain the manner in which the advantages and features of the present disclosure can be obtained, a description of the disclosure will be rendered with reference to specific embodiments thereof that are illustrated in the accompanying drawings. These drawings depict only exemplary embodiments of the present disclosure and are therefore not to be considered as limiting its scope. [Figure 1] 1 shows a schematic diagram illustrating a computing device according to some embodiments of the present disclosure. [Diagram 2] 1 shows a schematic diagram illustrating the operation of a framework according to some embodiments of the present disclosure. [Diagram 3] 1 is a flowchart of a method according to some embodiments of the present disclosure. [Figure 4A]1 shows a confusion matrix illustrating performance according to some embodiments of the present disclosure. [Figure 4B] 1 shows a confusion matrix illustrating performance according to some embodiments of the present disclosure. [Figure 4C] 1 shows a confusion matrix illustrating performance according to some embodiments of the present disclosure. [Figure 4D] 1 shows a confusion matrix illustrating performance according to some embodiments of the present disclosure. [Figure 5A] 1 illustrates performance and error distribution according to some embodiments of the present disclosure. [Figure 5B] 1 illustrates performance and error distribution according to some embodiments of the present disclosure. [Figure 5C] 1 illustrates performance and error distribution according to some embodiments of the present disclosure. [Figure 5D] 1 illustrates performance and error distribution according to some embodiments of the present disclosure. [Figure 6A] 13 illustrates results for different chunk amounts and chunk sizes according to some embodiments of the present disclosure. [Figure 6B] 13 illustrates results for different chunk amounts and chunk sizes according to some embodiments of the present disclosure. [Figure 6C] 13 illustrates results for different chunk amounts and chunk sizes according to some embodiments of the present disclosure. [Figure 6D] 13 illustrates results for different chunk amounts and chunk sizes according to some embodiments of the present disclosure. [Figure 7A] 13 illustrates the resulting distribution as chunk amount decreases according to some embodiments of the present disclosure. [Figure 7B] 13 illustrates the resulting distribution as chunk amount decreases according to some embodiments of the present disclosure. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0013] The following disclosure provides many different embodiments or examples for implementing different features of the provided subject matter. In the following, specific examples of operations, components, and arrangements are described to simplify the disclosure. These are, of course, merely examples and are not intended to be limiting. For example, a first operation performed before or after a second operation in the description may include embodiments in which the first and second operations are performed together, and may also include embodiments in which additional operations may be performed between the first and second operations. For example, forming a first feature on, on, or in a second feature in the following description may include embodiments in which the first and second features are formed in direct contact, and may also include embodiments in which additional features may be formed between the first and second features such that the first and second features are not in direct contact. In addition, the disclosure may repeat reference numbers and / or letters in various examples. This repetition is for the purpose of simplicity and clarity, and does not in itself dictate a relationship between the various embodiments and / or configurations being described.

[0014] Time relative terms, such as "prior to," "before," "posterior to," "after," and the like, may be used herein to facilitate describing the relationship of one action or feature to another action or feature, as shown in the figures. The time relative terms are intended to encompass the different sequences of actions depicted in the figures. Additionally, space relative terms, such as "beneath," "below," "lower," "above," "upper," and the like, may be used herein to facilitate describing the relationship of one element or feature to another element or feature, as shown in the figures. The space relative terms are intended to encompass different orientations of the device during use or operation in addition to the orientation depicted in the figures. The device may be oriented in other ways (rotated 90 degrees or at other orientations) and the space relative descriptors used herein may be interpreted accordingly. Relative connection terms such as "connect," "connected," "connection," "couple," "coupled," "incommunication," and the like may be used herein to facilitate describing an operational connection, coupling, or link between two elements or features. Relative connection terms are intended to encompass different connections, couplings, or links of devices or components. Devices or components may be directly or indirectly connected, coupled, or linked to each other, for example, through another set of components. Devices or components may be wired and / or wirelessly connected, coupled, or linked to each other.

[0015] As used herein, the singular terms "a," "an," and "the" may include plural referents unless the context clearly dictates otherwise. For example, a reference to a device may include a plurality of devices unless the context clearly dictates otherwise. The terms "comprising" and "including" may indicate the presence of stated features, integers, steps, operations, elements, and / or components, but may not exclude the presence of one or more combinations of the features, integers, steps, operations, elements, and / or components. The term "and / or" may include any or all combinations of one or more listed items.

[0016] Additionally, amounts, ratios, and other numerical values ​​may be presented herein in a range format, with it being understood that such range formats are used for convenience and brevity and include numerical values ​​expressly specified as the limits of the range, but should be understood flexibly to also include all individual numerical values ​​or subranges subsumed within that range, as if each numerical value and subrange was expressly specified.

[0017] The nature and use of the embodiments are described in detail below. It should be understood, however, that the present disclosure provides many applicable inventive concepts that can be embodied in a wide variety of specific contexts. The specific embodiments described are merely illustrative of specific ways to embody and use the present disclosure, and are not intended to limit its scope.

[0018] FIG. 1 shows a schematic diagram illustrating a computing device 100 according to some embodiments of the present disclosure. The computing device 100 may be capable of performing one or more procedures, operations, or methods of the present disclosure. The computing device 100 may be a server computer, a client computer, a personal computer (PC), a tablet PC, a set-top box (STB), a personal digital assistant (PDA), a mobile phone, or a smartphone. The computing device 100 includes a processor 101, an input / output interface 102, a communication interface 103, and a memory 104. The input / output interface 102 is coupled to the processor 101. The input / output interface 102 enables a user to operate the computing device 100 to perform the procedures, operations, or methods of the present disclosure (e.g., the procedures, operations, or methods disclosed in FIGS. 2 and 3).

[0019] The communications interface 103 is coupled to the processor 1101. The communications interface 103 allows the computing device 100 to communicate with data external to the computing device 100, for example, to receive data including patient cytometric data, patient information, methods, algorithms, programs, or software to be performed, or configurations of methods, algorithms, programs, or software. Data received via the communications interface 103 may be stored in one or more databases external to the computing device 100.

[0020] The memory 104 may be a non-transitory computer-readable storage medium. The memory 104 is coupled to the processor 101. The memory 104 stores program instructions that may be executed by one or more processors (e.g., the processor 101). Upon execution of the program instructions stored in the memory 104, the program instructions perform one or more procedures, operations, or methods disclosed in the present disclosure. For example, the program instructions may cause the computing device 100 to receive a first data matrix indicative of a first plurality of properties of a first set of cells, encode the first brain image by the processor 101 to generate a latent vector, divide the first data matrix into a first plurality of first sub-matrices by the processor 101, encode each of the first sub-matrices into a corresponding vector representation to obtain the first plurality of vector representations by the processor 101, and aggregate the first plurality of vector representations into a first ensemble representation by the processor 101. In some embodiments, the program instructions may cause the computing device 100 to perform the following: concatenating, by the processor 101, multiple ensemble representations to obtain a concatenated representation; and classifying, by the processor 101, the cytometric data based on the concatenated representation.

[0021] To alleviate these long-standing problems in interpreting FC data, machine learning (ML) for FC data modeling is a viable approach. Most of these computational studies focus on improving the efficiency of the manual gating process by identifying cell-level features. They build on the manual gating results for cell-based modeling. For efficient visualization, some studies have utilized dimensionality-reducing ML algorithms, e.g., principal component analysis (PCA), t-distributed stochastic neighbor embedding (t-SNE), uniform manifold approximation and projection (UMAP), and self-organizing maps (SOM), to visualize FC data as scatter plots in the gating process. Other ML algorithms have been developed to automatically detect cell populations after cell clustering. For example, blast recognition has been explored. Autoencoder feature transformation approaches have been widely used to detect ALL minimal residual disease and rate cell populations. Based on the detected cell types, sample-level results could only be derived by setting a predefined threshold on the total number of abnormal cells.

[0022] Recently, it has been found that classifying the outcome of sample-level diagnosis has a greater impact on clinical decision support than cell-level characterization. Therefore, directly modeling sample-level FC data to perform disease type classification or disease state prediction has become the next step in automated modeling of FC data. Because sample-level labels are obtained from the physician's or examiner's final interpretation, sample-level modeling can be formulated as a supervised learning task without relying on the laborious efforts of manual cell cluster labeling. However, in contrast to the aforementioned cell-level predictions, where each cell can be easily represented by a single vector consisting of the measured dimensions of multiple fluorescently labeled antibodies, adequately representing the entire FC data (i.e., the aggregated fluorescence measurements of thousands or millions of cells) as a sample-level vector to be used in ML training is not so straightforward and has become a significant technical endeavor.

[0023] In some embodiments, calculating statistical functions is used as an intuitive way to vectorize FC samples. One example is to represent samples as the percentage of threshold-over-threshold cells for each antibody and classify the subtype of B-cell non-Hodgkin's lymphoma as input. However, these statistically-based approaches underestimate the variability of the data, as the limited number of functions and empirically defined rules cannot fully capture the properties in the FC data samples.

[0024] In addition to representing complex antigen expression by computing statistical functions, distributional approaches are becoming state of the art (SOTA) to encode FC data as embedding vectors. The proportion of cells belonging to learned Dirichlet Process Gaussian Mixture Model (DPGMM) clusters can be computed as representations. In other embodiments, a similar cluster-based feature distribution encoding approach is used for MRD classification in ALL and AML. To distinguish AML and myelodysplastic syndromes (MDS) from normal samples, Fisher Vectors (FVs) can be introduced to calculate the gradient of clusters in Gaussian Mixture Models (GMMs) to obtain sample-level representation vectors. The FV representations can be utilized to achieve SOTA accuracy for distinguishing types of hematological malignancies. Although the aforementioned distributional approaches are effective in learning sample-level FC representations, they remain discriminatively suboptimal. That is, these approaches treat sample-level representation learning and classifier training as two decoupled and independent modules. Instead of implementing sample-level representation learning and result classifiers at different stages, the overall performance can be better optimized by constructing discriminative networks in an end-to-end manner. Previous SOTA distribution modeling, i.e., FV coding, consists of non-differentiable functions and is infeasible for end-to-end learning. We extend the FV coding approach by introducing NetFV, which reorganizes the underlying assumptions to allow discriminative gradient propagation in deep layers for FC representation learning. Rather than simply relying on unsupervised data clustering, the NetFV framework conditions label backpropagation to learn latent cell clusters.

[0025] Although these end-to-end approaches are attractive, parameterized maximum likelihood optimization usually suffers from GPU memory bottlenecks during practical implementation. This technical problem becomes increasingly challenging and important as the need to detect different antigens continues to evolve, leading to an increasing ability to simultaneously detect more fluorescent markers in one tube. The increasing diversity of recognized hematological malignancies calls for the development of more customized marker panels, which in turn generates even higher dimensional FC data. This can make downsampling cells unavoidable in some FC representation learning implementations. Random downsampling not only introduces undesirable variability, but also risks discarding important or residual tumor cells.

[0026] The present disclosure solves two major problems that exist in FC data modeling: suboptimal representation and incomplete data usage, by developing a deep discriminative FC representation learning framework. One of the features of the present disclosure is the "chunking for pooling" process. The chunking for pooling process segments each FC data into fixed-size "chunks", pools cells into chunks using a supervised network, and then aggregates the extracted chunk-level embedding vectors using an ensemble classification strategy. The GPU memory bottleneck problem can be solved by the use of chunks, and the pooling mechanism is jointly optimized with the supervised network weights. In some embodiments of this framework, the chunk-level representations can be learned by deep embedding networks such as NetFV and NetVLAD, which jointly optimize the latent GMM assumptions and encoding parameters in an end-to-end discriminative manner. In the hematological malignancy classification task, this embedding network embeds the discriminative information of different diseases within each chunk, maximizing the usage of FC data overall (as no downsampling is applied).

[0027] The disclosed framework is evaluated by using two hematological malignancy datasets. The method and device using the disclosed framework achieves a 4-class unweighted average recall (UAR) of 93.2% on the UPMC (University of Pittsburgh Medical Center) dataset and a 5-class UAR of 85.0% on the hema.to dataset. The disclosed chunking-for-pooling framework is compared with a downsampling approach to demonstrate the robustness of the chunking-for-pooling framework. Further analysis of the prediction results and the impact of chunk size illustrated the properties of different malignancy categories and the details of the chunking-for-pooling framework. Here, we summarize the application scenarios of the main contributions of this paper as follows:

[0028] This disclosure proposes a chunking-for-pooling framework that addresses the robustness issue when modeling FC data with varying numbers of cells across samples.

[0029] ●This disclosure introduces deep embedding networks to learn discriminative sample-level FC representations.

[0030] ● Comprehensive experiments and analyses were conducted on two clinical datasets to validate the disclosed chunking-for-pooling framework.

[0031] Sections A, B, and C describe the two FC datasets and the chunking for pooling framework. Sections D, E, and F contain the experiments and results. Section G concludes the paper.

[0032] A. Dataset A.1. UPMC Dataset This study was approved by the Institutional Review Board of the University of Pittsburgh and the Research Ethics Committee of the National Taiwan University Hospital. This disclosure refers to this dataset as the UPMC dataset. It includes bone marrow specimens collected at UPMC for patient care. 531 specimens were from independent newly diagnosed patients, and FC data was registered only when a full five-tube panel for antibody fluorescence measurements was performed on these specimens (shown in Table I). Antibody fluorescence measurements may be optical measurements such as forward and side light scatter. Diagnostic labels were derived from comprehensive bone marrow evaluations performed at UPMC, including morphological evaluation, manual flow cytometry analysis, cytogenetic studies, and other studies (e.g., molecular studies) as appropriate. Tables II and III show the statistics of hematological malignancy class distribution (APL, AML, ALL, and cytopenias) and blast percentages, respectively.

[0033] Table I shows the fluorophore and antibody combinations used in the UPMC and hema.to datasets. The terms "FITC", "PE", "PerCP-Cy5-5", "PE-Cy7", "APC", "APC-H7", "V450", "V500", "KrOr", "ECD", "PC5.5", "APCA750", "PC7", and "PacBlue" refer to the fluorophores that stain the cells being examined. The terms "Tube 1" through "Tube 5" indicate that the cells of one patient (e.g., one case) are divided into five tubes and different antibodies are examined in different tubes. The terms "Tube 1" through "Tube 3" indicate that the cells of one patient (e.g., one case) are divided into three tubes and different antibodies are examined in different tubes. One tube may be referred to as one sample in this disclosure. The terms "CD36", "CD15", "Kappa", "CD16&57", "FMC7", "CD8", "Lambda", "IgM", "HLA-DR", etc. refer to the antibodies being examined.

[0034] [Table 1]

[0035] Table II shows the data distribution of the two hematological malignancy datasets. The term "Type" indicates the different types of hematological malignancies. The term "N" indicates the number of cases. The term "%" indicates the percentage of the number of cases of different types of hematological malignancies to the total number of cases.

[0036] [Table 2]

[0037] Table III shows the blast percentage distribution of the UPMC dataset. The term "type" refers to different types of hematological malignancies. The terms "mean" and "SD" refer to the mean and standard deviation of the percentage distribution, respectively. The terms "min" and "max" refer to the minimum and maximum values ​​of the percentage distribution, respectively. The terms "Q1", "Q2", and "Q3" refer to the first, second, and third quartiles of the percentage distribution, respectively. The term "Q2" also refers to the median of the percentage distribution.

[0038] [Table 3]

[0039] A.2.hema.to Dataset This disclosure uses another dataset collected at the Munich Leukemia Institute (MLL) between January 1, 2016 and December 31, 2018, which is partially open for research. This dataset is called the hema.to dataset based on the name of the technology demonstration website. This dataset contains 20,622 routine diagnostic samples from patients with suspected B-cell neoplasms, of which 2528 samples are publicly available. As shown in Table II, the dataset includes normal controls, AML, and eight types of mature B-cell neoplasms, namely multiple myeloma (MM), chronic lymphocytic leukemia (CLL) and its precursors monoclonal B-cell lymphocytosis (MBL), prolymphocytic leukemia (PL), and hairy cell leukemia (HCL). We included human leukemia (HCL) and four other B-cell lymphomas, including marginal zone lymphoma (MZL), mantle cell lymphoma (MCL), follicular lymphoma (FL), and lymphoplasmacytic lymphoma (LPL). We considered MBL, PL, HCL, and the four B-cell lymphomas as a single class called "lymphoma." For a nine-color FC panel acquired on a Navios cytometer (Beckman Coulter, Miami, FL), three tubes were run with forward and side light scatter parameters as shown in Table I, resulting in 26 unique fluorescence-antibody dimensions for FC data interpretation.

[0040] B. Deep Chunking for Pooling Framework FIG. 2 shows a schematic diagram of a framework 200 provided in the present disclosure. FIG. 2 discloses a flowchart of one framework of the present disclosure. In a chunking operation 240, a flow cytometry data matrix 230 is divided into chunks 241 (or sub-matrices). Each chunk 241 is sent to a chunk-level pooling network 250 to extract a corresponding chunk representation 252. In the chunk-level pooling network 250, a transposition operation 251 may be performed on each of the chunks 241 (or sub-matrices). Finally, an ensemble prediction 260 is performed by aggregating multiple chunk representations 252 using a function (e.g., an aggregation function 261) to predict the type of hematological malignancy.

[0041] The framework shown in FIG. 2 includes three parts. The first part refers to pre-processing and chunking of FC data. The first part is described in Section B.1. The second part refers to the training method and architecture of the deep embedding network used in the chunk-level pooling network 250. The second part is described in Section B.2. The third part refers to the ensemble classification method that aggregates chunks and makes a decision per sample. The third part is described in Section B.3.

[0042] B.1. Chunk-level Data Preprocessing 2, the data set 210 may include multiple samples from several patients. For the nth (n∈N) sample 211 in the data set 210 (e.g., one tube from a patient), the FC data X n ∈R T*D can be obtained by fluorescent antibody measurement performed by flow cytometry 220. The FC data can be represented as a data matrix 220 having D columns and T columns. The FC data X n ∈R T*D is data X n,c ∈R C*D The data chunks may be represented as chunks 241 or sub-matrices. Each chunk 241 or sub-matrix may have D columns and C rows, where C is a constant chunk size. N is the total number of FC samples. D is the number of fluorescence and antibody combinations. T is the number of cells in the FC data. The number of cells T is typically consistent between samples, but in real-world situations there may be occasional variations, resulting in a variable number of chunks N. c = T / C. Number of chunks N c is also referred to as "chunk amount" in this disclosure to avoid confusion with chunk size or other terms. The FC data from the UPMC dataset had an average of 8.82 chunks per specimen with a standard deviation of 0.96, while the hema.to dataset had 14 chunks with a standard deviation of 2.26. Each chunk is assigned a categorical label of the patient's hematological malignancy that is used to train the chunk-level pooling network 250 (a deep embedding network is used) (described in Section B.2). The chunking process is performed by dividing the data from the sample-level data by a factor of N in supervised training. c = T / C times. The augmented chunks are aggregated by the ensemble mechanism or aggregation functions described in Section B.3.

[0043] B.2 Deep embedding networks used in chunk-level pooling networks In this stage, we aim to encode the cells in each chunk and represent the collective phenotype of the cells using a latent network embedding. This disclosure combines immune phenotype representation learning and classifier training in a discriminative deep network using GMM probability distribution assumptions for the hematological malignancy type classification task. In traditional GMM-based encoding approaches, the GMM parameter λ is a weight of the kth mixture π to characterize the mixture of different cell types. k , average μ k , and covariance σ k 2 The encoding approach is as follows: C*D Each chunk-level FC data is simplified as X n,c We calculate the gradient between the GMM distribution learned from the entire training dataset and the GMM mixture. Thus, the coding vector can represent the relationship between that chunk and all the GMM mixtures based on a probability derivative function. However, these representation learning approaches optimize the maximum likelihood in an unsupervised manner, which may not be optimal for classification tasks. Some coding functions can be rewritten by converting the parameters into learnable weights, allowing end-to-end learning. As a result, a supervised deep network can optimize the latent GMM weights for the targeted hematological malignancy labels. After training, we can then extract latent embeddings in the network (e.g., chunk-level pooling network 250) to represent each chunk 241 of the sample 211.

[0044] Specifically, this disclosure briefly describes an FC distributed coding approach, Fisher Vector (FV), and another popular GMM-based distributed coding approach, Vector of Locally Aggregated Descriptors (VLAD). We then describe the key elements that enable gradient updates in FV and VLAD, and thereby derive the corresponding end-to-end formulations, NetVLAD and NetFV. These two coding networks can run discriminative pooling networks on the raw FC data to embed a large number of distinct cells as fixed-dimensional vectors.

[0045] In some embodiments, the FC data matrix (for one sample, one tube, one chunk of samples, or one chunk of tubes) may be encoded into a corresponding representation based on an FV-based encoding method, a VLAD-based encoding method, a NetFV encoding network, or a NetVLAD encoding network. The FV-based encoding method includes an FV encoding method using a GMM-based FV. The FV-based encoding method includes an FV-A encoding method that combines Fisher Vector and an autoencoder, which has been used in some AML MRD prediction studies. The VLAD-based encoding method includes a VLAD encoding method that uses a VLAD feature aggregation method. The NetFV encoding network is derived by applying a gradient update function to the FV encoding method. The NetVLAD encoding network is derived by applying a gradient update function to the VLAD encoding method.

[0046] B.2.1.FV&NetFV encoding For FV, the GMM density function p λ Calculate the gradient vector of the FC sample X (one tube of a patient) with respect to the parameter λ of (X). The gradient function is defined as:

[0047]

number

[0048] The posterior probability of each chunk-level FC data x∈X for the Kth GMM component can be calculated as follows:

[0049]

number

[0050] Then, the inventors can derive the first and second vectors by rewriting (1) as follows:

[0051]

number

[0052]

number

[0053] First- and second-order statistical estimation of the gradients is done by applying the learned distribution λ to a probability p λ (X) represents the direction that best fits each sample X. Then,

[0054]

number

[0055] and

[0056]

number

[0057] are concatenated as a vectorized FC representation.

[0058] FV can represent chunk-level FC data as vectors using pre-trained GMM parameters, but the GMM training is independent of the classifier training. Here, we introduce NetFV to further improve the chunk-level representation in a supervised learning manner. NetFV estimates the final FV mathematical form using learnable parameters and embeds the information of hematological malignancy type into the network. To reduce the complexity of network training, the GMM distributions are assumed to have equal weights, and p λ (x i ) is written as follows:

[0059]

number

[0060] w k =1 / σ k And b k =-μ k and the rear of the cell looks like this:

[0061]

number

[0062]

number

[0063] represents the Hadamard product of matrices. Finally, the first and second order gradient vectors are also differentiable parameters w k and b k It is represented by:

[0064]

number

[0065]

number

[0066] Following the NetFV layer, we use a fully connected network to perform supervised training to predict the type of hematological malignancy. In the embodiment shown in FIG. 2, the learnable terms in Equations 7 and 8 are weighted terms (a μ and a σ ) and the residual term b μ It is separated as.

[0067] B.2.2.FV&NetFV encoding Another distributional coding approach, VLAD, also performs variable-length cell pooling based on the calculation of the sum of the residuals for each GMM cell cluster. This method is an improvement over the traditional bag-of-words algorithm and can better describe the relationship between the target cell and each learned cluster center. For the same chunk-level FC data input X with various cell numbers and GMM cluster centers μ k ∈R K*D Given V, the weighted residual matrix V is calculated as follows:

[0068]

number

[0069] Here, a ki The k-th cluster is cell x i is a binary indicator of whether the cluster center is the closest to the cluster center. The sum residual vector represents the total distance between the cluster center and the entire population of cell data assigned to it. The matrix V is smoothed into a final fixed-length vector, then normalized by the column-wise L2 norm and the overall L2 norm.

[0070] NetVLAD is able to encode cells as chunk-level representations by generalizing the approach as a trainable VLAD layer. To ensure that the parameters are differentiable, cells use normalized weights derived from the distances instead of using binary values ​​(hard assignment). ki is used as a soft assignment to each cluster.

[0071]

number

[0072] where α is a positive constant that determines the decay rate of the overall exponential term.

[0073]

number

[0074] and

[0075]

number

[0076] By substituting, the soft allocation weights are derived as follows:

[0077]

number

[0078] The NetVLAD layer consists of the following:

[0079]

number

[0080] In (12), we generate chunk-level FC representations by regularizing with the L2 norm. This end-to-end learning network is constructed with a deep feedforward network followed by a NetVLAD layer to classify hematological malignancy categories. In this work, we experiment with the aforementioned SOTA distribution-based deep chunk-level embedding (or chunk-level representation252) for the task of sample-level FC data modeling.

[0081] B.3. Chunk Ensemble Prediction To aggregate chunk-level representations, the present disclosure leverages a technique called the "implicit ensemble" approach. We extracted chunk-level embeddings (e.g., chunk representations 252) from the deep embedding network described in Section B.2. Using an aggregation statistical function such as maximum, we can derive an aggregate representation (e.g., representation 262 or ensemble representation) from the chunk-level embeddings (e.g., chunk representations 252) as input to the following dense layer (e.g., the dense layer shown in ensemble prediction 260) for one sample (tube). Multiple aggregate representations of multiple samples (tubes) can be concatenated for a final classification or decision.

[0082] In this disclosure, different types of aggregation functions 261 applied across the chunk representations are used to maintain the most prominent values ​​in each feature dimension across all chunks in a sample (e.g., tubes). For example, the aggregation functions 261 may include at least one of a majority voting function, a max pooling function, an average pooling function, a probabilistic pooling function, or a median pooling function.

[0083] Chunk representations 252 of the same sample (e.g., tube) may be vector representations with the same number of feature dimensions. For one chunk representation 252, it has a first feature value of a first feature dimension, a second feature value of a second feature dimension, a third feature value of a third feature dimension, etc. In the ensemble prediction 260, several chunk representations 252 are aggregated based on the feature dimensions. For example, if the aggregation function 261 is a majority function, a first value of a first feature dimension of the aggregate representation (e.g., representation 262 or ensemble representation) is determined by performing the majority function on the first values ​​of the vector representations (e.g., chunk representations 252) of the corresponding chunks, a second value of a second feature dimension of the aggregate representation is determined by performing the majority function on the second values ​​of the vector representations of the corresponding chunks, a third value of a third feature dimension of the aggregate representation is determined by performing the majority function on the third values ​​of the vector representations of the corresponding chunks, and so on.

[0084] For example, if the aggregation function 261 is a max pooling function, then a first value of a first feature dimension of an aggregated representation (e.g., representation 262 or an ensemble representation) is determined by performing a max pooling function on a first value of a vector representation of a corresponding chunk (e.g., chunk representation 252), a second value of a second feature dimension of an aggregated representation is determined by performing a max pooling function on a second value of a vector representation of a corresponding chunk, a third value of a third feature dimension of an aggregated representation is determined by performing a max pooling function on a third value of a vector representation of a corresponding chunk, and so on. Thus, a first value of a first feature dimension of an aggregated representation is the maximum value of the first values ​​of a vector representation of a corresponding chunk, a second value of a second feature dimension of an aggregated representation is the maximum value of the second values ​​of a vector representation of a corresponding chunk, and a third value of a third feature dimension of an aggregated representation is the maximum value of the third values ​​of a vector representation of a corresponding chunk, and so on.

[0085] The main advantage of the ensemble process (e.g., ensemble prediction 260) network proposed in this disclosure is that it requires limited memory consumption and computational power, unlike explicit ensemble methods that replicate multiple models for diverse outputs. With a properly selected chunk size, each chunk should provide sufficient discrimination power using small cell sample sizes. The ensemble pooling process (e.g., ensemble prediction 260) is designed to maintain the maximum value in each feature dimension to maintain high discrimination power and low feature dimension.

[0086] C. Architectural Details The hyperparameters are obtained via grid search from a defined set. The deep embedding network described in Section B.2 consists of either NetFV or NetVLAD modules with K clusters, where K is chosen from values ​​between 16 and 128, with a fixed step of 16. It has an output layer with [64, 128, 256, 1024] nodes. The following dense layer has [32, 64, 128, 256] nodes with ReLU or tanh activation functions. The dropout rate is searched in the range of 0 to 0.5, with a fixed step of 0.05. In the ensemble prediction network, a single softmax layer projects the aggregate representation into a prediction space with the number of classes as the number of nodes. Using the ADAM optimizer, the network is optimized by selecting either cross entropy or KL divergence as the loss function, based on the best validation performance. The training process includes early stopping if the validation performance does not improve for five consecutive iterations. The learning rate is adjusted from 0.001 to 0.01 using a log-distributed sampler.

[0087] 3 is a flowchart of a method 300 according to some embodiments of the present disclosure. The method 300 may be a method for processing cytometric data. The method 300 includes operations 301, 303, 305, 307, 309, 311, 313, 315, 317, and 319.

[0088] In operation 301, one or more data matrices may be received. The one or more data matrices correspond to cytometric data obtained from flow cytometry. The number of data matrices may correspond to the number of samples (or analytes) tested by flow cytometry (e.g., flow cytometer 220). In particular, one data matrix may be generated from samples tested by flow cytometry. The number of data matrices may correspond to the number of tubes of a patient (or case), of which antibody fluorescence measurements may be performed for each of one or more tubes of a patient via flow cytometry. In particular, one data matrix may be generated from a tube of a patient tested by flow cytometry. In some embodiments, one sample (or one analyte) corresponds to a tube of a patient.

[0089] In operation 303, a data matrix is ​​received. In some embodiments, the data matrix is ​​selected from the one or more data matrices received in operation 301. The data matrix indicates a plurality of properties of a set of cells, the set of cells corresponding to cells of a sample or tube. In some embodiments, the plurality of properties of the set of cells corresponds to properties of an antibody shown in one of rows tube 1 through tube 5 for the UPMC dataset. In some other embodiments, the plurality of properties of the set of cells corresponds to properties of an antibody shown in one of rows tube 1 through tube 3 for the hema.to dataset. The data matrix in operation 303 may correspond to data matrix 230 of FIG. 230. The data matrix in operation 303 may have D columns and T rows, where D is the number of properties examined and T is the number of cells examined (or the number of cells in the set of cells).

[0090] In operation 305, the data matrix is ​​divided or chunked into multiple sub-matrices. The sub-matrices may correspond to the chunks 241 in Figure 2. Operation 305 may correspond to the chunking operation 240 in Figure 2.

[0091] In operation 307, each of the multiple sub-matrices is encoded into one corresponding vector representation. The multiple sub-matrices are encoded into corresponding vector representations. The number of the multiple sub-matrices may be related to or equal to the number of vector representations. In operation 307, multiple vector representations are obtained. The vector representations may correspond to the chunk representation 252 in FIG. 2 or the chunk-level embedding described above. Operation 307 may correspond to the chunk-level pooling network 250 in FIG. 2.

[0092] In operation 307, each of the sub-matrices may be transposed (corresponding to transpose operation 251 in FIG. 2). In some embodiments, since the sub-matrices are transposed, the number of rows of the sub-matrix may correspond to the number of rows of the data matrix (i.e., variable D mentioned above), and after encoding, the number of feature dimensions of the vector representation may correspond to or be related to the number of rows of the data matrix (i.e., variable D mentioned above). The number of feature dimensions of each vector representation of the same data matrix (or the same sample or tube) may be the same. In some embodiments, one vector representation may be represented as a series of values ​​where the number of values ​​corresponds to the number of feature dimensions, with a first value corresponding to a first feature dimension and a second value corresponding to a second feature dimension.

[0093] In operation 307, each of the sub-matrices may be encoded into one corresponding vector representation based on at least one of an FV-based encoding method, a VLAD-based encoding method, a NetFV encoding network, or a NetVLAD encoding network. The FV-based encoding method includes an FV encoding method using a GMM-based FV. The FV-based encoding method includes an FV-A encoding method that combines Fisher Vector and an autoencoder, which has been used in some AML MRD prediction studies. The VLAD-based encoding method includes a VLAD encoding method that uses a VLAD feature aggregation method. The NetFV encoding network is derived by applying a gradient update function to the FV encoding method. The NetVLAD encoding network is derived by applying a gradient update function to the VLAD encoding method.

[0094] In operation 309, the multiple vector representations are aggregated or ensembled into an ensemble representation, which may correspond to representation 262 in FIG.

[0095] In some embodiments, the ensemble representation may be aggregated or ensembled by aggregating multiple vector representations based on a feature dimension of the multiple vector representations.

[0096] In some further embodiments, aggregating the plurality of vector representations based on a feature dimension may be performed by performing at least one of a majority function, a max pooling function, an average pooling function, a probabilistic pooling function, or a median pooling function on each feature dimension of the plurality of vector representations.

[0097] For example, if the aggregation function 261 is a max pooling function, the first value of the first feature dimension of the ensemble representation is determined by executing the max pooling function on the first value of the first feature dimension of the vector representation, the second value of the second feature dimension of the ensemble representation is determined by executing the max pooling function on the second value of the second feature dimension of the vector representation, the third value of the third feature dimension of the ensemble representation is determined by executing the max pooling function on the third value of the third feature dimension of the vector representation, and the rest can be inferred accordingly. Thus, the first value of the first feature dimension of the ensemble representation is the maximum value of the first values ​​of the first dimension of the vector representation, the second value of the second feature dimension of the ensemble representation is the maximum value of the second values ​​of the second feature dimension of the vector representation, and the third value of the third feature dimension of the ensemble representation is the maximum value of the third values ​​of the third feature dimension of the vector representation, and the rest can be inferred accordingly.

[0098] In operation 311, it is determined whether there is a next data matrix to be processed. For example, if only one data matrix is ​​received in operation 301, it is determined in operation 311 that there is no next data matrix to be processed. In some embodiments, if two data matrices are received in operation 301, it is determined that there is a next data matrix to be processed the first time operation 311 is performed, and operations 303, 305, 307, and 309 are performed again. Thus, operations 303, 305, 307, 309, and 311 are performed until all data matrices received in operation 301 have been processed.

[0099] In operation 313, it is determined whether more than one ensemble representation is obtained in the previous operation. For example, if only one data matrix is ​​received in operation 301, only one ensemble representation is obtained in the previous operation, and in operation 313, it is determined that there is no more than one ensemble representation.

[0100] If in operation 313 it is determined that there is no more than one ensemble representation, then operation 315 is performed. In operation 315, the cytometric data is classified based on only one ensemble representation, where the only one ensemble representation is the only data matrix received in operation 301 or generated based thereon, and the only one data matrix corresponds to the cytometric data obtained from one sample or one tube via flow cytometry.

[0101] In some embodiments, if more than one data matrix is ​​received in operation 301, more than one ensemble representation is obtained in a previous operation, and it is determined that there is more than one ensemble representation in operation 313. For example, if five data matrices are received in operation 301, five corresponding ensemble representations are obtained in a previous operation.

[0102] If it is determined in operation 313 that there are two or more ensemble representations, operation 315 is performed. In operation 317, the two or more ensemble representations are concatenated to obtain a concatenated representation. For example, if three ensemble representations are calculated or obtained from operations 301, 303, 305, 307, 309, and 311, the head (e.g., first feature dimension) of the second ensemble representation is concatenated to the tail (e.g., last feature dimension) of the first ensemble representation, and the head (e.g., first feature dimension) of the third ensemble representation is concatenated to the tail (e.g., last feature dimension) of the second ensemble representation to generate and obtain a concatenated representation.

[0103] In operation 319, the cytometric data is classified based on the concatenated representation, of which two or more ensemble representations are calculated or generated based on two or more data matrices received in operation 301, where the two or more data matrices correspond to cytometric data obtained from two or more samples (or tubes) via flow cytometry. For example, if three ensemble representations are calculated or generated based on the three data matrices received in operation 301, where the three data matrices correspond to cytometric data obtained from three samples or three tubes via flow cytometry, the cytometric data is classified based on the concatenated representation that is based on the three ensemble representations.

[0104] By classifying the cytometric data based on the corresponding concatenated representation (e.g., corresponding to operation 319) or ensemble representation (e.g., corresponding to operation 315), the type of hematological malignancy can be classified, predicted, or detected with high accuracy.

[0105] D. Experimental Setup In this disclosure, we conducted experiments on two datasets using 5-fold patient-independent cross-validation, where in each fold, 80% was used for training and 20% was used for blind testing. We randomly selected 20% of the training data as a validation set to tune the hyperparameters in each training fold. For all performance evaluation experiments, we calculated the unweighted F1 score (UF1), weighted F1 score (F1), accuracy (ACC), area under the ROC (Receiver Operating Characteristic) curve (AUC), and unweighted average recall (UAR). The following sections include classification results of discriminant ability and analysis of robustness and computational cost.

[0106] In section E.1, we compare our results with results from the following list of methods. These algorithms are either from previous studies or related methods.

[0107] ● Func: Calculates six statistical functional features.

[0108] ●SOM-CNN: Use SOM to reduce FC data to two-dimensional input and use CNN to classify (as used in M. Zhao et al., “Hematologist-level classification of mature B-cell neoplasm using deep learning on multi-parameter flow cytometry data,” Cytometry Part A, vol. 97, no. 10, pp. 1073-1080, 2020).

[0109] ●PCA-CNN: Uses PCA to reduce the data to two dimensions for a convolutional neural network.

[0110] ●GMM: Use the average cell posterior vector of the sample from the trained GMM (similar to the method proposed in B. Rajwa, PK Wallace, EA Griffiths, and M. Dundar, “Automated assessment of disease progression in acute myeloid leukemia by probabilistic analysis of flow cytometry data,” IEEE Trans. Biomed. Eng., vol. 64, no. 5, pp. 1089-1098, May 2017).

[0111] ●FV: Using GMM-based FV (B.-S. Ko et al., “Clinically validated machine learning algorithm for detecting residual diseases with multicolor flow cytometry analysis in acute myeloid leukemia and myelodysplastic syndrome,” EBioMedicine, vol. 37, pp. 91-100, 2018, SA Monaghan et al., “A machine learning approach to the classification of acute leukemias and distinction from nonneoplastic cytopenias using flow cytometry data,” Amer. J. Clin. Pathol., vol. 157, no. 4, pp. 546-553, 2021, and J. Sanchez, F. Perronnin, T. Mensink, and J. Verbeek, “Image classification with the Fisher vector: Theory and practice,” Int. J. Comput. Vis., vol. 105, no. 3, pp. 222-245, as used in 2013).

[0112] ●FV-A: Combine Fisher Vector and autoencoder (autoencoder was used in AML MRD prediction study, J. Li, Y. Wang, B. Ko, C. Li, J. Tang, and C. Lee, "Learning a cytometric deep phenotype embedding for automatic hematological malignancies classification," in Proc. 41st Annu. Int. Conf. IEEE Eng. Med. Biol. Soc., 2019, pp. 1733-1736).

[0113] ●Vlad: Use the Vlad feature aggregation method (as used in H. Jegou, M. Douze, C. Schmid, and P. Perez, “Aggregating local descriptors into a compact image representation,” in Proc. IEEE Comput. Soc. Conf. Comput. Vis. Pattern Recognit., 2010, pp. 3304-3311).

[0114] ● N-VLAD: Use NetVLAD as described in Section B.2 of this disclosure.

[0115] ● N-FV: Use NetFV, as described in Section B.2 of this disclosure.

[0116] ● Ev-X: A majority function is used in ensemble prediction 260 (eg, operation 309), using the methods proposed by the inventors (eg, framework 200 or method 300).

[0117] Ef-X: A max pooling function is used in the ensemble prediction 260 (eg, operation 309), using the method proposed by the inventors (eg, framework 200 or method 300).

[0118] These comparison approaches can generally be divided into non-GMM-based algorithms, GMM-based algorithms, and ensemble (chunking for pooling) methods. Func, SOM-CNN (self-organizing map convolutional neural network), and PCA-CNN (principal component analysis convolutional neural network) are non-GMM-based algorithms. They use simple statistical functions (Func) to compress large cell vectors or reduce dimensionality using algorithms such as SOM and PCA. SOM-CNN is a recently proposed deep framework that utilizes the traditional SOM algorithm in the automatic FC modeling domain and introduces CNN to handle downsampled data such as images. PCA-SOM is another baseline included to compare different dimensionality reduction approaches resulting from the widely used PCA approach for FC visualization.

[0119] There is also a set of distribution learning algorithms, including GMM, FV, FV-A, VLAD, N-VLAD, and N-FV. Traditional approaches such as VLAD and FV explicitly compute residuals and gradients with learned GMM parameters. FV-A adds an additional autoencoder to transform the feature space. Two end-to-end networks, NetVLAD and NetFV, directly use supervised network learning for discriminative GMM-based representations.

[0120] In the chunking-for-pooling framework, we use chunks as the network input and further perform chunk aggregation. Thus, we compare two different aggregation approaches, Ev-X and Ef-X, to implement chunk aggregation for sample-level recognition. The voting strategy of Ev is a majority voting strategy, and Ef builds a fully connected network to classify the aggregated chunk representations by a max-pooling function. The "X" in Ev-X and Ef-X can be either N-VLAD or N-FV, which represents the choice of deep embedding network architecture. In Table IV (split into Table IV(a) and Table IV(b)), we select the best-performing algorithms on each dataset for comparison of the ensemble (chunking-for-pooling) framework (e.g., corresponding to framework 200 or method 300).

[0121] Table IV (split into Table IV(a) and Table IV(b)) shows the classification results of hematological malignancies for the UPMC and hema.to datasets.

[0122] [Table 4]

[0123] [Table 5]

[0124] E. Classification result In this section, we report the results of classification experiments, including a comparison of representation learning algorithms, a comparison of ensemble (chunking for pooling) approaches, and error analysis. In Section III-B1, we include state-of-the-art algorithms and ensemble (chunking for pooling) approaches for FC data modeling and analyze the impact of different parameter selections, such as different chunk amounts, blast percentages, and categories of hematological malignancies, on the classification results.

[0125] E.1. Comparison of Representation Learning Algorithms This disclosure compares different algorithms using FC data and the results are shown in Table IV. First, we compare the coding approaches and network architectures except for the ensemble (chunking for pooling) results (Ev-X and Ef-X) in Table IV. It is observed that N-FV achieves the best 4-class hematological malignancy type classification performance in UPMC dataset with 89.9% for UF1, 92.3% for ACC, and 88.0% for UAR. N-VLAD outperforms other algorithms in 5-class blood type classification in hema.to dataset. In general, except for the ensemble (chunking for pooling) results (Ev-X and Ef-X), N-FV and N-VLAD have better performance than others.

[0126] We included widely used encoding algorithms as baselines. For example, Func achieved 83.2% UAR and 75.1% on the UPMC and hema.to datasets, respectively. The recently proposed SOM-CNN achieved 52.9% UF1, 67.4% ACC, and 54.7% UAR on the UPMC dataset, and 56.9% UF1, 75.6% ACC, and 55.0% UAR on the hema.to dataset. Although the results on the hema.to dataset were evaluated based on their partially published data, our comparison of two clinically collected datasets for full validation overcomes the problem of previous studies that usually lacked a comprehensive comparison of algorithms across different data cohorts. The same CNN architecture was used when comparing SOM and PCA, and PCA-CNN performed better. PCA-CNN performs worse than Func, with UF1 -22.7%, ACC -9.8%, and UAR -21.8% on the UPMC dataset, and UF1 -11.3%, ACC -4.4%, and UAR -10.1% on the hema.to dataset. Compared to dimensionality reduction approaches (often reduced to 2D plots), using statistical functions (Func) is more effective at summarizing statistical properties in FC data.

[0127] GMM-based algorithms are the leading distributional branch in modeling FC data, and their corresponding encoding approaches have been shown to be SOTA in AML and ALL MRD detection tasks. We compared these approaches with the aforementioned baselines to provide validation of a comprehensive computational framework (Table IV). GMM obtains low accuracy in that the oversimplified averaged posterior vector contains only a coarse probabilistic summary of the sample distribution. In contrast, VLAD, FV, N-VLAD, and N-FV are algorithms designed based on GMM to calculate complex functions to describe the relationship between clusters and individual data samples as high-dimensional vectors. Both VLAD and FV are approaches that do not use deep network learning. We observed that FV outperformed VLAD, with UF1 at 88.5%, ACC at 89.5%, and UAR at 86.5% on the UPMC dataset, and UF1 at 78.6%, ACC at 85.6%, and UAR at 77.0% on the hema.to dataset. This is mainly because VLAD only represents sample distances to cluster centers, and the assignment to a particular cluster is a hard assignment. Unassigned clusters do not contribute to the representation, and the residual calculation only considers cluster centers, without considering the covariance of the GMM distribution. In contrast, FV produces a higher dimensional representation, since it estimates gradients in terms of the mean and covariance parameters of the GMM. Thus, the FV representation contains a more complete description of the data by simultaneously taking into account cluster centers and covariance with respect to each sample point. FV-A transforms the feature space of FV, which is employed for the MRD detection task, by an autoencoder. However, the low accuracy means that the transformation is only suitable for the AML MRD recognition task, not the multi-class recognition task in this work.

[0128] These comparisons were made using representations derived in an unsupervised manner, independent of the classifier. By leveraging an end-to-end network, N-VLAD and N-FV improve on the performance of VLAD and FV using supervised representation learning. On the UPMC dataset, N-FV achieved 1.58% higher relative UF1, 3.13% higher relative ACC, and 1.73% higher relative UAR than FV. Similarly, N-VLAD outperformed VLAD by 25.1% UF1, 17.3% ACC, and 24.7% UAR. Improvements were also shown on the hema.to dataset. UF1 and UAR were improved in terms of N-FV relative to FV, with N-VLAD achieving 39.1% UF1, 16.6% ACC, and 39.2% UAR improvements over VLAD. The large difference between N-VLAD and VLAD is due to the hard-allocation design of VLAD. When N-VLAD employs soft assignment and derives parameters by learning, it can perform comparable to N-FV. Deep networks provide significant gains for both N-FV and N-VLAD, achieving the best performance across the five different metrics in Table IV.

[0129] Overall, the advantage of N-VLAD and N-FV is their strong discriminatory ability with their end-to-end optimization strategy, whereas other distributed learning approaches such as VLAD and FV are not discriminatively learned in an end-to-end manner. However, these deep learning-based approaches require training by GPUs, which can be a disadvantage when computational resources are limited. The distributional approach has advantages over traditional statistical and dimensionality reduction approaches in terms of model accuracy. Some previous studies have used GMMs to visualize patterns in FC data, and therefore another advantage of the distributional learning approach is the ability to provide intuitive visualization to the physician or examiner. The disadvantage of N-VLAD and N-FV is that they require a more complicated process to provide intuitive interpretation to the physician or examiner. Therefore, we performed a series of analyses to detail the behavior of the model.

[0130] E.2. Comparison of ensemble methods In this disclosure, the ensemble method may correspond to a chunking for pooling framework (e.g., framework 200) or method 300.

[0131] The best performing models on the UPMC and hema.to datasets are N-FV and N-VLAD, respectively. Therefore, we applied the chunking-for-pooling framework with the best performing networks. Ef-N-FV and Ef-N-VLAD consistently produced better performance of the Ef ensemble strategy than other algorithms on the UPMC and hema.to datasets. Ef-N-FV achieved the best 4-class performance with 92.3% UF1, 93.4% ACC, and 92.3% UAR on the UPMC dataset, which improved UF1 by 2.4%, ACC by 1.1%, and UAR by 4.3% over N-FV. Similarly, Ef-N-VLAD achieved the best 5-class performance with 85.1% UF1, 87.7% ACC, and 85.0% UAR on the hema.to dataset. Ev-N-FV and Ef-N-VLAD, using the chunking and pooling process, obtained performance gains from N-FV and N-VLAD. The improvements using the ensemble approach show advantages in predictive capabilities, and the resulting parameters such as chunk size are explained in Section F.2.

[0132] Comparing the two ensemble strategies, Ev and Ef, the advantage of Ef was relatively small on the UPMC dataset but more prominent on the hema.to dataset. For different evaluation metrics, the main improvement using Ef was in UF1 and UAR. Ef-N-FV had 2.67% and 4.89% relatively higher UF1 and UAR than N-FV on the UPMC dataset, and Ef-N-VLAD had 5.06% and 6.92% relatively higher UF1 and UAR than N-VLAD on the hema.to dataset. These results indicate that Ef can successfully address the inter-class imbalance problem. When a model is less discriminative, it tends to predict classes using more samples, thereby leading to lower UF1 and UAR. Ef generally outperforms Ev in that the newly learned layers are able to adapt weights optimized for maximally aggregated samples, but the voting approach used in Ev relies primarily on individual chunk prediction results, leading to suboptimal classification performance.

[0133] E.3.Comparing network parameters The number of clusters for N-VLAD and N-FV is selected by grid search during training with the validation dataset. Thus, we investigated the selected number of clusters in each fold to gain insight into cellular diversity. Both N-FV and N-VLAD achieved best performance by specifying 48 clusters on the UPMC dataset, but produced slightly different results on the hema.to dataset. On the hema.to dataset, the most appropriate number of clusters varied between folds, with N-FV tending to work better with more clusters (112). Although N-VLAD performed better than N-FV on the hema.to dataset, most folds use 16 clusters in their best validated models. Thus, the results suggested that a larger cluster size does not necessarily translate to better performance.

[0134] According to previous studies, blood cells can be divided into several lineages, such as erythroid, lymphoid, and myeloid

[40] . The cells also include various different maturation stages of hematopoiesis. The types of hematopoiesis malignancies are mainly classified based on the altered cell types and distributions, which can be recognized by the FC patterns of antigen expression. A rough cell classification based on a tree-like hierarchy identifies dozens of subtypes across lineages. Intuitively, the number of cell type categories is a potential factor that affects the cluster size. The variation in cluster size may depend on the data distribution in each fold. If a certain cell type population cannot be distinguished between different hematopoietic malignancies, the cluster will be merged with other similar cells from the same lineage during supervised learning optimization. N-FV tended to obtain larger clusters because it computed both primary and secondary statistics and observed more cell-level details. Overall, we searched up to 128, but the maximum selection of cluster size was 112. This range of cluster sizes would be sufficient to represent the cell patterns in the classification of blood types. The lineage commitment of some hematopoietic stem cells cannot be easily identified, and this will affect the automatically learned cluster sizes.

[0135] E.4. Error Analysis In this section, we analyze the results of the best-performing models found in the previous section. First, we consider the confusion matrices in Figures 4A-4D, respectively, by models that applied the chunking for pooling framework or models that did not apply the chunking for pooling framework. Figures 4A-4D show the confusion matrices using the best-performing network architectures and Ef approaches on the UPMC and hema.to datasets.

[0136] In the first analysis, the major misclassified samples of N-FV on the UPMC dataset were from the AML class, and the Ef-N-FV proposed by us could reduce the misclassification of AML. Specifically, N-FV mispredicted 59 AML samples as other classes, while Ef-N-FV misclassified only 17 AML samples. We observed that the classification of multi-class hematological malignancies was more affected by classes with a large number of samples compared to others due to the diversity of sample size. In the framework proposed by us, all of the cellular diversity is included in the chunks and aggregated into the final model. The ability to capture large sample variability can better represent the classes.

[0137] On the Hema.to dataset, predictions for AML were also improved by the Ef approach proposed by the inventors. The model tended to correctly predict lymphoma classes, especially samples misclassified as normal. Among them, the 95 lymphoma samples misclassified as normal were mainly taken from MBL and LPL, as shown in Table V. MBL, a non-cancer precursor of CLL, may show normal B lymphocyte counts or mild abnormalities, leading to diagnostic uncertainty. The diagnosis of LPL based on morphology and immunophenotype is complex as it contains a wide variety of mixed cell types (e.g., plasma cells, plasmacytoid cells, lymphocytes and mast cells), and LPL is usually described as a diagnosis based on the exclusion of other small B cell lymphomas. Thus, MBL and LPL are inherently more difficult to distinguish from other subtypes. Increasing the number of samples in these categories may improve the classification of these subtypes. The prediction of MM was also improved from 73 correctly classified samples to 86 correctly classified samples. However, misclassification between lymphoma and normal classes still occurred, and Ef-N-VLAD tended to predict normal samples as lymphoma. If the chunks contained more information to describe the diverse lymphoma subtypes, the model was more likely to accurately predict the lymphoma class. This public hema.to dataset contains only a small portion of the entire data cohort. Therefore, misclassification between lymphoma and normal classes would be mitigated when training on a larger dataset.

[0138] Table V shows the misclassified sample distribution of lymphoma subtypes.

[0139] [Table 6]

[0140] F. Framework Analysis In this section, we analyze the effect of applying our proposed framework for FC data modeling on several different aspects other than classification performance. In Section F.1, we explain the variability of the model prediction results and the benefit of including all cells without downsampling. Then, in Section F.2, we analyze the impact on chunk size and total number of chunks to further demonstrate the robustness of the proposed framework. Finally, we report the computational resources consumed by the deployment of the model in Section F.3.

[0141] F.1. Examination of variability in model predictions In these experiments, we investigated the variability of model prediction results using a downsampling strategy compared to the “chunking for pooling” ensemble framework proposed by us. The approach proposed by us has the advantage of allowing model classification without discarding cells. Therefore, this experiment helps to show how much robustness can be improved by the method proposed by us. The downsampled approach using N-FV or N-VLAD was performed 17 times to derive 17 independent results. We created box plots of the accuracy and predicted outcome distributions of these randomly replicated experiments, as shown in Figure 5A-D. For Ef-N-FV and Ef-N-VLAD on the UPMC and hema.to datasets, each bar had only one accurate value, since the ensemble approach uses all available cells without downsampling.

[0142] Figures 5A-D show the performance and error distributions for downsampling (e.g., N-FV and N-VLAD legends) and chunking-for-pooling (e.g., Ef-N-FV and Ef-N-VLAD legends) experiments on the UPMC and hema.to datasets.

[0143] As shown in Figures 5A-5D, the mean values ​​of UF1, WF1, ACC, AUC, and UAR using N-FV and N-VLAD all deviated from the results in Table IV. The two highest standard deviations for UF1 and UAR were 0.0163 and 0.0165 on the UPMC dataset. The two highest standard deviations for UF1 and UAR were 0.0070 and 0.0123 on the Hema.to dataset. When approximating the confidence intervals to cover 95% of the resampling results, the model has an interval of 4 times the standard deviation on the UPMC dataset, with UF1 at 6.52% and UAR at 6.60%. For the hema.to dataset, the variability is smaller, but caution is advised. Its 95% confidence interval is 4.92%, which not only affects the comparison of the algorithms but more importantly raises serious concerns about the validity of the clinical model. We performed a Student's t-test (Figures 5A-D) and found that all results of Ef-N-FV and Ef-N-VLAD on different metrics were significantly higher than those of N-FV and N-VLAD (p-value < 10), except for ACC (p-value = 0.055) in the hema.to dataset. -3 ) was found to be significantly higher than

[0144] For samples in each hematological malignancy class, we also report the proportion of misclassified samples by the same box plot diagrams in Figures 5A-5D, which show the risk of robustness problems. In the UPMC dataset, the deviation from Ef-N-FV is significant when observing the average percentage of classification errors for each class. The standard deviation values ​​of the misclassified numbers are 2.31%, 4.32%, 3.47% and 2.53%, and the number of correct samples can be obtained by multiplying the percentage by the total number of samples for each class in Table II. The shortcomings of the robustness of the model using naive downsampling were also evident when considering each class separately. With N-FV achieving a good performance (ACC of 0.923 and UAR of 0.880), the prediction error and the explainable model prediction behavior are key for clinical application. For example, the tendency of N-FV to misclassify AML samples in Figures 4A-4D as cytopenic or APL may give rise to different clinical effects. The reduced prediction variability can establish a basis for further interpretation of model behavior. In the Hema.to dataset, we observed that the distribution of AML, lymphoma, and MM with N-VLAD was widely dispersed and introduced significantly more errors than Ef-N-VLAD. The errors of CLL and normal classes had fewer errors, but the variability of N-VLAD was still observable.

[0145] Compared to Ef-N-VLAD and N-VLAD, the robustness of classification errors for lymphoma reflects a significant improvement for lymphoma, which is described in Section E.4. Indeed, lymphoma includes different subtypes, for which there are few samples, which are described in Section A. The limited amount of lymphoma subtype data reduces the representativeness of the learned latent distribution, which is therefore vulnerable to even slight changes in the training samples. We speculate that these hematological malignancy types would suffer more variability in the downsampling process if their natural diversity were greater. This experiment shows that downsampling randomizes the model's behavior, so that researchers cannot determine which samples can be correctly predicted. Deviations in model performance in different downsampling trials also introduce unacceptable uncertainty in real-world use. In contrast, the framework proposed by us (e.g., chunking-for-pooling framework, framework 200, or method 300) accounts for all cells for deterministic prediction results, without variability in all resampling experiments. The inventors believe that this advantage is a significant breakthrough in facilitating the application of automated classification systems to achieve clinical grades.

[0146] F.2. Effect of chunk size and chunk amount In this section, we further analyze the impact of chunk size in the framework proposed by us (e.g., chunking-for-pooling framework, framework 200, or method 300). The chunking process (e.g., chunking operation 240 or operation 305) serves as a key step to enable efficient GPU memory usage and improved accuracy. The chunk size can be simply determined by the available GPU memory size, and we investigated the performance change with different chunk sizes. The FC data from UPMC and hema.to datasets mainly contain a standard number of collected cells. Therefore, when the chunk size changes, the chunk amount also changes. That is, when the chunk size is small, only a few cells are used as training samples for the deep network, but the total number of training samples is large. In Figures 6A-6D, we investigate the output of the chunk-level pooling network 250 and the ensemble prediction 260 in the framework 200 to report the chunk-level and sample-level performance. The evaluation of chunk-level prediction was achieved by replicating the sample-level labels of chunks, and the sample-level performance was evaluated after the chunk-level outputs were aggregated by Ef. We chose UAR as the metric to avoid bias from imbalanced classes.

[0147] 6A-6D show the results of our proposed framework (e.g., chunking-for-pooling framework, framework 200, or method 300) with different chunk amounts and chunk sizes on the UPMC and hema.to datasets. The chunk-level results show the results before ensemble aggregation (e.g., ensemble prediction 260 or operation 309), and the sample-level results show the results after ensemble aggregation.

[0148] For classification of four-class hematological malignancies on the UPMC dataset, chunk-level prediction using 3381 cells in a chunk achieves 92.4% UAR, as shown in FIG. 6A, and 92.3% UAR, as shown in FIG. 6B. The chunk-level performance drops when using smaller chunk sizes (e.g., 676, 135, and 27), but the sample-level performance remains at a similar level. Since not all cells from a sample are abnormal cells, some chunks will provide less information about abnormal patterns of hematological malignancies. Chunk error can be removed by Ef, which optimizes the aggregated maximum of the representation. When using a chunk size of 3381, on average, 8 chunks perform the final pooling stage. By adjusting the chunk size, we found that the sample-level UAR is the best when using 135 cells in a chunk, at 93.4%. From this point on, decreasing the chunk size from 27 cells to only one cell per chunk resulted in a gradual decrease in performance. The decrease in performance from chunk size 5 to 1 is relatively significant at the sample level. The reason why a single cell can produce discriminatory power may be because of the high ratio of abnormal leukemia cells or lymphocytes that have different expression from normal cells. Compared to the deterioration of chunk-level classification results, the sample-level results using Ef-N-FV showed a relatively small decrease in UAR. Even using a single cell in a chunk, it achieved a UAR of 89.2%, which was 3.1% lower than the UAR when using 3381 cells in a chunk. Sufficient pooling capacity for the supervised learning deep network was achieved when the chunk amount was increased to 29339. We concluded that despite the inaccuracy of chunk-level prediction, the representations extracted using Ef still retained the cellular features.

[0149] For the 5-class recognition task on the Hema.to dataset, the decrease in chunk size did not help the chunk-level performance. As the chunk size went from 3381 to 1, the UAR dropped from 78.3% to 39.9%. The sample-level results using chunk sizes of 3381, 676, and 135 were not significantly different from each other, but the decreasing trend was still evident when using chunk sizes from 27 to 1. The single-cell chunk size, which achieved a sample-level UAR of 66.6%, still shows the effectiveness of Ef for aggregating chunks with a chunk-level UAR of only 39.9%. Comparing the 4-class and 5-class tasks on the two datasets, the decrease in performance is more significant in the hema.to dataset for predicting the types of 5 different hematological malignancies. Because the FC data in the Hema.to dataset contains more cells than the UPMC dataset, we can speculate that the high performance in distinguishing the types of 5-class hematological malignancies would depend on the specific cells. If a cell is rare but important, a small chunk size will result in a large number of incompletely observed chunks, diluting the information in the final pooling step. If the task includes classes that belong to the same lineage or similar cell distribution, many more cells will be needed in a single chunk to maintain discrimination power.

[0150] To further investigate the robustness of the chunking process, we investigated the effect of reducing chunk amount in the best-performing chunk size conditions shown in Figures 6A-6D. The implementation was similar to that of the robustness experiment in Section F.1, and UAR was used as the metric. We replicated training and testing several times and obtained a condition-by-condition distribution of chunk amount. Based on the data shown in Figures 6A-6D, we used 135 and 3381 as chunk sizes for the UPMC and hema.to datasets, and the results of reduced chunk amount are shown in Figures 7A and 7B. We observed that although the standard deviation was relatively large when only a very small number of chunks were included, the model still achieved high performance as the chunk amount was reduced. This situation reflects the robustness of Ef, which can eliminate errors by ensemble chunk aggregation. Compared with N-FV and N-VLAD, which downsample the FC data without chunking and pooling processes, Ef-N-FV and Ef-N-VLAD, which use arbitrary chunk amounts, show significantly better UAR (p-value < 10 -3 ) can be achieved. These results show that the framework proposed by the inventors (e.g., the chunking for pooling framework, framework 200, or method 300) is robust even though the data is downsampled.

[0151] 7A and 7B show the resulting distribution with decreasing chunk amount when using the framework proposed by the inventors (e.g., chunking for pooling framework, framework 200, or method 300). The chunk size is fixed to be the best performing size from Figures 6A-6D.

[0152] F.3. Computational Resource Analysis To evaluate the usefulness of the framework disclosed in this disclosure, we focused on computational consumption. Using the chunking process, the model input size can be reduced by a factor of the total number of chunks. As a result, the memory used was much smaller than that used by models stacked with full-size FC data input. For example, the input is split into about 9 chunks in the UPMC dataset. The model size was reduced by 4.4 times compared to N-FV and Ef-N-FV. Similarly, the model size was reduced by 1.53 times in the hema.to dataset, as the FC data was split into an average of 14 chunks. The model size using the framework proposed by the inventors (e.g., Ef) can reduce memory requirements. We use a GeForce RTX 2080Ti with 11 GB of GPU memory for the implementation of the framework. That is, the maximum allowable number of cells in a chunk of raw FC data with 37 antibody fluorescence was 70,000 in the RTX 2080Ti for N-FV. This number of allowed cells is usually insufficient for some clinical FC measurement scenarios. Another factor of usefulness is the computation time. In a comparison between a model using a downsampling strategy and a model using the chunking-for-pooling framework proposed by the inventors, the training computation time per epoch was 0.242 seconds and 0.109 seconds for N-FV and Ef-N-FV, respectively, on the UPMC dataset when using a batch size of 64 and a chunk size of 3381. Similarly, the training time per epoch was 1.143 seconds and 1 second for N-VLAD and Ef-N-VLAD on the hema.to dataset. Using the same settings in the testing phase, N-FV and Ef-N-FV took 0.202 seconds and 0.1 seconds for each batch with 16 samples on the UPMC dataset. N-VLAD and Ef-N-VLAD took 1.095 seconds and 1.007 seconds for each batch on the hema.to dataset. The “chunking for pooling” framework disclosed in this disclosure (eg, framework 200 or method 200) further provides for accelerating the training and testing process.

[0153] G. Conclusion The present disclosure proposes a chunking-for-pooling framework (e.g., framework 200 or method 300) to improve the robustness and predictive performance of automated hematological malignancy classification using FC data. The disclosed framework solves the problems of suboptimal unsupervised representations and incomplete data usage in prior studies. Specifically, the disclosed framework segments (e.g., chunks or partitions) the FC data matrix into chunks and further aggregates (or ensembles) the chunk representations, allowing sample-level predictions to be made using very large FC cell-level data (complete cell counts). This approach not only outperforms other algorithms, but also mitigates the robustness issues of the traditional downsampling step. Our further analysis explores various factors such as total chunk volume, blast percentage, and disease type that may lead to misclassification. Quantitative statistics of the downsampling results and experiments of reducing chunk size show the robustness of our model. Even when chunk-level predictions are not accurate, the sample-level performance of the disclosed framework remains high. A reduction in computational consumption and an increase in training speed are highly desirable for practical clinical usefulness.

[0154] The scope of the present disclosure is not intended to be limited to the particular embodiments of the processes, machines, manufacture, and compositions of matter, means, methods, steps, and operations described herein. As one skilled in the art will readily appreciate from the disclosure of the present disclosure, any currently existing or later developed processes, machines, manufacture, compositions of matter, means, methods, steps, or operations that perform substantially the same function or achieve substantially the same result as the corresponding embodiments described herein can be utilized in accordance with the present disclosure. Accordingly, the appended claims are intended to include within their scope any processes, machines, manufacture, and compositions of matter, means, methods, steps, or operations. In addition, each claim constitutes a separate embodiment, and combinations of the various claims and embodiments are within the scope of the present disclosure.

[0155] The methods, processes, or operations according to the embodiments of the present disclosure may also be implemented on a programmed processor. However, the controllers, flowcharts, and modules may also be implemented on hardware electronic or logical circuitry, such as a general-purpose or special-purpose computer, a programmed microprocessor or microcontroller and peripheral integrated circuit elements, integrated circuits, discrete element circuits, or programmable logic devices. In general, any device on which a finite state machine capable of implementing the flowcharts shown in the figures exists may be used to implement the processor functions of the present disclosure.

[0156] Alternative embodiments preferably implement the methods, processes, or operations according to embodiments of the present disclosure on a non-transitory computer-readable storage medium that stores computer programmable instructions. The instructions are preferably executed by a computer-executable component that is preferably integrated with the network security system. The non-transitory computer-readable storage medium may be stored in any suitable computer-readable medium, such as a RAM, a ROM, a flash memory, an EEPROM, an optical storage device (CD or DVD), a hard drive, a floppy drive, or any suitable device. The computer-executable component is preferably a processor, but the instructions may alternatively or additionally be executed by any suitable dedicated hardware device. For example, embodiments of the present disclosure provide a non-transitory computer-readable storage medium having computer programmable instructions stored therein.

[0157] Although the present disclosure has been described in its specific embodiments, it is apparent that many alternatives, modifications, and variations may be apparent to those skilled in the art. For example, various components of the embodiments may be exchanged, added, or substituted in other embodiments. Also, not all elements of each figure are necessary for the operation of the disclosed embodiments. For example, a person skilled in the art of the disclosed embodiments could make and use the teachings of the present disclosure by simply adopting the elements of the independent claims. Thus, the embodiments of the present disclosure described herein are intended to be illustrative, not limiting. Various changes can be made without departing from the spirit and scope of the present disclosure.

[0158] Although numerous features and advantages of the present disclosure have been set forth in the foregoing description, together with details of the structure and function of the present invention, the present disclosure is merely illustrative, and changes may be made within the principles of the present invention, particularly in the shape, size and arrangement of parts, to the fullest extent indicated by the broad general meaning of the terms in which the appended claims are expressed.

Claims

1. 1. A method for processing cytometric data, comprising: dividing a first data matrix into a first plurality of first sub-matrices, the first data matrix indicative of a first plurality of properties of a first set of cells; encoding each of the first sub-matrices into a corresponding vector representation to obtain a first plurality of vector representations; aggregating the first plurality of vector representations into a first ensemble representation.

2. dividing a second data matrix into a second plurality of second sub-matrices, the second data matrix indicative of a second plurality of properties of a second set of cells; encoding each of the second sub-matrices into a corresponding vector representation to obtain a second plurality of vector representations; aggregating the second plurality of vector representations into a second ensemble representation. The method of claim 1.

3. dividing a third data matrix into a third plurality of third sub-matrices, the third data matrix indicative of a third plurality of properties of a third set of cells; encoding each of the third sub-matrices into a corresponding vector representation to obtain a third plurality of vector representations; aggregating the third plurality of vector representations into a third ensemble representation; concatenating the first ensemble representation, the second ensemble representation, and the third ensemble representation to obtain a concatenated representation; and classifying the cytometric data based on the concatenated representation. The method of claim 2.

4. The method of claim 1 , wherein the step of encoding each of the first sub-matrices comprises the step of transposing each of the first sub-matrices.

5. 2. The method of claim 1, wherein each of the first sub-matrices is encoded into a corresponding vector representation based on at least one of a Fisher Vector (FV) encoding method or a Vector of Locally Aggregated Descriptors (VLAD) encoding method.

6. applying a gradient update function to at least one of the FV encoding method or the VLAD encoding method; A NetFV coding network is derived by applying the gradient update function to the FV coding method; A NetVLAD coding network is derived by applying the gradient update function to the VLAD coding method. The method according to claim 5.

7. 2. The method of claim 1 , wherein the step of aggregating the first plurality of vector representations into the first ensemble representation comprises aggregating the first plurality of vector representations based on a feature dimension of the first plurality of vector representations.

8. The step of aggregating the first plurality of vector representations based on the feature dimensions comprises: Majority function, max pooling function, average pooling function, probabilistic pooling function, or median pooling function for each feature dimension of the first plurality of vector representations.

9. The method of claim 7 , wherein a number of the feature dimensions of the first plurality of vector representations is related to a number of the first plurality of properties.

10. The method of claim 1 , wherein the first data matrix is ​​obtained from antibody fluorescence measurements of the first set of cells.

11. A device for processing cytometric data, comprising: A processor; a memory coupled to the processor; The processor executes computer readable instructions stored in the memory to cause the device to perform operations, the operations including: receiving a first data matrix indicative of a first plurality of properties of a first set of cells; dividing, by the processor, the first data matrix into a first plurality of first sub-matrices; encoding, by the processor, each of the first sub-matrices into a corresponding vector representation to obtain a first plurality of vector representations; aggregating, by the processor, the first plurality of vector representations into a first ensemble representation. The device.

12. The operation includes: receiving a second data matrix indicative of a second plurality of properties of a second set of cells; dividing, by the processor, the second data matrix into a second plurality of second sub-matrices; encoding, by the processor, each of the second sub-matrices into a corresponding vector representation to obtain a second plurality of vector representations; aggregating, by the processor, the second plurality of vector representations into a second ensemble representation. The device of claim 11.

13. The operation includes: receiving a third data matrix indicative of a third plurality of properties of a third set of cells; dividing, by the processor, the third data matrix into a third plurality of third sub-matrices; encoding, by the processor, each of the third sub-matrices into a corresponding vector representation to obtain a third plurality of vector representations; aggregating, by the processor, the third plurality of vector representations into a third ensemble representation; concatenating, by the processor, the first ensemble representation, the second ensemble representation, and the third ensemble representation to obtain a concatenated representation; classifying, by the processor, the cytometric data based on the concatenated representation. The device of claim 12.

14. The device of claim 11 , wherein encoding each of the first sub-matrices comprises transposing each of the first sub-matrices.

15. 12. The device of claim 11, wherein each of the first sub-matrices is encoded into a corresponding vector representation based on at least one of a Fisher Vector (FV) encoding method or a Vector of Locally Aggregated Descriptors (VLAD) encoding method.

16. The operation includes: applying a gradient update function to at least one of the FV encoding method or the VLAD encoding method; A NetFV coding network is derived by applying the gradient update function to the FV coding method; A NetVLAD coding network is derived by applying the gradient update function to the VLAD coding method.

16. The device of claim 15.

17. 12. The device of claim 11, wherein aggregating the first plurality of vector representations into the first ensemble representation comprises aggregating the first plurality of vector representations based on a feature dimension of the first plurality of vector representations.

18. Aggregating the first plurality of vector representations based on the feature dimensions includes: Majority function, max pooling function, average pooling function, probabilistic pooling function, or median pooling function for each feature dimension of the first plurality of vector representations.

19. The device of claim 17 , wherein a number of the feature dimensions of the first plurality of vector representations is related to a number of the first plurality of properties.

20. The device of claim 11 , wherein the first data matrix is ​​obtained from antibody fluorescence measurements of the first set of cells.

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