Method and apparatus for classification

Abstract

The present disclosure provides a computer-implemented method for classification, comprising: obtaining features for a set of inputs; the features are represented by using von Mises Fisher (vMF) distribution; obtaining a classifier by using vFM distribution according to the Bayesian theorem, where the feature is an input of the classifier; and optimizing the classifier based on the set of inputs by estimating parameters of a vMF distribution of the feature using a maximum posteriori (MAP) estimate.

Description

Technical Field

[0001] The various aspects of this disclosure generally relate to artificial intelligence (AI), and in particular to methods and apparatus for classification. Background Technology

[0002] Modern deep neural networks for classification typically involve optimizing a Softmax classifier by applying cross-entropy loss and gradient descent. This approach has consistently demonstrated effectiveness across a wide range of domains, particularly for finely balanced academic datasets. However, unlike academic datasets, real-world data often exhibits a long-tailed distribution across classes; for example, its characteristics can be characterized by a significant decrease in the number of samples per class from the head (e.g., high-frequency or majority classes) to the tail (e.g., low-frequency or minority classes). Given this imbalance, typical Softmax cross-entropy correlation methods suffer a significant performance degradation.

[0003] Unfortunately, in many critical application areas such as medical diagnostics and autonomous driving, the data is inherently severely imbalanced, and a few categories are particularly important because these categories may be, for example, patients or accidents.

[0004] Therefore, long-tailed or imbalanced datasets can pose significant challenges to classification tasks, and there may be a desire to provide methods or techniques suitable for classification on long-tailed or imbalanced datasets. Summary of the Invention

[0005] The following presents a simplified overview of one or more aspects of this disclosure in order to provide a basic understanding of these aspects. This overview is not a comprehensive summary of all anticipated aspects and is neither intended to identify key or essential elements of all aspects nor to depict the scope of any or all aspects. Its sole purpose is to present some concepts of one or more aspects in a simplified form as a prelude to the more detailed description that follows.

[0006] In one aspect of this disclosure, a computer-implemented method for classification is provided, comprising: obtaining features for a set of inputs; representing the features using a von Mises-Fisher (vMF) distribution; obtaining a classifier by employing the vMF distribution according to Bayes' theorem, wherein the features are inputs to the classifier; and optimizing the classifier based on the set of inputs by estimating parameters of the vMF distribution of the features using maximum a posteriori (MAP) estimation.

[0007] In another aspect of this disclosure, a computer-implemented method for classification is provided, comprising: obtaining features for a set of images; representing the features using a von Mises-Fisher (vMF) distribution; obtaining a classifier by employing the vMF distribution according to Bayes' theorem, wherein the features are inputs to the classifier; and optimizing the classifier based on the set of images by estimating parameters of the vMF distribution of the features using maximum a posteriori (MAP) estimation; wherein the optimized classifier is used to classify images into categories.

[0008] In another aspect of this disclosure, an apparatus for classification is provided, including a memory and at least one processor coupled to the memory. The at least one processor is configured to: obtain features for a set of inputs; represent the features using a von Mises-Fisher (vMF) distribution; obtain a classifier by employing the vMF distribution according to Bayes' theorem, wherein the features are inputs to the classifier; and optimize the classifier based on the set of inputs by estimating parameters of the vMF distribution of the features using maximum a posteriori (MAP) estimation.

[0009] In another aspect of this disclosure, a computer program product for classification is provided, comprising processor-executable computer code for: obtaining features for a set of inputs; representing the features using a von Mises-Fisher (vMF) distribution; obtaining a classifier by employing the vMF distribution according to Bayes' theorem, wherein the features are inputs to the classifier; and optimizing the classifier based on the set of inputs by estimating parameters of the vMF distribution of the features using maximum a posteriori (MAP) estimation.

[0010] In another aspect of this disclosure, a computer-readable medium stores computer code for classification. When executed by a processor, the computer code causes the processor to: obtain features for a set of inputs; represent the features using a von Mises-Fisher (vMF) distribution; obtain a classifier by employing the vMF distribution according to Bayes' theorem, wherein the features are inputs to the classifier; and optimize the classifier based on the set of inputs by estimating the parameters of the vMF distribution of the features using maximum a posteriori (MAP) estimation.

[0011] The classification methods proposed according to one or more aspects of this disclosure can be used in a variety of tasks and / or application areas, such as image classification, visual recognition, medical diagnosis, autonomous driving, etc. Although the following disclosure can be described with reference to image classification for illustrative purposes only, this disclosure is applicable to many other application areas.

[0012] By explicitly modeling the Bayesian decision process by explicitly modeling the data distribution and estimating its parameters, the need for gradient descent, which is susceptible to long-tailed data distributions due to gradient imbalance, can be eliminated, while still adhering to optimal decision rules.

[0013] Other aspects or variations of this disclosure, as well as its other advantages, will become apparent from the following detailed description and accompanying drawings. Attached Figure Description

[0014] The disclosed aspects will be described below in conjunction with the accompanying drawings, which are provided for illustrative purposes and not for limiting the scope of the disclosure.

[0015] Figure 1 An exemplary workflow for a classification method based on one or more aspects of this disclosure is shown.

[0016] Figure 2 A schematic diagram showing a comparison between an LA classifier based on one or more aspects of this disclosure and a classifier proposed herein.

[0017] Figure 3 An exemplary workflow for a classification method based on one or more aspects of this disclosure is shown.

[0018] Figure 4 An exemplary framework for a classification method based on one or more aspects of this disclosure is shown.

[0019] Figure 5 Another exemplary framework for a classification method based on one or more aspects of this disclosure is shown.

[0020] Figure 6 Examples of hardware implementations for a device based on one or more aspects of this disclosure are shown. Detailed Implementation

[0021] The present disclosure will now be discussed with reference to several example implementations. It should be understood that these implementations are discussed only to enable those skilled in the art to better understand and thus implement embodiments of the present disclosure, and are not intended to limit the scope of the present disclosure.

[0022] Recently, many machine learning methods or algorithms have proven effective for classification on balanced academic datasets. These methods or algorithms are typically designed to implicitly estimate posterior probabilities based on the training dataset, which usually involves optimizing a Softmax classifier by applying cross-entropy loss and gradient descent. However, these methods or algorithms may not be suitable for real-world data. Real-world data often exhibits an imbalanced or long-tailed distribution across classes, where a few classes may contain many instances (e.g., head classes), while many classes may contain only a few instances (e.g., tail classes). This imbalance can lead to performance degradation for these typical learning methods, as head classes may dominate the training process and negatively impact the decision boundaries of tail classes. While the number of instances or samples is crucial for training, obtaining more instances or samples from tail classes is often impractical or even impossible in many application domains.

[0023] Therefore, much research has been conducted in the field on classification of imbalanced data distributions. Several methods have been proposed, such as resampling, reweighting, boundary recalibration, and logit adjustment (LA). However, these currently proposed methods share an important common foundation: they all continue to employ the paradigm of implicit estimation of the posterior distribution. This implicit estimation has been developed and proven to be effective for most balanced training data, but may lead to suboptimal algorithms in the context of realistic long-tailed training data.

[0024] Specifically, current typical learning methods can be equationd as follows. Given a training dataset... Training the model to receive data from space Image mapping from space The category. Typically, mapping functions... It can be modeled as a neural network, which consists of a backbone feature extractor. and linear classifier Composition. For samples in the training dataset. The typical Softmax cross-entropy loss can be expressed as: Equation (1) in, and They are categories The weights and biases of the linear classifier. From equation (1), it can be observed that the model can implicitly estimate the posterior probability of the class by using gradient descent.

[0025] However, when the training dataset has a long-tailed distribution, the typical Softmax cross-entropy algorithm can lead to minority collapse due to gradient imbalance. That is, as the gradient is gradually suppressed as the imbalance level increases, classifiers for the minority classes tend to become closer to each other. At the same time, Bayesian optimal decision rules are generally not guaranteed.

[0026] To mitigate the effects of imbalance, the logit adjustment (LA) method modifies the predicted logits of the class bias model by introducing a prior distribution over the class labels as follows: Equation (2) in, It represents the class frequencies in the training dataset.

[0027] However, it can be observed from equation (2) that the LA method still implicitly estimates the posterior probability of the class by using gradient descent, and is therefore susceptible to gradient imbalance.

[0028] To better address classification problems on long-tailed data distributions, this disclosure proposes to explicitly model the Bayesian decision process by explicitly modeling the data distribution and estimating its parameters, thereby eliminating the need for gradient descent while adhering to optimal decision rules.

[0029] Because it is based on Bayesian decision theory, a Bayesian classifier is often identified as the optimal classifier that minimizes the risk in a machine learning task. For example, a Bayesian classifier can be expressed as follows: Equation (3) However, the complex and often difficult-to-handle nature of the real data distribution poses a significant challenge to the direct computation of the posterior distribution, and thus hinders the realization of Bayesian optimal decision-making.

[0030] In this context, typical learning methods are designed to implicitly estimate posterior probabilities by approximating a Bayesian classifier based on the training data, using the model's output, and gradient descent, as shown in equations (1) and (2). However, as mentioned above, these methods may suffer from two main problems when the dataset has a long-tailed distribution. From an optimization perspective, these methods suffer from a few collapses due to gradient imbalance, and from a Bayesian decision-making perspective, the optimal Bayesian decision rule is often not guaranteed.

[0031] This disclosure relates to explicitly modeling data distributions and estimating their parameters. However, translating this idea into practice is not straightforward, as methods for modeling real-world data distributions typically involve complexities, such as the necessity of training deep generative models. This is also evident in current typical learning methods that use the model's output to approximate a Bayesian classifier, thus avoiding capturing the true distribution of real-world data.

[0032] To address this challenge, this disclosure proposes modeling the data distribution in the feature space, rather than modeling the data distribution in its original form. It can be observed that features tend to collapse toward the mean of their corresponding class during imbalanced learning. This disclosure makes the distribution assumption that the feature norm (e.g., indicator length) is equal for samples from each class, and that the feature distribution can be represented by a von Mises-Fisher (vMF) distribution on a unit sphere. By adopting such a distribution assumption for the feature distribution, modeling the data distribution can be more elegant and manageable.

[0033] Specifically, the vMF distribution is a unit hypersphere. exist The probability distribution on the [surface / space]. It is used for random [distributions / methods]. 1D unit vector The probability density function can be given by the following equation: Equation (4) in, yes 1D unit vector ,as well as Indicates the order is The first kind of modified Bessel function is defined as: Equation (5) parameter and These are respectively called the mean direction and concentration of the distribution. For example, in a distribution with a large... In the case of a value, the average direction can be observed. The surrounding high concentration, and when At that time, the distribution on the sphere becomes uniform.

[0034] Based on the distribution assumption and cross-entropy loss, the optimization objective and classifier according to Bayes' theorem can be obtained as follows: Equation (6) or Equation (7) in, It is input The corresponding feature embedding, It is the class frequency in the training or test set. and It is a category The parameters of the vMF distribution.

[0035] Based on equation (6) or equation (7), it can be observed that the classifier proposed in this paper is a linear classifier in the feature space. The essential difference between our method and existing methods lies in the explicit construction of the classifier based on Bayes' theorem and the direct estimation of the classifier's parameters, without relying on gradient descent.

[0036] In the following description, we will propose a method for estimating the parameters of the classifier during the training process (e.g., in equations (6) and / or (7)). and The method described above involves assuming a vMF distribution, where parameters can be estimated using maximum likelihood estimation (MLE). However, during the early stages of training, the random distribution of features can lead to unstable optimization of the classifier. To address this issue, maximum a posteriori (MAP) estimation can be employed, incorporating the prior distribution of the parameter estimation.

[0037] As an example, suppose a unit hypersphere A series of vector These are independent and identically distributed (i.e., iid) observations from the vMF distribution. The prior distribution of the classifier's parameters (e.g., equations (6) and / or (7)) can be defined as: Equation (8) in, These are the parameters of the prior distribution, and It is an unknown normalization constant.

[0038] Given , and The posterior distribution can take the following form: Equation (9) in, and Assuming a unit hypersphere A series of vector These are independent and identically distributed (i.e., iid) observations from the vMF distribution. The average orientation of the classifier. and concentration (For example, the maximum a posteriori (MAP) estimates of equations (6) and / or (7) can satisfy the following equations: Equation (10) Based on MAP estimation, A simple approximation can be given as: Equation (11) Furthermore, the sample mean for each category can be estimated as follows: Equation (12) in, Indicate steps Category of place The estimated sample mean, and Indicates the categories in the current mini-batch. The sample mean. and These represent the number of samples in the previous mini-batch and the current mini-batch, respectively.

[0039] As shown in equation (12), the calculation of the sample mean for each category only requires obtaining the input by aggregating the statistics from the current mini-batch. The first-order momentum of the corresponding embedded vector can be efficiently computed online across various mini-batches (or batches) during the training process, making our method computationally simple and efficient.

[0040] Furthermore, parameters of the prior distribution, such as those derived from the MAP estimation of the vMF distribution, can be interpreted from the perspective of spurious observations (e.g., For example, parameters and These can represent the direction and length of the pseudo-observation, respectively. Parameters This can represent the number of spurious observations. This understanding can help in choosing appropriate hyperparameters for the prior distribution.

[0041] Figure 1An exemplary workflow for a classification method according to one or more aspects of this disclosure is shown. Method 100 can be performed during training. At step 110, corresponding features for a set of inputs can be obtained, such as by using a backbone feature extractor (e.g., ResNet-32, ResNet-50, etc.). For example, the set of inputs can be mini-batch (or batch) samples from a dataset. The dataset can have a long-tailed distribution, for example, with an imbalance factor. Imbalance factor It can be defined as (in Indicates category The number of samples in the dataset is used to measure the degree of imbalance in the dataset.

[0042] At step 120, parameters with average direction and concentration (e.g., from equation (4)) can be used. and The corresponding features are represented by the von Mises-Fisher (vMF) distribution.

[0043] In step 130, a classifier can be obtained by using the vFM distribution according to Bayes' theorem, for example, by constructing or modeling the optimal Bayesian decision process as equation (6) or equation (7).

[0044] In step 140, based on this set of inputs, the classifier can be optimized by estimating the parameters of the vMF distribution of the features using maximum a posteriori (MAP) estimation, for example, as shown in equations (9), (10), (11) and (12).

[0045] In the example, optimizing the classifier could include estimating the mean direction and concentration values ​​for each class. For instance, it could be calculated for each class. of and The estimated values ​​(e.g., as shown in equation (6) and / or equation (7)).

[0046] For example, the parameter settings for the prior distribution can be configured for each category. set up This forms a simplex isotropic tight frame (ETF). Then, the ETF can be constructed, and the corresponding ETFs for each class can be obtained as follows. : Equation (13) in, Feature Dimension , It is a partially orthogonal matrix. yes The identity matrix, and It is 1. Dimensional vector. When At that time, we can calculate based on the "targeted supervised contrastive learning for long-tail recognition" proposed by Li et al. at CVPR (2022). .

[0047] In the example, to improve stability during the initial phase of training, gradient updates can be used to compute the parameters of the prior distribution. .

[0048] In the example, to improve stability during the initial training phase, optimization of the classifier can be performed jointly with a logit adjustment (LA) classifier. For example, the loss function can be weighted and summed, and the total loss function can be given as follows: Equation (14) in, This represents the weights of the LA classifier.

[0049] In the examples, the classifier proposed in this paper (e.g., as shown in Equations (6) and (7)) is compatible with most existing long-tail learning algorithms. For example, these existing long-tail learning algorithms can be designed primarily on the principle of implicitly estimating Bayesian posterior probabilities and can contribute to stable convergence at earlier learning stages, while the classifier proposed in this paper, based on explicitly modeling the Bayesian decision process, can significantly improve the final generalization performance. In other words, the gain attributable to explicitly modeling the Bayesian decision process by explicitly estimating the data distribution through the classifier proposed in this paper can be orthogonal to existing methods. Therefore, the classifier and / or method proposed in this paper can be implemented on top of existing methods to improve performance.

[0050] For example, in equation (14) It can be replaced by any existing long-tail learning algorithm.

[0051] Figure 2 A schematic diagram illustrating a comparison between an LA classifier based on one or more aspects of this disclosure and a classifier proposed herein. Figure 2 In the diagram, the left axis shows the concentration 210 value within the proposed classifier, the horizontal axis represents the class index, and the right axis shows the norm 220 value calculated from the LA classifier (e.g., the product of the weight norm and the feature norm). Figure 2It can be observed that the LA classifier is biased and produces a norm that is strongly correlated with the class frequency, while the classifier proposed in this paper can effectively overcome this imbalance and focus on the learning essence rather than the frequency of each class, thus resulting in frequency-independent concentration.

[0052] Figure 3 An exemplary workflow for a classification method according to one or more aspects of this disclosure is shown. Method 300 can be performed during testing or inference. In step 310, the optimized classifier according to method 100 can be adjusted. The distributions of training and test data can often differ due to the finite size of the data in practice. For example, the test dataset can exhibit arbitrary imbalance factors, which may differ from the imbalance factors of the training dataset. This difference may mean that a classifier trained on the training dataset may not deliver optimal performance when applied to the test dataset. To better adapt to the test data, the concentration value within the optimized classifier of method 100 can be adjusted to have the same value for all classes. For example, as Figure 2 As shown, the concentration parameter can have similar values ​​across different categories, and when there may be no prior information available for the conditional distribution of the test data. In this case, a reasonable assumption could be that the concentration values ​​for each category are equal. The adjusted classifier can be expressed as: Equation (15) or Equation (16) in, This represents the frequency of the categories in the test dataset.

[0053] At step 320, an adjusted classifier can be used to predict the category of the input image.

[0054] As shown in Table 1, this adjustment can significantly improve performance without incurring any additional costs.

[0055] Table 1

[0056] Where √ indicates that we performed adjustments during this phase, majority represents a sufficient sample class with more than 100 images, moderate represents a moderate sample class with 20 to 100 images, and minority represents a minority sample class with fewer than 20 images. The dataset is from CIFAR-100-LT. Adjustments in the LA classifier can involve normalization of both weights and features, and we also compare it with an unadjusted version of our proposed method.

[0057] For example, an optimized or trained classifier can be deployed in various environments to make predictions to control or guide corresponding operations in a specific environment. In an exemplary application scenario, an optimized classifier with adjusted parameters can be provided with data from sensors as input (e.g., images captured by a vision sensor) and output data or signals to control actuators or actuators to perform corresponding actions (such as slowing down in response to the pedestrian category).

[0058] Figure 4 An exemplary framework for a classification method according to one or more aspects of this disclosure is shown. Framework 400 may include a neural network 420, which may include a backbone network 422 for feature extraction and a classifier 424 proposed herein (e.g., as shown in Equation (6) or Equation (7)). During the training process, mini-batches (or batches) from the dataset may be provided as input 410 to the neural network 420, and the output of the neural network 420 may be passed to a loss function 430 (e.g., as shown in Equation (6)). The parameters of neural network 420 (e.g., the weights of backbone network 422) are updated until convergence. For example, the parameters of the proposed classifier 424 can be updated by aggregating statistics from the current mini-batch during forward propagation, and the parameters of backbone network 422 can be updated during backpropagation.

[0059] In one aspect of this disclosure, regarding the parameters of the prior distribution within classifier 424 and (which can represent the number and length of pseudo-observations, respectively), and associate them with each category Setting the sample size proportionally is reasonable. Following this idea, the new hyperparameter can be defined as... , In order to and After selecting an appropriate value, for example All can be calculated accordingly. and .

[0060] Figure 5 Another exemplary framework for a classification method according to one or more aspects of this disclosure is shown. Framework 500 may be similar to framework 400, except that it includes an additional classifier 426 (e.g., an LA classifier) ​​that can share a common backbone network 422 with classifier 424, and the loss function 430 may have the form of equation (14). For example, to reduce coupling between the two classifiers during optimization, a projection head may be used for classifier 422. One view and two views of the input image may be generated separately for the LA classifier and the classifier proposed herein.

[0061] In the example, the weights of loss function 430 can be set to 1, i.e. This allows for the allocation of equal control weights to the two classifiers during optimization. In another example, the two classifiers can be assigned unequal weights during optimization, i.e. .

[0062] To further demonstrate the advantages of this disclosure, experimental results are presented in Table 2 below.

[0063] Table 2

[0064] Among them, CB-Focal refers to the "Class Balance Loss Based on Effective Sample Count" proposed by Yin Cui et al. at CVPR (2019); LDLM-DRW refers to the "Learning Imbalanced Datasets Through Label Distribution-Aware Boundary Loss" proposed by Kaidi Cao et al. at NeurIPS (2019); BBN refers to the "BBN: A Two-Branch Network with Cumulative Learning for Long-Tail Visual Recognition" proposed by Boyan Zhou et al. at CVPR (2020); SSP refers to the "Thinking About Label Values ​​for Improving Class Imbalanced Learning" proposed by Yuzhe Yang et al. at NeurIPS (2020); VS refers to the "Label Imbalance and Group Sensitive Classification under Hyperparameterization" proposed by Ganesh Ramachandra Kini et al. at NeurIPS (2021); TSC refers to the "Nested Collaborative Learning for Long-Tail Visual Recognition" proposed by Jun Li et al. at CVPR (2022); and Casual Model refers to the "Casual Model" proposed by Kaihua Tang et al. at NeurIPS (2022). The method proposed in (2020) is "Long-tail classification by maintaining good and removing bad momentum causality effects"; CDT refers to "Identifying and compensating for feature bias in imbalanced deep learning" proposed by Han-Jia Ye et al. in the arXiv preprint (2020); ETF classifier refers to "Do we really need a learnable classifier at the end of a deep neural network?" proposed by Yibo Yang et al. in NeurIPS (2022); LADE refers to the decoupled label distribution for long-tail visual recognition proposed by Youngkyu Hong et al. in CVPR (2021); MetaSAug-LDAM refers to "MetaSAug: Metasemantic Augmentation for Long-tail Visual Recognition" proposed by Shuang Li et al. in CVPR (2021); GCL refers to "Long-tail visual recognition adjusted by Gaussian fuzz logit" proposed by Yang LuMengke Li et al. in CVPR (2022); LogitAdj refers to "Long-tail learning adjusted by logit" proposed by Aditya Krishna Menon et al. in ICLR (2021); and the method in this paper adopts the following... Figure 5 The frame shown.

[0065] Figure 6 Examples of hardware implementations of device 600 according to one or more aspects of this disclosure are shown. Device 600 for classification may include memory 610 and at least one processor 620. Processor 620 may be coupled to memory 610 and configured to implement the above-referenced... Figure 1 , 3Methods 100, 300 and / or frameworks 400, 500 are described in sections 4 and 5. Processor 620 may be a general-purpose processor or may be implemented as a combination of computing devices, such as a combination of a DSP and a microprocessor, multiple microprocessors, one or more microprocessors combined with a DSP core, or any other such configuration. Memory 610 may store input data, output data, data generated and / or processed by processor 620 (e.g., parameters of a classifier), and / or instructions executed by processor 620.

[0066] The various operations, models, and networks described in conjunction with this disclosure can be implemented in hardware, software executed by a processor, firmware, or any combination thereof. According to embodiments of this disclosure, computer program products used for classification may include those for implementing the above-described embodiments. Figure 1 , 3 The processor-executable computer code of methods 100, 300 and / or frameworks 400, 500 described in 4 and 5. According to another embodiment of this disclosure, a computer-readable medium may store computer code for classification, which, when executed by a processor, enables the processor to implement the above-described methods. Figure 1 , 3 Methods 100, 300 and / or frameworks 400, 500 described in 4 and 5. A computer-readable medium includes both non-transitory computer storage media and communication media, wherein the communication media includes any medium that facilitates the transfer of a computer program from one place to another. Any connection may be appropriately referred to as a computer-readable medium. Other embodiments and implementations are within the scope of this disclosure.

[0067] A prior description of the disclosed embodiments is provided to enable those skilled in the art to implement or use various embodiments. Those skilled in the art will readily understand various modifications to these embodiments and can apply the general principles defined herein to other embodiments without departing from the scope of the various embodiments. Therefore, the claims are not intended to limit them to the embodiments shown herein, but are consistent with the widest scope consistent with the appended claims and the principles and novel features disclosed herein.

Claims

1. A computer-implemented method for classification, comprising: To obtain features for a set of inputs; The features are represented using the von Mises Fisher (vMF) distribution; A classifier is obtained by applying the vFM distribution according to Bayes' theorem, wherein the features are the inputs to the classifier; and Based on the set of inputs, the classifier is optimized by estimating the parameters of the vMF distribution of the features using maximum a posteriori (MAP) estimation.

2. The computer-implemented method according to claim 1, wherein, The parameters of the vMF distribution of the feature include the mean direction and concentration.

3. The computer-implemented method according to claim 2, wherein, Optimizing the classifier by estimating the parameters of the vMF distribution of the features includes: Estimate the average orientation and concentration values ​​for each category.

4. The computer-implemented method according to claim 1, wherein, Optimizing the classifier by estimating the parameters of the vMF distribution of the features includes: Calculate the first-order momentum of the features for the set of inputs.

5. The computer-implemented method according to claim 3, further comprising: In order to predict the category of the input using the optimized classifier, the value of the concentration for each category of the optimized classifier is adjusted to the same value.

6. The computer-implemented method according to claim 1, wherein, The optimization of the classifier is performed in conjunction with a logit adjustment (LA) classifier.

7. The computer-implemented method according to claim 5, wherein, The predicted category is used to control the actuator to perform operations according to the category.

8. A computer-implemented method for classification, comprising: Obtain features for a set of images; The features are represented using the von Mises Fisher (vMF) distribution; A classifier is obtained by applying the vFM distribution according to Bayes' theorem, wherein the features are the inputs to the classifier; and Based on the set of images, the classifier is optimized by estimating the parameters of the vMF distribution of the features using maximum a posteriori (MAP) estimation. The optimized classifier is used to classify images into categories.

9. An apparatus for sorting, comprising: Memory; as well as At least one processor coupled to the memory and configured to perform the method according to any one of claims 1-7.

10. A computer program product for classification, comprising: A processor for performing the method according to any one of claims 1-7 may execute computer code.

11. A computer-readable medium storing computer code for classification, said computer code, when executed by a processor, causing the processor to perform the method according to any one of claims 1-7.

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