Open set identification decision method based on extreme value Copula joint model

Abstract

The invention discloses an open set identification decision-making method based on an extreme value Copula joint model. The method comprises the following implementation steps: firstly, extracting training sample features through a deep neural network, forming a known category compact cluster and determining a center; calculating the distance from each training sample to the center of each cluster, and fitting generalized extreme value distribution for each known category as edge distribution; secondly, introducing an extreme value Copula function, constructing a multivariate joint extreme value distribution model in combination with a plurality of edge distributions, and depicting an extreme value distance dependent structure between clusters; and finally, calculating a new sample joint extremum probability based on the model, and setting a threshold to judge whether the new sample joint extremum probability is a known or open set unknown category. According to the method, the multi-edge distribution and cluster dependency relationship is unified, the traditional'tail independence 'constraint is broken through, the feature space geometrical relationship is quantified, and the accuracy, interpretability and robustness of open set recognition are remarkably improved.

Description

Technical Field

[0001] This invention relates to the field of open set recognition in pattern recognition, and specifically to an open set recognition decision method based on the extreme value Copula joint model. Background Technology

[0002] Open set recognition (OSR) is an important branch of pattern recognition, requiring models to not only accurately classify samples from known, pre-trained classes but also effectively identify samples from unknown classes. With the development of deep learning, deep feature-based methods have become the mainstream of OSR. Among these, prototype-based methods are particularly prominent. Their core idea is to learn a prototype center for each known class in the feature space and use the distance from sample features to each prototype center to measure the probability that a sample belongs to that class. Although these methods have achieved some success by optimizing the feature space, reducing intra-class distances and increasing inter-class distances, they still have inherent drawbacks: after model optimization, the location of the prototype center is often not the true geometric center of the feature cluster, and may even be located outside the cluster, which undoubtedly affects the reliability of distance-based probability measures.

[0003] To overcome the aforementioned problems, extremum theory was introduced into OSR. This theory treats unknown samples in the feature space as extremum events, thereby introducing a generalized extremum distribution (GEV) to model the distribution of sample distances and determine classification probabilities. In the academic paper "Towards Open Set Deep Networks" published by Bendale A and Boult TE (see 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 1563-1572, doi:10.1109 / CVPR.2016.173), a pioneering OSR scheme based on extremum theory was disclosed. The core of this scheme is: first, before the output layer (usually a Softmax layer) of the deep network, the class mean vector of each known class is computed; then, the distance from each training sample to its true class mean is computed, and based on the distance distribution of all samples,

[0004] This method fits a unified Weibull distribution (a generalized extreme value distribution) to the entire model to model the tail probability of the distance a sample should have to a known class. Finally, during testing, the probability of a sample's feature distance to each class mean within this Weibull distribution is used to determine if it belongs to an unknown class. The problem is that this method is based on theories such as the feature space extreme value convergence theorem, and its core assumption is that clusters of different classes in the feature space are independent, thus allowing for independent extreme value analysis of each cluster. This strong independence assumption (i.e., "tail independence") is often difficult to hold in complex real-world feature spaces. Different class clusters in the feature space may have complex geometric relationships and dependencies. Ignoring this joint distribution characteristic and performing isolated extreme value analysis leads to inaccurate assessments of the openness of unknown samples, thus limiting further improvements in model performance.

[0005] While the framework based on the feature space extreme value convergence theorem provides a new approach, its strong assumption of cluster independence constitutes a major bottleneck, and overcoming this bottleneck has become an urgent problem to be solved. Summary of the Invention

[0006] This invention provides an open set identification decision method based on the extreme value Copula joint model, which overcomes the problem that existing technologies perform isolated extreme value analysis, resulting in inaccurate assessment of the openness of unknown samples.

[0007] To achieve the objectives of this invention, the proposed technical solution is: an open set identification decision method based on the extreme value Copula joint model, comprising the following steps:

[0008] Step 1, Feature Extraction and Cluster Formation: Obtain a training sample set containing N known categories; extract its feature vectors through a deep neural network; map the feature vectors to the feature space to form multiple compact clusters corresponding to the known categories, and determine the center of each cluster;

[0009] Step 2, Extreme Value Distance Calculation and GEV Fitting: For each sample in the training set, calculate the distance from the sample to the center of all known class clusters, and based on the distance distribution from all training samples to each cluster center, fit a generalized extreme value distribution (GEV) as the marginal distribution function for each known class.

[0010] Step 3: Construction of the multivariate joint extreme value distribution model: Calculate the probability value of each sample corresponding to each class; use the maximum likelihood estimation method to solve for the estimated value of the dependent structure parameter θ of the extreme value Copula function. And based on the N generalized extreme value distributions and marginal distributions G1,…,G obtained in step two NUsing the extremum Copula function Construct the multivariate joint extreme value distribution function H, whose expression is:

[0011]

[0012] Where N is the total number of known categories, D i G represents the extreme distance from the test sample to the i-th known class center, i = 1, ..., N. i Let be the generalized extreme value distribution function of the i-th known category; The parameter is The extreme values ​​of the Copula function, These are the parameter estimates obtained by the maximum likelihood estimation method.

[0013] Step 4, Open Set Identification Decision: For the test sample x′ to be identified, calculate the probability that the test sample x′ belongs to the joint distribution of known categories using the probability function; calculate the conditional probability that the test sample x′ belongs to the k-th known category using the conditional probability function; and make an open set identification decision based on the decision function.

[0014] Furthermore, in step four above, the probability function is:

[0015] P(x′∈F k )=1-H(D1,…,D N )

[0016] Furthermore, in step four above, the conditional probability function is:

[0017]

[0018] Where k is the index of the known category, k∈{1,…,N}, N is the total number of known categories, and D k G is the extreme distance from the test sample x′ to the k-th known class center. k Let be the generalized extreme value distribution function of the k-th known category.

[0019] Furthermore, the decision function formula in step four above is as follows:

[0020]

[0021] in The preset threshold is used, and N+1 represents the label of an unknown category;

[0022] If the probability P(x′∈F) that the test sample x′ belongs to the joint distribution of the k-th known class is greater than or equal to a preset threshold Then it is divided into groups that make the conditional probability P(x′∈F) k |D1,…,DN The known category corresponding to the maximum value;

[0023] If the probability P(x′∈F) is less than a preset threshold Then the sample is determined to belong to the unknown category.

[0024] Compared with the prior art, the present invention has the following beneficial effects:

[0025] 1. This invention introduces the Copula function to construct a joint model that unifies the dependencies between multiple marginal distributions and clusters. It breaks through the strong constraint assumption of "tail independence" in the traditional feature space extreme value convergence theorem, and realizes effective modeling of the extreme value distance correlation between multiple known category clusters in the feature space, thereby more realistically reflecting the complex data distribution structure.

[0026] 2. This invention unifies the dependency between multiple marginal distributions and clusters through the extreme value Copula parameter θ. The key is that parameter θ can be automatically learned from the data, allowing the framework to adaptively adjust the decision boundary without pre-setting complex decision rules. This flexibility significantly reduces the dependence on hyperparameter settings and enhances the model's generalization ability and robustness when facing different data distributions.

[0027] 3. This invention improves the accuracy of open set identification by quantifying the correlation between different clusters in the feature space, thereby overcoming the strong assumption of their mutual independence. The provided unified probabilistic framework can clearly quantify the multidimensional geometric relationship between test samples and known category clusters in the feature space, providing a reliable basis for open set identification decisions that combines high accuracy, strong robustness, and good interpretability. Attached Figure Description

[0028] Figure 1 This is a flowchart provided in an embodiment of the present invention. Detailed Implementation

[0029] The present invention will be further described in detail below with reference to specific embodiments. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0030] The design concept of this invention is as follows: First, feature representations of training samples are extracted using a deep neural network, and multiple compact clusters of known categories are formed in the feature space, with the center of each cluster determined. Then, for each sample in the training set, the distance to the center of all known category clusters is calculated, and based on the distribution of distances from all training samples to each cluster center, a generalized extreme value distribution is fitted as a marginal distribution function for each known category. Subsequently, an extreme value Copula function is introduced as a connection function to unite the marginals of the multiple independent generalized extreme value distributions, constructing a unified multivariate joint extreme value distribution model, thereby accurately characterizing the interdependent structure of extreme value distances between known category clusters. Finally, the joint extreme value probability of a new sample is calculated based on this joint model, and a decision threshold is set accordingly to determine whether the sample belongs to a known category or an unknown open set category.

[0031] Example: This example aims to illustrate in detail the specific implementation of the present invention. See also... Figure 1 An open set identification decision method based on the extreme value Copula joint model includes the following steps:

[0032] Step 1: Feature Extraction and Cluster Formation

[0033] 1.1 Obtain a training sample set containing multiple known categories.

[0034] 1.2. A pre-trained deep neural network is used as the feature extraction function Θ(·). All training sample sets of known categories are input into the network to extract their feature vectors.

[0035] 1.3 Map the feature vectors to the feature space to form multiple compact clusters corresponding to the known categories, forming N compact clusters of known categories in the feature space; calculate the mean of the feature vectors of all training samples under each known category, and use the mean point as the center of each cluster.

[0036] Step 2: Extreme value distance calculation and GEV fitting:

[0037] 2.1 For each sample x in the training sample set i Its mapping feature is z i =Θ(x i ). Calculate z i Distances to all known cluster centers. Distance calculation uses Mahalanobis distance; specifically, for the k-th class center u... k (where k = 1, ..., N), and D is the distance D from the sample to the cluster center. k (z i The calculation is as follows:

[0038]

[0039] 2.2 For each known category k (k = 1, ..., N), collect the distance data from all training samples to the kth cluster center, i.e., construct the distance dataset D. k ={D k (z1),…,D k (z M )}, where M is the total number of training samples. Maximum likelihood estimation is used to estimate the distance to the dataset D for each known class. k By fitting a generalized extremum distribution (GEV), the marginal distribution function G of this class is obtained. k (D k ;α k ,β k ,γ k ).

[0040] Step 3: Construction of the multivariate joint extreme value distribution model:

[0041] 3.1. The feature vector z of each training sample is obtained. i and its distance D from the center of each category k (z i Substitute it into its corresponding GEV distribution G k The probability value of each sample i corresponding to each category k is calculated. Where i is the sample index.

[0042] 3.2. The maximum likelihood estimation method is used to obtain the estimated values ​​of the dependent structure parameter θ. Based on the probability value obtained in step 3.1 Solve for the estimated value Specifically, this is achieved through the following four sub-steps:

[0043] 3.2.1, By analyzing the extreme value of the Copula function C θ For all its variables u1,…,u N Taking the partial derivative, we obtain the density function c of the copula. θ Its expression is:

[0044]

[0045] 3.2.2, through the density function c θ Construct a likelihood function L(θ) with respect to the parameter θ using the probability vector of all training samples:

[0046]

[0047] 3.2.3 Constructing the log-likelihood function l(θ):

[0048]

[0049] 3.2.4. Using the maximum likelihood estimation method, the estimated value of the dependent structure parameter θ is obtained by solving the following optimization problem.

[0050]

[0051] 3.3 Constructing the multivariate joint extreme value distribution function H: After obtaining the estimated values ​​of the dependent structure parameters... Afterwards, by The N marginal distribution functions G1,…,G obtained in step two N Substitute them together into the selected extremum Copula function The final multivariate joint extremum distribution function H is constructed, and its expression is:

[0052]

[0053] Where N is the total number of known categories, D i G represents the extreme distance from the test sample to the i-th known class center, i = 1, ..., N. i Let be the generalized extreme value distribution function of the i-th known category; The parameter is The extreme values ​​of the Copula function, These are the parameter estimates obtained by the maximum likelihood estimation method.

[0054] Step 4: Open Set Identification Decision:

[0055] 4.1 For a test sample x′ to be identified, perform the following operations to calculate the probability that the test sample x′ belongs to the joint distribution of known classes:

[0056] 4.1.1 Extract the test sample features z′=Θ(x′), and calculate the extreme distances D1,...,D from z′ to the N known class centers. N .

[0057] 4.1.2. Calculate the distance vector D1,…,D N Given the joint distribution function H, calculate the probability that the sample belongs to the joint distribution of the known classes. Its expression is:

[0058] P(x'∈F k )=1-H(D1,…,D N ).

[0059] 4.2 Simultaneously, using the joint distribution H and the marginal distribution G... k and parameters According to Bayes' theorem, we can calculate whether the test sample x′ belongs to the k-th known category F given the distance information. kThe conditional probability of . Its expression is:

[0060]

[0061] One of the core aspects of this invention lies in the parameters of the extreme value Copula. By learning the inter-category dependencies, decision preferences are adaptively adjusted. This adjustment is directly reflected in the conditional probability formula:

[0062] When the estimated value When -ln G in the formula k (D k powers of ) At this point, the distance D to the center of a certain category k The larger the value, the more amplified the conditional probability will be. Therefore, when the model makes decisions within a known range of categories, it will tend to classify samples into the category furthest away. This approach can effectively handle complex scenarios with moderate overlap in feature spaces.

[0063] When the estimated value When, power At this time, the distance from D k The smaller the value, the higher the conditional probability. Therefore, the model tends to classify samples into the nearest class. This approach is suitable for scenarios with good class discrimination and clear decision boundaries.

[0064] When the estimated value When the condition is equal, the formula degenerates into a uniformly weighted formula, where the conditional probabilities of all categories are equal.

[0065] In summary, this adjustment allows the model to flexibly adapt to different data distribution characteristics, thereby significantly improving the accuracy and robustness of open set identification.

[0066] 4.3 Execute open set identification decision:

[0067] Set a decision threshold for open set identification in The final decision function is:

[0068]

[0069] If the probability that the test sample belongs to the joint distribution of known categories is greater than or equal to a preset threshold, then it is classified into categories such that the conditional probability P(x′∈F) is greater than or equal to a preset threshold. k |D1,…,D N The known category corresponding to the maximum value; if the probability is less than a preset threshold. Then the sample is determined to belong to the unknown category.

[0070] The beneficial effects of the present invention will be verified and explained through simulation experiments below.

[0071] 1. Simulation conditions

[0072] The hardware platform for the simulation experiment in this embodiment is:

[0073] Processor: Intel(R) Core(TM) i9-10980XE, clock speed 3.00GHz, memory 256GB.

[0074] The software platform for the simulation experiment in this embodiment is: Ubuntu 20.04 operating system and Python 3.9.

[0075] 2. Dataset and Experiment Setup

[0076] To fully verify the effectiveness of this invention, the simulation experiments were conducted on several recognized standard datasets, including SVHN, CIFAR10, and TinyImageNet. The specific settings are as follows:

[0077] Known and unknown class classification: In the SVHN and CIFAR10 datasets, 6 classes were randomly selected as known classes, and the remaining 4 classes were designated as unknown classes. In the TinyImageNet dataset, 20 classes were randomly selected as known classes, and the remaining 180 classes were designated as unknown classes.

[0078] Comparison method: This invention is compared with several cutting-edge OSR methods such as SoftMax, GCPL, RPL, ARPL, and RAD. The implementation of this invention is marked with "+P" in the figure.

[0079] Evaluation metrics: The area under the receiver operating characteristic curve (AUROC) is used to evaluate the model's ability to distinguish unknown samples, and the open-set classification rate (OSCR) is used to comprehensively evaluate the model's overall recognition performance for known and unknown classes.

[0080] 3. Simulation Result Analysis

[0081] The overall performance comparison results on the standard OSR task are shown in the table below. The data shows that the proposed extreme value Copula joint model, when combined with various advanced feature extraction methods, achieves significant improvements on the dataset.

[0082]

[0083] In summary, the method of this invention shows a significant performance improvement compared to the baseline model, fully demonstrating its powerful ability and robustness in dealing with complex open environments, accurately identifying unknown categories, and classifying known categories.

[0084] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications made within the spirit and principles of the present invention are permitted.

[0085] Any modifications, equivalent substitutions, improvements, etc., made should be included within the scope of protection of this invention.

Claims

1. An open set identification and decision-making method based on the extreme value Copula joint model, characterized in that, Includes the following steps: Step 1, Feature Extraction and Clustering: Obtain a training sample set containing N known categories; extract its feature vectors using a deep neural network; The feature vectors are mapped to the feature space to form multiple compact clusters corresponding to the known categories, and the center of each cluster is determined. Step 2, Extreme Value Distance Calculation and GEV Fitting: For each sample in the training set, calculate the distance from the sample to the center of all known class clusters, and based on the distance distribution from all training samples to each cluster center, fit a generalized extreme value distribution (GEV) as the marginal distribution function for each known class. Step 3: Construction of the multivariate joint extreme value distribution model: Calculate the probability value of each sample corresponding to each class; use the maximum likelihood estimation method to solve for the estimated value of the dependent structure parameter θ of the extreme value Copula function. And based on the N generalized extreme value distributions and marginal distributions G1,…,G obtained in step two N Using the extremum Copula function Construct the multivariate joint extreme value distribution function H, whose expression is: Where N is the total number of known categories, D i G represents the extreme distance from the test sample to the i-th known class center, i = 1, ..., N. i Let be the generalized extreme value distribution function of the i-th known category; The parameter is The extreme values ​​of the Copula function, These are the parameter estimates obtained by the maximum likelihood estimation method. Step 4, Open Set Identification Decision: For the test sample x′ to be identified, calculate the probability that the test sample x′ belongs to the joint distribution of known categories using the probability function; calculate the conditional probability that the test sample x′ belongs to the k-th known category using the conditional probability function; and make an open set identification decision based on the decision function.

2. The method according to claim 1, characterized in that, In step four, the probability function is: P(x′∈F k )=1-H(D1,…,D N ) 3. The method according to claim 1, characterized in that, In step four, the conditional probability function is: Where k is the index of the known category, k∈{1,…,N}, N is the total number of known categories, and D k G is the extreme distance from the test sample x′ to the k-th known class center. k Let be the generalized extreme value distribution function of the k-th known category.

4. The method according to claim 1, characterized in that, The decision function formula in step four is as follows: in The preset threshold is used, and N+1 represents the label of an unknown category; If the probability P(x′∈F) that the test sample x′ belongs to the joint distribution of the k-th known class is greater than or equal to a preset threshold Then it is divided into groups that make the conditional probability P(x′∈F) k |D1,…,D N The known category corresponding to the maximum value; If the probability P(x′∈F) is less than a preset threshold Then the sample is determined to belong to the unknown category.

Images