Method for determining correspondences between the biological properties of cells

Abstract

A method for determining a correspondence between a first biological property of a cell and one or more other biological properties of the cell is provided, where the first biological property and the other biological properties are determined by different analytical techniques and are each included in a respective set of biological properties. The method includes converting the set of biological properties into corresponding representations in a representation format that is invariant to the techniques used to derive the biological properties, determining, in the representation format, an expression from each of the converted set of other biological properties that most closely matches the first representation for the first biological property, and converting the determined expression from the representation format back into a biological property associated with the determined expression, thereby determining a correspondence between the first biological property and each of the other biological properties.

Description

[Technical Field]

[0001] The present invention relates to a method for determining correspondences between the biological properties of cells. In particular, the present invention relates to, but is not limited to, a method for determining correspondences between the biological properties of cells when their biological properties have been determined using different single-cell analysis techniques. [Background technology]

[0002] The ability to dissect tissues into cellular components and study them individually, or to investigate interactions between different cell-type fractions, is a relatively new possibility in biological research, but it has already yielded important insights into the dynamics of various diseases, including cancer (Tirosh et al., 2016; Chevrier et al., 2017). Recent advances in single-cell technology have enabled more granular molecular profiling of samples at the transcriptome, proteome, genomic, and other levels (Rozenblatt-Rosen et al., 2017; Irmisch et al., 2020). Each data format generates information in different forms and levels, but to understand the mechanisms at play in the tissue microenvironment and to deepen our overall molecular understanding of the study sample, these must be integrated and related to one another. While techniques are emerging that can measure two modes simultaneously (Stoeckius et al., 2017; Zhu et al., 2020), their scalability and widespread use remain limited.

[0003] Furthermore, recent technological advancements have led to an increase in the generation and availability of single-cell data (in terms of both many formats and large datasets). However, in most cases, profiling techniques consume the cells used, and therefore pairwise correspondences between data sets are unavailable, i.e., lost. Access to a combined set of measurements from multiple techniques would allow for the identification of biologically or clinically meaningful observational findings, for example, by unifying the perspectives provided by each technique. However, due to the large size of single-cell data sets, there is a need for a scalable method that can universally match single-cell measurements performed on one cell to their corresponding siblings in other techniques.

[0004] Only a few methods with similar capabilities have been proposed. For example, "MAGAN" (Amodio and Krishnaswamy, 2018) does not, in principle, require feature correspondence. However, their results imply that accurate matching cannot be achieved without including feature correspondence.

[0005] Yang and Uhler (2019) proposed the use of latent space from which expression profiles can be generated. However, decoding from latent space requires the generation of expression profiles. [Overview of the Initiative]

[0006] Therefore, the object of the present invention is to provide a method for determining correspondences between different biological properties of cells, particularly those obtained from single-cell analysis techniques. Another object of the present invention is to provide a scalable method for determining correspondences, particularly when there are numerous observational findings in two or more technologies that do not overlap in features.

[0007] Another object of the present invention is to provide an improved matching technique for use in determining correspondences between the biological properties of cells. In particular, improvements (one or more) can be obtained with respect to accuracy, computational cost, and / or time required.

[0008] Another object of the present invention is to provide a platform that can be used in an improved clinical decision support system that can combine and utilize knowledge of the biological properties of cells derived from different single-cell analysis techniques.

[0009] In its broadest sense, the present invention provides a method for determining correspondences between biological properties of cells, which have been determined using different analytical techniques, by converting these biological properties into a representation format that is invariant to the technique used.

[0010] A first aspect of the present invention provides a method for determining the correspondence between a first biological property of a cell included in a first set of biological properties determined by a first analytical technique and a second biological property of a cell included in a second set of biological properties determined by a second different analytical technique. The method includes the steps of: converting the first and second sets of biological properties into corresponding expressions in an expression format that is invariant to the technique used to derive these biological properties; determining a second expression from the converted second set of biological properties in the expression format that most closely matches the first expression of the first biological property; and converting the second expression from the expression format back into a biological property associated with the second expression, thereby determining the correspondence between the first and second biological properties.

[0011] A second aspect of the present invention provides a method for determining the correspondence between a first biological property of a cell and several other biological properties of the cell. The first biological property and the other biological properties are each determined by different analytical techniques and each is included in each of several sets of biological properties. The method includes the steps of: converting the several sets of biological properties into corresponding expressions in an expression format that is invariant to the techniques used to derive these biological properties; determining the expression in the expression format that most closely matches the first expression of the first biological property from each of the converted sets of other biological properties; and converting the expression determined from the expression format back into a biological property associated with the determined expression, thereby determining the correspondence between the first biological property and each of the other biological properties.

[0012] Furthermore, it will be acknowledged that the first and second embodiments share several common features and are primarily distinguished by the presence of at least three sets of different biological properties in the second embodiment. The following optional and preferred features apply equally to both the first and second embodiments described above.

[0013] As noted earlier, the present invention particularly focuses on, but is not limited to, determining correspondences between data derived from different single-cell analysis techniques (also called single-cell omics techniques). Therefore, at least one of the analysis techniques is preferably a single-cell analysis technique, and more preferably, all of the analysis techniques are single-cell analysis techniques.

[0014] Each single-cell analysis technique can determine specific useful biological properties of the cells being analyzed. However, because the nature of the analysis techniques differs, the information that can be derived from each technique differs; in other words, each analysis technique can only provide a partial picture of the complete biological picture of a particular cell or cell type in the sample.

[0015] To clarify the understanding of the biological properties of a particular cell or cell type, it is advantageous to combine the results from different analytical techniques. However, the nature of single-cell analysis means that only one analytical technique can be performed on each individual cell. Thus, when performing multiple analytical techniques on cells taken from a single sample, a direct link between each biological property is not available. For the purpose of addressing this, in aspects of the present invention, a correspondence can be identified between cells analyzed by one technique (and the biological properties so determined) and cells analyzed by a different technique (and the biological properties so determined). By pairing or matching cells analyzed by one technique with the closest (preferably, the closest) "sibling" cells in the sample analyzed by another technique, the biological properties determined by both techniques can be linked in further evaluation or analysis, and thus combined.

[0016] Examples of single-cell analysis techniques include single-cell RNA sequencing ("scRNA-Seq"), cytometry by time of flight (CyRTOF), and imaging mass cytometry ("IMC"), although it will be appreciated by those skilled in the art that the methods according to the above aspects are not limited to data derived using these techniques, but are equally applicable to other techniques, including those not yet known at the time of writing of this specification.

[0017] Similarly, examples of biological properties may be the transcriptome and proteome, although it will be appreciated by those skilled in the art that the methods of the above aspects are not limited to such properties, but are equally applicable to other biological properties, including those not yet derivable at the time of writing.

[0018] Preferably, at least one of the biological properties is sequencing information determined by scRNA-Seq. At the time of writing, scRNA-Seq is the most detailed and information-rich single-cell analysis technique. However, each single-cell analysis technique only represents partial observations of the properties of the cells. By using the correspondences identified by the methods of the above aspects and combining information from more than one analysis technique, more information about the properties of the cells can be determined and a more complete overall picture of the cells can be constructed.

[0019] The methods of the previous aspects can be advanced by assuming that cells share a common (low-dimensional) underlying structure and that the underlying distribution of cells with specific biological properties is roughly constant across different analysis techniques. As a result, for example, an autoencoder framework that can have adversarial objectives can be used to create a representation invariant to the technology.

[0020] The methods described above can integrate multimodal datasets by using a matching method that operates on the low-dimensional representation to match cells across multiple technologies. The methods described above can use neural networks and / or end-to-end training to generate the representation format, and / or use a fast bipartite matching algorithm for the matching step. By either or both of these features, the methods described above can correctly scale multiple cells in the input.

[0021] Generally, since a sample is exhausted by individual analytical techniques (especially single-cell analytical techniques), each sample undergoing an analytical technique to create multiple sets of biological properties can be divided into separate aliquots for analysis. Nevertheless, since the technique-specific data sets are obtained from the same sample, i.e., the cell mix, they can be expected to exhibit the same underlying distribution. Therefore, this method can assume a latent representation shared between techniques, but unlike other methods, it does not necessarily require a one-to-one correspondence or overlapping correspondence between feature sets.

[0022] Furthermore, as shown in the second embodiment above, the aforementioned training method can accommodate (allow for) the addition of any number of techniques, and these techniques can be trained in parallel. Preferably, only the representation format is used to match cells. As a result, the true marked abundance observed per cell pair by measurement using different analytical techniques or methods becomes available for use in any downstream analysis.

[0023] Representations that are invariant to the techniques used to derive biological properties may be considered latent spaces. In certain embodiments, the latent space can be constructed by creating a neural network with a) an encoder for each data set, b) a decoder for each data set, and c) a discriminator that acts on the representation.

[0024] In certain embodiments, a two-layer architecture having eight hidden units can be used as an encoder and / or decoder for one or more data sets. In certain embodiments, a two-layer architecture having 64 hidden units may be used as an encoder and / or decoder for one or more data sets.

[0025] Gaussian activation may be used for one or more decoders. These networks may be optimized using the ADAM optimizer. A discriminator can also be a binary classifier.

[0026] In certain embodiments, the latent space may be constructed by adversarially deceiving the discriminator while minimizing the reproduction error between the encoder and decoder for each data set.

[0027] While it is preferable for the representation formats to be optimally integrated, even representation formats that are not optimally integrated can be compensated for by using optimal matching techniques to determine matching between representations. This provides another advantage over simple decoding.

[0028] The method may further include a step of determining a divergence score for the expression created in the expression format. The divergence score may be the Kullback-Leibler (KL) divergence or a variation thereof. In certain embodiments, the divergence score may be calculated as follows:

[0029]

number

[0030] Here, Zs and Zt are sets of codes, and furthermore,

[0031]

number

[0032] Here, ν k (p i ) and ρ k (p i ) is the set P and Q respectively, and all p i ∈R d In pi This is the distance from the first location to the kth nearest neighbor. In certain embodiments, the method may further include a step of comparing the divergence score with a predetermined threshold. In certain embodiments, if the divergence score exceeds the predetermined threshold, the step of converting multiple sets of biological properties into corresponding expressions may be repeated until a divergence score below the predetermined threshold is obtained.

[0033] Training a neural network can be unstable and / or dependent on initial choices. Checking for divergence in the representation format makes it possible to determine whether an acceptable representation format has been created.

[0034] Preferably, the determination step uses a bipartite matching method between each pair of transformed sets. The determination step preferably includes a substep that narrows the search space, ideally before any matching is performed, in order to reduce the number of possible correspondences. This can reduce the complexity of the matching step by decreasing the number of potential matches for a particular expression. By reducing complexity, the amount of computational power and / or time required to complete the matching step can be reduced. If the reduction is chosen correctly, this can be achieved with very little, and preferably, imperceptible, reduction in matching accuracy.

[0035] The number of possible matches may be reduced to a predetermined maximum value per match, for example, by using the k-nearest neighbors method. This predetermined maximum value may vary depending on the size of the data set, and in each case, there is a trade-off between matching accuracy and reduced complexity.

[0036] However, it has been found that a high level of accuracy can be obtained in matching even when the number of possible matches is limited to 50 or less. As the number of possible matches increases, such as 100 or less, 200 or less, 250 or less, or 500 or less, further improvements in accuracy can be obtained, albeit with decreasing amounts. Conversely, limiting the number to 2000 or less, preferably 1000 or less, and even more preferably 500 or less, significantly reduces the memory and CPU time required for the matching process. Therefore, the predetermined maximum value is preferably between approximately 50 and approximately 2000, and more preferably between approximately 50 and approximately 500. In certain embodiments, the number of matches may be limited to 50, 100, 200, 250, or 500.

[0037] In certain embodiments, the bipartite matching method, for example, uses the Euclidean distance as the "cost" in the representation format when generating the cost matrix, and attempts to find the combination that minimizes the overall cost.

[0038] In certain embodiments, bipartite matching uses the Jonker-Volgenant algorithm, which has been shown to have excellent computational performance even in high-dimensional settings.

[0039] In alternative embodiments, a minimum cost maximum flow algorithm may be used. Many existing matching methods (bipartite and others) assume a one-to-one correspondence between data sets. However, this is unlikely in actual cell analysis and different analytical techniques. For example, the cellular composition of tissue samples examined by each analytical technique may differ. Or, in addition, there may be biases in the analytical techniques (e.g., certain genes may be overpresented in scRNA-Seq data, while certain proteins may be overpresented in CyTOF data). Or, in addition, the nature of analytical techniques may mean that if there are multiple analytical techniques for a given sample, different numbers of data points will be generated.

[0040] Therefore, the matching process preferably includes further characteristics that adjust and / or correspond to this possibility. In one configuration, the determination step addresses the possibility of undiscovered correspondences by adding a null node to each transformed set. The null nodes are preferably tightly connected and have high capacity (e.g., the size of the largest of the opposing datasets). It is preferable to assign a high assignment cost to the null nodes to bias the technique against selecting them unless there are no other viable options. However, these null nodes will also capture correspondences with cells that would otherwise be poorly matched.

[0041] Alternatively, or in addition, the determination step may also accommodate many-to-one matching for the representation of a transformed set if the transformed set has few elements. This may be done by increasing the capacity of the edges at the nodes of data sets with a small number of entries. Preferably, the method further includes a penalty provision for any unmatched cells (regardless of whether the match is to a null node or a real node), for example, by restricting the sum of the capacities of the smaller data set(s) to the cardinality of the largest data set.

[0042] These changes to the matching process may be applied before or after reducing the number of possible matches. The aforementioned method has specific applications, for example, as part of an integrated platform that provides clinical decision support in the diagnosis and treatment planning of tumors in patients with cancer. By enabling the integration of all information obtained from multiple different analytical techniques performed on the same patient sample, it is possible to improve the understanding of the tumor and guide or select an appropriate clinical pathway.

[0043] In yet another aspect of the present invention, a computer program is provided, which, when executed on a processor, is configured to perform the methods of the first or second aspect described above, and which includes, or does not include, some of the preferred or optional features of those aspects. Furthermore, a computer program product having non-temporary memory for storing such a computer program is also provided.

[0044] Clinical decision support systems are used in clinical settings, particularly by clinicians, to analyze and visualize information obtained through different (diagnostic) analytical techniques, and to facilitate the combination of acquired data with the clinician's knowledge and expertise. Such clinical decision support systems are being developed in increasing numbers to utilize data from high-throughput next-generation analytical techniques such as whole genome sequencing (WGS) and whole RNA sequencing (RNA-Seq).

[0045] Current single-cell analysis techniques, such as scRNA-Seq and CyTOF, maintain a correlation between individually measured data points and the original cells from which the analyte material was obtained throughout the analysis. For example, this can be done by barcoding molecules derived from a single cell in a heterogeneous sample and reading the barcode information along with the biological properties, such as the data points of each (barcoded) mRNA molecule.

[0046] However, when analyzing samples from the same patient (e.g., tumor samples) using multiple analytical techniques, correspondences between individual cells are not maintained between different techniques. This invention provides a method for determining such correspondences between different biological properties (e.g., transcriptome and proteome) at the single-cell level.

[0047] The method of the present invention can be used, for example, in a clinical decision support system to aggregate data from different single-cell analysis techniques. The clinical decision support system can visualize and present the aggregated data to assist clinicians in making decisions about how to treat patients based on molecular mark-ups of patient tumor samples.

[0048] Alternatively, or in addition, clinical decision support systems can also suggest treatment options to clinicians based solely on aggregated data or in combination with clinical and medical history data.

[0049] In another aspect of the present invention, a clinical decision support computer system is provided. This clinical decision support computer system has a processor, which is configured to perform the methods of the first or second aspect described above, and which includes, or does not include, some of the preferred or optional features of those aspects. This computer system may have a display that shows the results of the determined correspondence(s) to the user.

[0050] In yet another aspect of the present invention, a clinical decision support computer program is provided. This program, when executed on a processor, is configured to perform the methods of the first and second aspects described above, with or without including some or all of the preferred or optional features of those aspects. Furthermore, a clinical decision support computer program product having non-temporary memory for storing such a computer program is also provided. [Brief explanation of the drawing]

[0051] Hereafter, with reference to the attached drawings, embodiments of the present invention will be described as non-limiting examples. In the drawings, [Figure 1] A schematic diagram illustrates a method according to an embodiment of the present invention, which performs pair-by-pair cell matching across multiple single-cell analysis techniques. [Figure 2] A schematic matching graph structure forming section of the method according to an embodiment of the present invention is shown. [Figure 3] This shows a tree used to simulate the PROSSTT data set used to examine the method according to embodiments of the present invention. [Figure 4] The image shows a tree used to simulate another PROSSTT data set used to examine the method according to an embodiment of the present invention, as well as a density plot of pseudo-time labels between a pair of matched cells between the source and target technologies. [Figure 5] Figure 3 shows a tSNE (perplexity = 32) plot of the integrated latent space for the simulated data derived from the tree structure shown. [Figure 6] This is a density plot of pseudo-time labels in simulation data between matched pairs of cells from source and target technologies. [Figure 7] Figure 4 shows a tSNE (perplexity = 32) plot of the integrated latent space for the simulation data derived from the tree structure. [Figure 8] This is a density plot of pseudo-time labels between matched pairs of cells between source and target technologies, using latent codes obtained from a prior art system called MATCHER. [Figure 9] This is a tSNE embedding (perplexity = 128) of an integrated latent space created by applying the method according to an embodiment of the present invention to a data set derived from human tumor cells, where cell matches are indicated by gray lines. [Figure 10] This is a series of density plots of HLA-DRA marker abundance measured by scRNA-Seq (gene, x-axis) and CyTOF (protein, y-axis). [Figure 11] This document compares the matching accuracy of cell type labels between sparsely and densely connected systems when the method according to an embodiment of the present invention is applied to a data set derived from human tumor cells. [Figure 12] Similar to Figure 6, this is a tSNE embedding where cell matching is obtained by matching in the data space indicated by the gray line. [Figure 13] This is a series of charts showing the progress of training the method according to an embodiment of the present invention on a data set derived from human tumor cells. [Modes for carrying out the invention]

[0052] Embodiments of the present invention that provide a method for matching cells from a source technology with cells in a target technology are described below. This method was tested on both simulated and real data networks, as will be further described below.

[0053] Figure 1 shows the configuration and operation of the method in this embodiment. This method assumes that the inputs for each technique come from a distribution of similar cells processed in parallel, e.g., a common sample. This method can faithfully reproduce the original cell signals from the latent space using an automated encoder framework and adversarial objective, as further described below, but proceeds by mapping cells to a technique-invariant latent space so that the techniques of each latent representation are indistinguishable. The best cell analogue across multiple techniques is then discovered using the obtained shared latent code and a fast bipartite matching framework. Construction of a technology-invariant latent space and model architecture The integrated latent space is ideally to have two properties. The integrated latent space must be able to decode the latent representations into faithful reproductions of their inputs, yet the source technology of each latent representation must be indistinguishable. For this purpose, the method of this embodiment has three types of networks. That is, a pair of encoders (Φ k ) and decoders (Ψ k ) networks for each technology k that map to and reproduce from the latent space, and one discriminator network (γ) that acts on the latent representations.

[0054] A discriminator is a binary classifier trained to distinguish the latent representation of the source technology from the latent representations of all other technologies. The discriminator uses binary cross-entropy.

[0055] The method of this embodiment creates the integrated latent space by minimizing the reproduction error while adversarially fooling the discriminator. Considering a set of cell measurements from the target technology χ t and a set of (fixed) latent representations of cells from the source technology z s =ψ s (χ s ), this method minimizes the following objective function.

[0056]

Number

[0057] Here,

[0058]

Number

[0059] is the reproduction of χ t , and

[0060]

Number

[0061] This is the negative log-likelihood of the input being reproduced. For Gaussian likelihood, the latter is,

[0062]

number

[0063] It has the form of L. adv is, z s / z t This is the discriminator's classification error when attempting to classify a technology as a target / source technology. β is a hyperparameter that weights the impact of adversarial loss.

[0064] All networks use ReLU activation. All models are configured with a latent dimension of 8, using a discriminator network with 2 layers and 8 hidden units, respectively. The SNGAN framework (Miyato et al., 2018) is used to train the discriminators.

[0065] For the simulation data network discussed further below, a two-layer architecture with 64 hidden units was used. For the real-world data network, a two-layer architecture with 8 hidden units was used for the CyTOF network, and a two-layer architecture with 64 hidden units was used for the scRNA-Seq network. Gaussian activation was used for all decoders. An architecture search was performed on the VAE code, revealing a trade-off between the number of features and the number of parameters (reflect).

[0066] Optimization was performed by repeatedly fixing one technology as the source and one as the target. If there are more than two technologies, the technology corresponding to the positive class of the discriminator must be either the source or the target technology. The code of the source technology is fixed, and a group χ tUsing the gradient calculated for the target technology, the encoder Φ t and decoder ψ t Equation (1) is minimized by updating the gradient with respect to z. After each update, z s and z t A discriminator is trained for this. This method first trains a VAE (Kingma and Welling, 2013) on one technique and then trains the latent representation for the first set of z s It is initialized by using it as such. The ADAM (Kingma and Ba, 2014) optimizer is used to optimize all networks.

[0067] Comparing models is challenging due to the minimax nature of adversarial training, as the minimized objective functions of converged models cannot be directly compared (Lucic et al., 2017). The computer vision community has introduced numerous image domain-specific metrics to facilitate model comparison (Heusel et al., 2017; Salimans et al., 2016). However, these can be used to assess the quality of a set of low-dimensional latent representations. As done by Wang et al. (2019), a k-neighborhood (kNN) based divergence estimator (Wang et al., 2009) is used to quantitatively evaluate the quality of the integrated latent space. Two code sets Zs and Z t The divergence score in between is calculated as follows:

[0068]

number

[0069] Here,

[0070]

number

[0071] ν k (p i ) and ρ k (p i ) is p in sets P and Q respectively. i This is the distance from the kth nearest neighbor, and all are p i ∈R d This is the result. This estimator uses only empirical data to approximate the symmetric variant of the Kullback-Leibler (KL) divergence, i.e., a measure of how different two distributions are. The divergence estimate is calculated between the latent representations of the source and target technologies. matching Next, the obtained shared latent representation can be used to find cells that are similar across techniques, i.e., cells within a sample that have been analyzed by each technique and are most closely related to one another. Each cell is characterized in the latent space by a low-dimensional vector of latent codes that have a one-to-one correspondence across techniques. To find the optimal pairwise match in a computationally efficient way, this task can be viewed as a combinatorial bipartite matching problem.

[0072] However, given the high dimensionality of single-cell data, as a first step, it is helpful to reduce the search space to the most likely latent matches. To accomplish this, a k-nearest neighbors (kNN) graph is constructed using the source data and then queried by target technology cells. Nodes correspond to cells, and edge weights correspond to the distance between cells. Since the latent codes are dense and directly comparable between technologies, the dissimilarity between each cell pair is measured using Euclidean distance. Sparsity of connections, regulated by the selection of the hyperparameter k, corresponds to a trade-off between computational performance (memory usage, execution time) and matching accuracy.

[0073] Considering a cost matrix based on the distance between all cell pairs across technologies (e.g., Euclidean distance in latent or data space), the objective is to find the row-cell pair with the smallest total cost. In this embodiment, the cost matrix is ​​generated using Euclidean distance in latent space. This objective then corresponds to solving a linear assignment problem (LAP), i.e., bipartite matching, which can be formulated as follows.

[0074]

number

[0075] Here, the cost matrix is ​​C, the Boolean assignment matrix is ​​X, and the cell indices are i∈{1,...,n} and j∈{1...,m}, where n and m represent the number of cells in the source and target data sets, respectively. In classical bipartite matching, n=m, and when formulated as a graph of cell nodes, the capacity of each edge is exactly 1. This is because bijective matching is forced. To efficiently solve LAP by sparse connections, we used the Jonker-Volgenant algorithm (1987). This algorithm has a worst-case complexity of O(n 3 Despite this, it has been shown to have excellent computational performance even in high-dimensional settings (Dell'Amico and Toth, 2000).

[0076] To relax the constraint on only one match, a generalized framework of the minimum cost maximum flow problem (Ahuja et al., 1993; Klein, 1967) can be applied. Assuming a directed graph G=(V,E), where V represents a vertex and E represents an edge, the minimum-cost maximum flow of G is the maximum flow that can be pushed from the source to the sink at the minimum cost. If u represents a non-negative edge capacity and c represents the corresponding cost, then a flow of f(v,w) units on the edge (v,w) contributes c(v,w).f(v,w) to its purpose.

[0077]

number

[0078] this is,

[0079]

number

[0080]

number

[0081] Follow the rules. Finding the minimum cost of flow through this network corresponds to finding the shortest path. Many algorithms have been designed to efficiently solve the minimum cost maximum flow problem in polynomial time (see, for example, Ahuja et al., 1993; Kovacs, 2015).

[0082] The methods described so far make a strong assumption that the same cell composition is observed across the data set; that is, each cell has a sibling that directly corresponds to it in other techniques. To address mismatches due to expected variability in cell composition, we extend the kNN graph with sparse connectivity by adding tightly connected null nodes with high capacity and high allocation costs, thereby capturing cells that otherwise do not match well.

[0083] This graph structure is shown in Figure 2. In Figure 2, the latent space is illustrated as a collection of nodes corresponding to cells in the source (S) and target (T) data sets, and edges to sparse connections between them. These were obtained from kNN search. Edge labels (a, b) indicate the matching cost and edge capacity, respectively. The gray-colored null nodes in the lower right capture matches with source cells that lack sufficiently close analogues in the target technique. Their capacity is equal to the concentration of the source data, and their cost is c *0 The value is relatively high. If the lines connecting the nodes are thick, they represent the actual matches selected by the algorithm.

[0084] Furthermore, to account for the difference in cell numbers between modalities, a many-to-one match is enabled by increasing the capacity of the outgoing source edge, assuming that the source corresponds to the smaller data set. To penalize cells left unmatched, the sum of the outgoing source capacities, excluding null nodes, is used to increase the concentration of the target set.

[0085]

number

[0086] The constraint is imposed so that it is equal to . The quality of matching is evaluated at different levels. First, the precision corresponding to the fraction of true positives for cell type labels is reported. Cell types can be determined in a technique-specific manner. If higher-granularity cell information, such as pseudo-time, is available, a direct comparison of this quality is performed.

[0087] Data set obtained from simulation First, we evaluate the method of this embodiment using two synthetic data sets generated by ROSSTT (Papadopoulos et al., 2019). ROSSTT simulates a transient bifurcation process that parameterizes a negative binomial model.

[0088] We simulated two single-cell analysis techniques by running PROSSTT under different seed and gene counts, while preserving the underlying branching structure (see Table 1). That is, these two data sets share a common latent structure, but their features do not correspond at all. We used a three-branching tree with different branching lengths, as shown in Figure 3. The first branch A was run from pseudo-time 0 to 30, branch B from 30 to 50, and branch C from 30 to 60. The data simulated with PROSSTT allows us to define the underlying latent structure.

[0089] [Table 1]

[0090] The method of this embodiment was implemented using the larger data set (i.e., the data set with more markers) as the source technology and the smaller data set as the target technology. The latent space was initialized by training a VAE on the source technology for 250 epochs. These latent representations were fixed, and then the target technology was trained for 250 epochs. Branch labels were provided to the discriminator to facilitate orientation of the latent space (Makhzani et al., 2015). For each target cell, the pair of cells most similar to it in the source data set was identified using the k-nearest neighbor algorithm with k=500, using Euclidean distance on the latent code. The optimal matching was then found by solving the minimum-cost maximum-flow problem, addressing many-to-one matches.

[0091] In the second method, we simulated three cell analysis techniques by running PROSSTT under different seeds but preserving the underlying branching structure. That is, these three data sets also have a common latent structure, but their features do not correspond at all. We used five-branch trees with different branching lengths, shown on the left side of Figure 4. Each data set contains 64,000 cells and 256 markers.

[0092] The method of this embodiment was performed on three simulation data sets. The latent space was initialized by training a VAE on the source technology for 256 epochs. These latent representations were fixed, and then two target technologies were trained for 256 epochs. For each target cell, the pair of cells most similar to it in the source data set was identified using the k-nearest neighbor algorithm with k=500 and Euclidean distance on the latent code. The optimal match was found by solving the bipartite matching problem. result The method of this embodiment was evaluated to ensure that, for the pair of data sets generated by PROSSTT, there is no feature correspondence between the two data sets, but that shared fundamental properties are preserved. In PROSSTT, branching defines an over-arching structure that mimics cell types. On the other hand, the transient component, i.e., pseudo-time, provides continuous interpolation from one branch to another, as defined by the tree.

[0093] In the latent space, the branching structure within the data generates large clusters, while the pseudo-temporal structure indicates orientation within each cluster and global smoothing of the manifold. For a 3-branch tree, the method of this embodiment was able to correctly capture this structure and orientation it across the data set, as shown in the tSNE embedding computed on a latent representation combined from both sources, as shown in Figure 5.

[0094] Each point in Figure 5 corresponds to the latent representation of a cell. On the first axis, points are colored by branching labels and shaded by source technology. Figure 5 shows that the branching structure of the tree is represented in the embedding, and the technology codes are globally classified by branching labels. On the second and third axes, source / technology codes are colored by pseudo-time labels. As shown in the figure, this method was able to correctly capture the orientation within the cluster.

[0095] The optimal matching algorithm was applied to a sparse kNN graph with k=1500. Figure 6 shows a quantitative evaluation of the match over pseudotime. The colored contours correspond to cells paired within the same branch. The gray contours correspond to cells paired in different branches. It can be seen that in most cases, this mismatch occurs around the branching point where cells from different branches are most similar.

[0096] The highest cell density is observed within the diagonal neighborhood, indicating that the derived matches reflect not only the overall branching but also subtle variations. Cells that are mismatched with respect to branching labels (gray) constitute 15% of the total cell population.

[0097] Table 2 below is the corresponding confusion table.

[0098] [Table 2]

[0099] The majority of mismatches occur around branching points where intercellular differences become indistinguishable. As expected, the overall accuracy of the matches increases when the branching point area (pseudo-time ∈[30-E, 30+E]) is not taken into account (accuracy: 98%, see Table 3 below). The Spearman and Pearson correlation coefficients for all matches reach 0.89 and 0.87, respectively. These results demonstrate that the method of this embodiment can accurately identify the best-matching cells across techniques based on shared latent representations, even without paired features.

[0100] [Table 3]

[0101] Even for a 5-branch data set, the method of this embodiment was able to correctly capture the underlying data structure and orient it correctly across the data sets, as shown in the tSNE embedding calculated for the latent representation combined from all data sets, as shown in Figure 7.

[0102] The optimal matching minimum cost maximum flow algorithm described earlier was applied to a sparse kNN graph with k=50. The plot on the right side of Figure 4 shows a quantitative evaluation of the match with respect to pseudotime.

[0103] The highest cell density is observed within the diagonal neighborhood, indicating that the derived matches reflect not only the overall branching but also subtle variations. Cells that mismatch with respect to branching labels (gray) constitute 15% of the total cell population. The corresponding confusion table is shown below as Table 4.

[0104] The majority of mismatches are located around branching points where the differences between cells become indistinguishable. The Spearman and Pearson correlation coefficients for all matches are 0.83 and 0.86, respectively. These results demonstrate that the method of this embodiment can accurately identify the best-matching cells across techniques based on shared latent representations, even without paired features.

[0105] [Table 4]

[0106] Furthermore, the method of this embodiment was compared with the MATRCHER method disclosed in Welch et al., 2017. MATRCHER assumes a one-dimensional latent structure and is violated by the branching structure in the simulated data. In addition, MATRCHER is a probabilistic model based on a Gaussian process and is therefore limited in terms of scalability. For this reason, a budget of 48 hours of computation time was set using a maximum of 40 Gb of memory. Subsequently, the matching step of this embodiment was applied to find matches using a kNN graph with k=50 and a null code cost of 95. Figure 8 shows a density plot of pseudo-time labels between matched pairs of cells between the source and target techniques using the latent codes obtained from MATRCHER. Colored contours correspond to cells paired within the same branch, while gray contours correspond to cells paired in different branches. The accuracy for branch labels was 4%, while 40% of the cells matched to null nodes. This is because a better match could not be identified. Single-cell profiles of melanoma patients The real-world data set used to further illustrate the operation of the method in this embodiment is generated by a Tumor Profiler (TuPro) consortium (Irmisch et al., 2020) that includes metastatic tumors from a deeply phenotyped cohort of individuals as part of a multicenter, multi-cancer clinical trial. Data from each patient is analyzed using multiple techniques, including scRNA sequencing (Tang et al., 2009), time-of-flight cytometry (Bandura et al., 2009, CyTOF), and imaging mass cytometry (Giesen et al., 2014, IMC). All of these can dissect the tumor microenvironment and provide complementary single-cell level information about the sample under consideration. While cell identity is lost during the process, the cells examined by both techniques originate from the same population (i.e., obtained from aliquots of a common cell suspension).

[0107] For the CyTOF data set, patient samples were profiled using CyTOF with a 40-marker panel designed for thorough characterization of the sample's immune compartment. Data preprocessing was performed following the workflow described in Chevrier et al., 2017, 2018. Cell type assignment was performed using a random forest classifier trained on multiple manually-gated samples. To investigate the usefulness of the method in this embodiment, only a subset of B and T cells containing m=135,334 cells was examined. This data set is hereafter referred to as the target data set.

[0108] Second aliquots of the same patient's samples were analyzed by droplet-based scRNA sequencing using a 10x Genomics platform. Pre-processing steps were applied, including standard QC measurements, removal of low-quality cells, and exclusion of mitochondria, ribosomes, and non-coding genes. Expression data were normalized by library size and corrected for cell cycle effects. Cell type identification was performed using a set of cell type-specific marker genes (Tirosh et al., 2016). The genes were then filtered to a set of 256, retaining those that could encode proteins measured in CyTOF channels, the top 32 T-cell / B-cell marker genes, and the remaining most mutable genes. The total number of B and T cells in this data set reached n=4,683. The scRNA-Seq data set is used as the source data set in the following example.

[0109] [Table 5]

[0110] A two-layer encoder and decoder were used for scRNA-Seq / CyTOF techniques, each having 64 / 8 units within its respective hidden layer. The discriminator was a two-layer network with 8 units, and its latent dimension was set to 8. All networks used ReLU activation. The discriminators were conditioned with cell type labels. These were trained over 256 epochs. Discrimination of cell analogs between scRNA-Seq and CyTOF data, downsampled to the size of the scRNA-Seq data (m=n=4,683 cells), was based on a sparse kNN graph with k=500, calculated using Euclidean distance. result As discussed earlier, the method of this embodiment was applied to integrate scRNA-Seq and CyTOF data sets generated from a single sample using the TuPro project. Integrating these techniques (and other single-cell analysis techniques) allows for a multi-perspective view of cell dynamics, thereby deepening our understanding of the biological processes performed.

[0111] Optimal matching of latent codes restores cell type labels with 97% accuracy. In comparison, matching within the same cell's data space yields only 72% accuracy for cell type labels.

[0112] In the tSNE embedding of the integrated latent space shown in Figure 9, a more fine-grained visual evaluation is performed by examining the matches marked with gray lines. The colors (blue, orange) represent cell types (B cells, T cells), and the color shade corresponds to the profiling technique (light: scRNA-Seq, dark: CyTOF). The data were randomly downsampled to the size of the scRNA-Seq data (n=4,683 cells).

[0113] Considering the differing proportions of cell types in the data, a certain percentage of mismatch, in this case 3%, is expected. This corresponds to a line connecting points that span two cell types. Note that, for the sake of this visualization and to investigate and demonstrate the accuracy of this method, null nodes are not included in the graph; however, if they were included, they would have captured most of the mismatches.

[0114] Figure 12 shows an equivalent plot using direct matching in the data space. Cell matches were obtained by matching against the data space, indicated by the gray line. The colors (blue, orange) represent cell types (B cells, T cells), and the hues correspond to profiling techniques (light: scRNA-Seq, dark: CyTOF). The data was randomly downsampled to the size of the scRNA-Seq data (n=4,683 cells). The accuracy of such matching is inferior to that using latent representation, and therefore, more links across cell types may be observed.

[0115] Furthermore, to quantitatively evaluate the quality of matching in both cases, marker expression correlation information was used in a more granular manner. This involved using correlation coefficients between the expression of cancer-related HLA-DRA genes and the number of individuals with corresponding HLA-DR proteins. HLA-DRA marker individuals were measured by scRNA-Seq (gene, x-axis) and CyTOF (protein, y-axis), and bivariate density plots are shown in Figure 10. Colored contours (bottom left, top right) correspond to cells paired within the same cell type. Gray contours (top left, bottom right) correspond to cells paired with different cell types. The intensity of the color is weighted by the proportion of cell types. These plots, from left to right, correspond to matching in latent space, matching in data space, and random matching. Spearman and Pearson correlation coefficients are shown for each plot to demonstrate the advantages of using shared latent expression (highest correlation coefficient) for this task, as it performs optimal matching (random matching has the lowest correlation coefficient).

[0116] These results demonstrate that matching using shared latent representations is far superior to using common features in the data space (Pearson coefficients: 0.64 and 0.22, respectively). Furthermore, in both cases, the optimal matching yields higher representational correlations compared to random cell matching between the two techniques (Pearson coefficient: 0.01). In other words, it has been proven that using shared latent representations is useful for discovering cell analogs even when a subset of features paired across techniques exists.

[0117] As previously described, an unbiased divergence estimator was used to evaluate the quality of the integrated latent space (Wang et al., 2009). Figure 11 shows the progress of training the method according to an embodiment of the present invention on cancer patient samples. The VAE was trained on scRNA-Seq data, and the CyTOF representation was integrated into the latent space defined by the scRNA-Seq code using the method according to the embodiment described above.

[0118] Figure 13 shows various metrics for model training. The top panel shows the negative log-likelihood of CyTOF reproduction. The middle panel shows the discriminator's performance in correctly classifying scRNA-Seq codes (critic-prior) and CyTOF codes (critic-code), and the encoder's ability to deceive the discriminator, i.e., misclassification accuracy (generator). The bottom left panel shows the divergence of the latent representation. To measure the degree of integration of the latent space, the estimated divergence is calculated for the latent representations of the two techniques, and the divergence and reproduction error are set to empirically defined thresholds (divergence < 0.3, L). nll Optimization is considered successful if it is lower than <47). As shown in Table 6 below, performance was found to depend on the tuning β as well as the learning rates of the encoder and critical network. With the most stable hyperparameter setting, the critical learning rate was 1 × 10⁻⁶. -3 and encoder / decoder learning rate 5 × 10 -4Therefore, we adopt a large weight for the adversarial gradient, β=512.

[0119] [Table 6]

[0120] Bipartite matching was chosen because it ensures globally optimal matching between the two techniques across all cells. As explained earlier, kNN search was combined with bipartite matching due to the large number of cells to be profiled by each technique for each sample, and the nature of the cell matching problem. Figure 11 shows a comparison of accuracy. In Figure 11, the number of neighbors k examined is shown on the x-axis. This is shown on a common logarithmic scale (log10-scale). The fractional number of true positive matches for cell type labels is shown on the y-axis. The accuracy level of close connection has already been achieved for k=500 and is within 1% of the absolute difference for k=100.

[0121] Thus, comparing bipartite matching alone with the combined approach, it is shown that equivalent accuracy can be achieved using only k=500 neighbors for a total of 4,683 cells. This is not surprising, because matching to excessively distant neighbors can only be justified in the case of many multiple ties, i.e., sets of indistinguishable cells. In other words, narrowing the matching in the search space to the closest neighbors corresponds to finding cell similarities based on a dense distance matrix.

[0122] Furthermore, solving this task using a combined approach is computationally efficient. This is because, using k=500, pairwise matches were found for all 4,683 cells with 0.5 Gb of memory usage and less than one minute of computation. As predicted, increasing k requires more computational resources to solve the optimal matching problem (Table 7 below). However, while the hyperparameter k can be set much smaller than the data dimension, in most cases a substantial gain in computational performance for matching is obtained on a fully connected graph.

[0123] [Table 7]

[0124] As shown in Table 8 below, similar results were obtained for the effect of varying the hyperparameter k when applying the minimum-cost maximum-flow matching algorithm. Although this algorithm is slower overall, this method has other advantages in terms of scalability and the trade-off between true and false positive rates.

[0125] [Table 8]

[0126] conclusion The method of this embodiment provides a technically immutable technique for matching single-cell measurements across multimodal data sets without requiring feature mapping, enabling practical multimodal single-cell analysis and opening up new opportunities to gain a multifaceted understanding of the dynamics of individual cells in various diseases or progression states. Scalability is ensured by combining the underlying automated encoder framework with a customized bipartite matching method.

[0127] By introducing a divergence scale, we addressed common problems in adversarial training, such as training instability and convergence problems. Scalability was achieved by efficiently matching corresponding cells across techniques using a modified bipartite matching solution. Modifications and extensions to bipartite matching can broaden the applicability of this method because a shift in cell type composition can be expected across disparate aliquots, even if they come from the same sample. Furthermore, the introduction of a null node ensures improved match quality by avoiding forced mismatches and thus increasing reliability in cell-to-cell assignment.

[0128] As the data dimension increases, more ties are likely to occur, and therefore the number of neighbors (k) should also increase. However, in the experiments we conducted, the difference in the number of true positives across various values ​​of k for the same data set remained within 5%, and thus the performance against this hyperparameter selection is considered to be very robust.

[0129] Although the specific embodiments described above used two data sets, it can be acknowledged that the described method can be extended to situations with three (or more) data sets. The latent space can be constructed by using all data sets simultaneously and appropriately adapting the objective function. Furthermore, we are confident that even as the number of data sets increases, performing matching between each pair of latent data sets using a bipartite matching method remains the most computationally efficient approach.

[0130] The systems and methods of the above embodiments can also be implemented in computer systems (particularly in computer hardware or computer software), in addition to the structural components and user interfaces described.

[0131] The term "computer system" includes hardware, software, and data storage devices for embodying the system or for performing the methods in accordance with the embodiments described above. For example, a computer system may include a central processing unit (CPU), input means, output means, and data storage. Preferably, the computer system has a monitor that provides a visual output display. The data storage may include RAM, disk drives, or other computer-readable media. The computer system may also include a plurality of computing devices connected by a network that can communicate with each other through this network.

[0132] The methods of the above embodiments may be provided as a computer program, a computer program product, or a computer-readable medium for storing (carrying) a computer program. The computer program is configured to perform one or more of the methods described above when executed on a computer.

[0133] The term “computer-readable media” includes, but is not limited to, one or more non-temporary media that can be directly read and accessed by a computer or computer system. These media may include, but are not limited to, magnetic storage media such as floppy disks, hard disk storage media, and magnetic tape, optical storage media such as optical disks or CD-ROMs, electrical storage media such as RAM, ROM, and flash memory, and combinations or mixes of the above, such as magnetic / optical storage media.

[0134] While embodiments of the present invention have been described above, those skilled in the art will recognize that the present invention is not limited to the specific configurations and methods disclosed in this description of preferred embodiments. Those skilled in the art will also recognize that the present invention has a broad scope of application, and that embodiments can be broadly modified without departing from any inventive concept defined in the appended claims.

[0135] The following references are hereby cited, and their entire contents are included in this application. Abadi, M. et al. (2015). TensorFlow: Large-scale machine learning on heterogeneous systems. The software is available from tensorflow.org.

[0136] Ahuja, RK et al. (1993). Network Flows: Theory, Algorithms, and Applications. Prentice-Hall, Inc., USA. Amodio, M. and Krishnaswamy, S. (2018). MAGAN: Aligning biological manifolds. In J. Dy and A. Krause, editors, Proceedings of the 35th International Conference on Machine Learning, volume 80 of Proceedings of Machine Learning Research, pages 215-223, Stockholmsmassan, Stockholm, Sweden. PMLR. Bandura, DR et al. (2009). Mass cytometry: Technique for real-time single-cell multitarget immunoassay based on inductively coupled plasma time-of-flight mass spectrometry. Analytical Chemistry, 81(16), 6813-6822. Chevrier, S. et al. (2017). An immune atlas of clear cell renal cell carcinoma, Cell, 169(4), 736 - 749.e18. Chevrier, S. et al. (2018). Compensation of signal spillover in suspension and imaging mass cytometry. Cell Systems, 6(5), 612 - 620.e5. Dell'Amico, M. and Toth, P. (2000). Algorithms and codes for dense assignment problems: the state of the art (Discrete Applied Mathematics, 100(1), 17 - 48). Giesen, C. et al. (2014). Highly multiplexed imaging of tumor tissues with subcellular resolution by mass cytometry. Nature Methods, 11(4), 417-422. Heusel, M. et al. (2017). GANs trained by a two time-scale update rule converge to a local Nash equilibrium. Irmisch, A. et al. (2020). The tumor profiler study: Integrated, multi-omic, functional tumor profiling for clinical decision support (medRxiv) Jonker, R. and Volgenant, A. (1987). A shortest augmenting path algorithm for dense and sparse linear assignment problems. Computing, 38(4), 325-340. Kingma, DP and Ba, J. (2014). Adam: A method for stochastic optimization. Kingma, DP and Welling, M. (2013). Auto-Encoding Variational Bayes. Klein, M. (1967). A primal method for minimal cost flows with applications to the assignment and transportation problems. Management Science, 14(3), 205-220. Kovacs, P. (2015). Minimum-cost flow algorithms: an experimental evaluation. Optimization Methods and Software, 30(1), 94-127. Liu, J. et al. (2019). Jointly embedding multiple single-cell omics measurements. BioRxiv, page 644310. Lucic, M. et al. (2017). Are GANs created equal? ​​A large-scale study. Makhzani, A. et al. (2015). Adversarial autoencoders. Miyato, T. et al. (2018). Spectral normalization for generative adversarial networks. Oetjen, KA et al. (2018). Human bone marrow assessment by single-cell RNA sequencing, mass cytometry, and flow cytometry. JCI Insight, 3(23). Papadopoulos, N. et al. (2019). PROSSTT: probabilistic simulation of single-cell RNA-seq data for complex differentiation processes (Bioinformatics, 35(18), 3517-3519). Rozenblatt-Rosen, O. et al. (2017). The human cell atlas: from vision to reality. Nature News, 550(7677), 451. Salimans, T. et al. (2016). Improved techniques for training GANs. In DD Lee, M. Sugiyama, UV Luxburg, I. Guyon, and R. Garnett, editors, Advances in Neural Information Processing Systems 29, pages 2234-2242. Curran Associates, Inc. Stoeckius, M. et al. (2017). Simultaneous epitope and transcriptome measurement in single cells. Nature Methods, 14, 865. Tang, F. et al. (2009). mRNA-seq whole-transcriptome analysis of a single cell. Nature Methods, 6(5), 377-382. Tirosh, I. et al. (2016). Dissecting the multicellular ecosystem of metastatic melanoma by single-cell rna-seq. Science, 352(6282), 189-196. Wang, Q. et al. (2009). Divergence estimation for multidimensional densities via k-nearest-neighbor distances. IEEE Transactions on Information Theory, 55(5), 2392-2405. Wang, T. et al. (2019). Bermuda: a novel deep transfer learning method for single-cell RNA sequencing batch correction reveals hidden high-resolution cellular subtypes. Genome Biology, 20(1), 165. Welch, JD et al. (2017). Matcher: manifold alignment reveals correspondence between single-cell transcriptome and epigenome dynamics. Genome Biology, 18(1), 138. Yang, KD and Uhler, C. (2019). Multi-domain translation by learning uncoupled autoencoders. CoRR, abs / 1902.03515. Zhu, C. et al. (2020). Single-cell multimodal omics: the power of many. Nature Methods, 17(1), 11-14.

Claims

1. A computer implementation method for determining the correspondence between the first biological properties of cells included in the first set of biological properties determined by a first analytical technique and the second biological properties of cells included in the second set of biological properties determined by a second different analytical technique, The steps include converting the first and second sets of biological properties into corresponding expressions in an expression format that is invariant to the technique used to derive the biological properties, In the aforementioned representation format, the step of determining the second representation that most closely matches the first representation of the first biological property from the converted second set of biological properties, The steps include: converting a second representation from the aforementioned representation format back into a biological property associated with the second representation, thereby determining the correspondence between the first biological property and the second biological property; Includes, The expression that is invariant to the technique used to derive the aforementioned biological properties is the latent space, A method in which the determination step addresses the possibility of undiscovered correspondences between each pair of the transformed sets by using a bipartite matching technique and adding a null node to each transformed tuplet.

2. A computer implementation method for determining the correspondence between a first biological property of a cell and several other biological properties of the cell, wherein the first biological property and the other biological properties are each determined by different analytical techniques and each is included in each of several sets of biological properties. The steps include converting the aforementioned sets of biological properties into corresponding representations in a representation format that is invariant with respect to the techniques used to derive these biological properties, In the aforementioned expression format, the step of determining the expression that most closely matches the first expression of the first biological property from each of the converted sets of other biological properties, The steps include: converting the expression determined from the expression format into a biological property associated with the determined expression, thereby determining the correspondence between the first biological property and each of the other biological properties; Includes, The expression that is invariant to the technique used to derive the aforementioned biological properties is the latent space, A method in which the determination step addresses the possibility of undiscovered correspondences between each pair of the transformed sets by using a bipartite matching technique and adding a null node to each transformed tuplet.

3. A method according to claim 1 or 2, wherein at least one of the analytical techniques is a single-cell analytical technique.

4. A method according to claim 1 or 2, wherein the latent space is constructed by creating a neural network for a) an encoder for each data set, b) a decoder for each data set, and c) a discriminator that acts on the representation.

5. The method according to claim 4, wherein the discriminator is a binary classifier.

6. A method according to claim 4 or claim 5, wherein the latent space is constructed by minimizing the reproduction error between the encoder and decoder for each data set while adversarially deceiving the discriminator.

7. A method according to any one of claims 1 to 6, wherein the determination step includes a substep of narrowing the search space using a k-nearest neighbor method to reduce the number of possible correspondences to a predetermined minimum.

8. A method according to any one of claims 1 to 7, wherein the bipartite matching method uses a minimum cost maximum flow algorithm.

9. A method according to any one of claims 1 to 8, wherein the determination step corresponds to a many-to-one match for the representation when the transformed set has few elements.

10. A computer program configured to perform the method described in any one of claims 1 to 9 when executed on a processor.

11. A computer program product having non-temporary memory for storing the computer program according to claim 10.

12. A computer system having a processor configured to perform the method according to any one of claims 1 to 9.

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