CN111814894A - A Multi-View Semi-Supervised Classification Method Based on Fast Seed Random Walk - Google Patents

Abstract

The invention relates to a multi-view semi-supervised classification method for fast seed random walk. First, a Gaussian kernel function is used to calculate the similarity matrix and transition probability matrix of each view of the input multi-view data; The learned class labels of the multi-view data establish the initial distribution state of each view of the multi-view data and calculate the arrival probability matrix of the first transition state of each view of the multi-view data; finally, iteratively calculate the multi-view data. The arrival probability matrix of multiple transition states of each view, and the weighted summation of the arrival probability matrices of all transition states of each view to obtain the reward matrix of each view to generate the class label of the multi-view data for testing. The present invention can accurately and effectively classify various types of data such as images, texts, and videos by using only a small amount of supervision information, and has certain practical value.

Description

A Multi-View Semi-Supervised Classification Method Based on Fast Seed Random Walk

technical field

The invention relates to the field of multi-view and semi-supervised learning, in particular to a multi-view semi-supervised classification method with fast seed random walk.

Background technique

Multi-view data is extremely common in practical applications, such as multi-camera image collection and multi-modal information acquisition. Data collected from heterogeneous sources often contain a lot of redundant and irrelevant information, which may degrade the performance of learning algorithms. In multi-view data, each view captures partial information rather than complete information. The full representation is latent and redundant, making it difficult to extract useful information for the task to be learned. On the other hand, single-view learning or simple concatenation of all multi-view features is usually ineffective. Therefore, it is crucial to learn enough discriminative features and use multi-view-driven algorithms to mine effective information from these data.

In recent years, there have been breakthroughs in random walk theory. The classic algorithm called PageRank plays a vital role in web search, where all the importance of the web is ranked using the web link structure. After that, many personalized PageRank methods have been proposed to solve various learning tasks. Random walk with restart (RWR) is a representative scheme that provides a good correlation score between any two nodes in an undirected weighted graph. According to whether the class label information is available, random walks can be mainly divided into unsupervised methods and supervised methods. The former focuses on data clustering and solving unsupervised learning tasks, such as image segmentation, while the latter aims to solve classification tasks and their corresponding specific applications. These research works demonstrate the wide applicability and high compatibility of random walks in various practical applications.

Multi-view learning aims to mine useful patterns from multi-view data. Numerous previous studies have shown that multi-view learning can fully exploit the similarity and complementarity information in multi-view data, and has better generative ability and superior performance than single-view learning. As one of the earliest representative paradigms of multi-view learning, co-training in an unsupervised mode maximizes the mutual consistency between two different views. Later, ordinary unsupervised multi-view learning methods received more and more attention, including unsupervised multi-view feature representation and multi-view clustering. Correspondingly, supervised multi-view learning methods have also attracted increasing research interest from different fields, such as image classification, gesture recognition, and image annotation. However, labeling enough multi-view training data is difficult and time-consuming, while only a small number of labeled samples are readily available, only a small amount of data is not sufficient for fully supervised learning, and underutilized for unsupervised learning. As a compromise between the two learning paradigms, multi-view semi-supervised classification can leverage a limited proportion of labeled samples to improve performance. To this end, the academic community proposes multi-view semi-supervised learning to maximize the use of a small proportion of labeled data points to mine effective information. But so far, the work done on multi-view semi-supervised classification is still limited, and more research is needed for this problem.

The current multi-view semi-supervised learning algorithms are mainly divided into two categories. The first method is a subspace-based method, which usually embeds a given label matrix in the objective function as a common regression objective, and learns a latent low-dimensional subspace to project the input data to mine commonalities between viewpoints. For example, Nie et al. model a convex problem to avoid local minima and propose a new adaptive weight learning strategy to learn the projection matrix. Xue et al. introduced label information into deep matrix factorization and learned a relevant prediction subspace for incomplete multi-view data classification. The second mode is a graph-based model, which treats each data point as a vertex of a joint graph fused from multiple viewpoints and propagates label information from labeled to unlabeled samples through weighted edges. As an early graph-based method, Karasuyama proposed a multi-graph ensemble method in the context of label propagation, which learns sparse multi-view weights through weight regularization to linearly combine multiple graphs. In contrast, Nie et al. learn the weights from the prior graph structure to fuse multi-views instead of learning the fusion weights through weight regularization. Currently, a variety of multi-view semi-supervised learning methods have been developed and their effectiveness has been demonstrated in specific applications. However, multi-view semi-supervised classification is largely understudied, and these models still suffer from some flaws. High computational complexity is a major limitation that most algorithms need to address when faced with large-scale learning problems, so more work is required. Furthermore, limited learning performance requires algorithms to mine more efficient patterns when only a small amount of labeled data is available for model training. Therefore, more effective and efficient multi-view semi-supervised learning methods remain to be developed.

SUMMARY OF THE INVENTION

In view of this, the present invention proposes a multi-view semi-supervised classification method with fast seed random walk, which can accurately and effectively classify various types of data sets such as text, images, and videos, and only uses a small amount of supervision information. , has achieved high classification performance on each dataset, and has certain practical value.

The present invention adopts the following scheme to realize: a multi-view semi-supervised classification method of fast seed random walk, comprising the following steps:

Step S1: using a Gaussian kernel function to calculate the similarity matrix and transition probability matrix of each view of the input multi-view data;

Step S2: establishing the initial distribution state of each view of the multi-view data according to the category label of the multi-view data for semi-supervised learning;

Step S3: Calculate the arrival probability matrix of the first transition state of each view of the multi-view data according to the initial distribution state of each view of the multi-view data established in S2;

Step S4: iteratively calculate the arrival probability matrix of the multiple transition states of each view of the multi-view data and perform a weighted summation of the arrival probability matrices of all the transition states of each view to obtain the reward matrix of each view;

Step S5: Predict the category label of each multi-view data for testing according to the reward matrix of each view of the multi-view data calculated in S4.

Further, the step S1 specifically includes the following steps:

Step S11 : using the Gaussian kernel function to calculate the similarity matrix of each angle of view of the input multi-angle data, the calculation formula is:

为第t个视角下的第i个数据点，σ为带宽，控制高斯核函数的局部作用范围；where [W _t ] _ij is the similarity between the i-th and j-th data points under the t-th view,

is the i-th data point under the t-th viewing angle, and σ is the bandwidth, which controls the local scope of the Gaussian kernel function;

Step S12: Calculate the transition probability matrix of each view of the multi-view data, and the calculation formula is:

为对角矩阵，且

P^t为多视角数据的第t个视角的转移概率矩阵。in,

is a diagonal matrix, and

P ^t is the transition probability matrix of the t-th view of the multi-view data.

Further, according to the category label of the multi-view data used for semi-supervised learning in step S2, the initial distribution state of each view of the multi-view data is established, and the calculation formula is:

[Q ^t ] ⁽⁰⁾ = [Q ₀ , O],

为全0矩阵,

c为多视角数据的类别数目，N为多视角数据的总数目，n为用于半监督学习的多视角数据的数目，[Q^y]⁽⁰⁾为多视角数据第t个视角的起始分布状态，Q₀的计算公式如下：in,

is an all-zero matrix,

c is the number of categories of multi-view data, N is the total number of multi-view data, n is the number of multi-view data used for semi-supervised learning, [Q ^y ] ⁽⁰⁾ is the start of the t-th view of multi-view data Distribution state, the calculation formula of Q ₀ is as follows:

Among them, C _i is the ith category. If the jth data point x _j of the multi-view data belongs to the ith category C _i , the value of [Q ₀ ] _ij is 1, otherwise, it is 0.

Further, in step S3, the arrival probability matrix of the first transition state of each view of the multi-view data is calculated according to the initial distribution state of each view of the multi-view data established in S2, and the calculation formula is:

α为根据先验知识确定的重启概率，[Q^t]⁽¹⁾为多视角数据的第t个视角在起始分布状态下的第一次转移状态的到达概率矩阵。in

α is the restart probability determined according to prior knowledge, [Q ^t ] ⁽¹⁾ is the arrival probability matrix of the first transition state of the t-th view of the multi-view data in the initial distribution state.

Further, the step S4 specifically includes the following steps:

Step S41: Iteratively calculate the arrival probability matrix of the multiple transition states of each view of the multi-view data, and the calculation formula is as follows:

[Q ^t ] ^(k) = (1-α)[Q ^t ] ^(kl) P ^t +α[Q ^t ] ⁽⁰⁾ for k≥2,

Among them, [Q ^t ] ^(k) is the arrival probability matrix of the k-th transition state of the t-th view of the multi-view data;

Step S42: Weighted summation is performed on the arrival probability matrices of all transition states of each view of the multi-view data to obtain the reward matrix of each view, and the calculation formula is as follows:

Among them, J is the number of transition steps determined according to the prior knowledge, [R ^t ] ^(s) is the reward matrix of the t-th view of the multi-view data under the number of transition steps, and γ is determined according to the prior knowledge. decay factor.

Further, according to the reward matrix of each view of the multi-view data calculated in step S5, the category label of each multi-view data for testing is predicted according to the reward matrix of S4, and the specific calculation formula is as follows:

为第j个数据点的预测标签。where V is the number of viewing angles of the multi-view data,

is the predicted label for the jth data point.

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

The algorithm adopted in the present invention is based on random walk with restart probability, which can effectively explore the correlation between data points and capture the global structure information of the data set, and has a large performance improvement compared with other similar algorithms. The invention can accurately and effectively classify various types of data such as images, texts, and videos. In the experiment, eight public data sets in practical applications are classified, including data sets of text, image and video types. In the case of using only a small amount of supervision information, high classification performance has been achieved on each dataset, which has certain practical value.

Description of drawings

FIG. 1 is a flowchart of an embodiment of the present invention.

FIG. 2 is a flow chart of the implementation of the overall method according to an embodiment of the present invention.

Detailed ways

The present invention will be further described below with reference to the accompanying drawings and embodiments.

It should be noted that the following detailed description is exemplary and intended to provide further explanation of the application. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.

It should be noted that the terminology used herein is for the purpose of describing specific embodiments only, and is not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly dictates otherwise, the singular is intended to include the plural as well, furthermore, it is to be understood that when the terms "comprising" and/or "including" are used in this specification, it indicates that There are features, steps, operations, devices, components and/or combinations thereof.

As shown in Figures 1 and 2, this embodiment provides a multi-view semi-supervised classification method with fast seed random walk, including the following steps:

Step S1: using a Gaussian kernel function to calculate the similarity matrix and transition probability matrix of each view of the input multi-view data;

Step S2: establishing the initial distribution state of each view of the multi-view data according to the category label of the multi-view data for semi-supervised learning;

Step S3: Calculate the arrival probability matrix of the first transition state of each view of the multi-view data according to the initial distribution state of each view of the multi-view data established in S2;

Step S4: iteratively calculate the arrival probability matrix of the multiple transition states of each view of the multi-view data and perform a weighted summation of the arrival probability matrices of all the transition states of each view to obtain the reward matrix of each view;

Step S5: Predict the category label of each multi-view data for testing according to the reward matrix of each view of the multi-view data calculated in S4.

In this embodiment, the step S1 specifically includes the following steps:

Step S11 : using the Gaussian kernel function to calculate the similarity matrix of each angle of view of the input multi-angle data, the calculation formula is:

为第t个视角下的第i个数据点，σ为带宽，控制高斯核函数的局部作用范围；where [W _t ] _ij is the similarity between the i-th and j-th data points under the t-th view,

is the i-th data point under the t-th viewing angle, and σ is the bandwidth, which controls the local scope of the Gaussian kernel function;

Step S12: Calculate the transition probability matrix of each view of the multi-view data, and the calculation formula is:

为对角矩阵，且

P^t为多视角数据的第t个视角的转移概率矩阵。in,

is a diagonal matrix, and

P ^t is the transition probability matrix of the t-th view of the multi-view data.

In this embodiment, the initial distribution state of each view of the multi-view data is established according to the category label of the multi-view data used for semi-supervised learning in step S2, and the calculation formula is:

[Q ^t ] ⁽⁰⁾ = [Q ₀ , O],

为全0矩阵,

c为多视角数据的类别数目，N为多视角数据的总数目，n为用于半监督学习的多视角数据的数目，[Q^t]⁽⁰⁾为多视角数据第t个视角的起始分布状态，Q₀的计算公式如下：in,

is an all-zero matrix,

c is the number of categories of multi-view data, N is the total number of multi-view data, n is the number of multi-view data used for semi-supervised learning, [Q ^t ] ⁽⁰⁾ is the start of the t-th view of multi-view data Distribution state, the calculation formula of Q ₀ is as follows:

Among them, C _i is the ith category. If the jth data point x _j of the multi-view data belongs to the ith category C _i , the value of [Q ₀ ] _ij is 1, otherwise, it is 0.

In this embodiment, in step S3, the arrival probability matrix of the first transition state of each view of the multi-view data is calculated according to the initial distribution state of each view of the multi-view data established in S2, and the calculation formula is:

α为根据先验知识确定的重启概率，[Q^t]⁽¹⁾为多视角数据的第t个视角在起始分布状态下的第一次转移状态的到达概率矩阵。in

α is the restart probability determined according to prior knowledge, [Q ^t ] ⁽¹⁾ is the arrival probability matrix of the first transition state of the t-th view of the multi-view data in the initial distribution state.

In this embodiment, the step S4 specifically includes the following steps:

Step S41: Iteratively calculate the arrival probability matrix of the multiple transition states of each view of the multi-view data, and the calculation formula is as follows:

[Q ^t ] ^(k) = (1-α)[Q ^t ] ^(kl) P ^t +α[Q ^t ] ⁽⁰⁾ for k≥2,

Among them, [Q ^t ] ^(k) is the arrival probability matrix of the k-th transition state of the t-th view of the multi-view data;

Step S42: Weighted summation is performed on the arrival probability matrices of all transition states of each view of the multi-view data to obtain the reward matrix of each view, and the calculation formula is as follows:

Among them, J is the number of transition steps determined according to the prior knowledge, [R ^t ] ^(s) is the reward matrix of the t-th view of the multi-view data under the number of transition steps, and γ is determined according to the prior knowledge. decay factor.

In this embodiment, according to the reward matrix of each view of the multi-view data calculated in step S4, the category label of each multi-view data for testing is predicted according to the step S5, and the specific calculation formula is as follows:

为第j个数据点的预测标签。where V is the number of viewing angles of the multi-view data,

is the predicted label for the jth data point.

This embodiment starts from practical application. First, the Gaussian kernel function is used to calculate the similarity matrix and transition probability matrix of each view of the input multi-view data; The initial distribution state of each view of the view data and the arrival probability matrix of the first transition state of each view of the multi-view data are calculated; finally, the arrival of multiple transition states of each view of the multi-view data is iteratively calculated The probability matrix, and the weighted summation of the arrival probability matrix of all transition states of each view to obtain the reward matrix of each view to generate the class label for the multi-view data for testing. Based on the random walk with restart probability, this embodiment can effectively explore the correlation between data points and capture the global structure information of the data set, so as to accurately and effectively classify various types of data such as images, texts, and audios , has certain application value.

The above descriptions are only preferred embodiments of the present invention, and all equivalent changes and modifications made according to the scope of the patent application of the present invention shall fall within the scope of the present invention.

Claims (6)

1. a multi-view semi-supervised classification method of fast seed random walk, is characterized in that: comprise the following steps: Step S1: using a Gaussian kernel function to calculate the similarity matrix and transition probability matrix of each view of the input multi-view data; Step S2: establishing the initial distribution state of each view of the multi-view data according to the category label of the multi-view data for semi-supervised learning; Step S3: Calculate the arrival probability matrix of the first transition state of each view of the multi-view data according to the initial distribution state of each view of the multi-view data established in S2; Step S4: iteratively calculate the arrival probability matrix of the multiple transition states of each view of the multi-view data and perform a weighted summation of the arrival probability matrices of all the transition states of each view to obtain the reward matrix of each view; Step S5: Predict the category label of each multi-view data for testing according to the reward matrix of each view of the multi-view data calculated in S4. 2. the multi-view semi-supervised classification method of a kind of fast seed random walk according to claim 1, is characterized in that: described step S1 specifically comprises the following steps: Step S11 : using the Gaussian kernel function to calculate the similarity matrix of each angle of view of the input multi-angle data, the calculation formula is:

where [W _t ] _ij is the similarity between the i-th and j-th data points under the t-th view,

is the i-th data point under the t-th viewing angle, and σ is the bandwidth, which controls the local scope of the Gaussian kernel function; Step S12: Calculate the transition probability matrix of each view of the multi-view data, and the calculation formula is:

in,

is a diagonal matrix, and

P ^t is the transition probability matrix of the t-th view of the multi-view data. 3. The multi-view semi-supervised classification method of a kind of fast seed random walk according to claim 1, it is characterized in that: described in step S2, establish multi-view data according to the class label of multi-view data used for semi-supervised learning The initial distribution state of each viewing angle of , the calculation formula is: [Q ^t ] ⁽⁰⁾ = [Q ₀ , O], in,

is an all-zero matrix,

c is the number of categories of multi-view data, N is the total number of multi-view data, n is the number of multi-view data used for semi-supervised learning, [Q ^t ] ⁽⁰⁾ is the start of the t-th view of multi-view data Distribution state, the calculation formula of Q ₀ is as follows:

Among them, C _i is the ith category. If the jth data point x _j of the multi-view data belongs to the ith category C _i , the value of [Q ₀ ] _ij is 1, otherwise, it is 0. 4. the multi-view semi-supervised classification method of a kind of fast seed random walk according to claim 1, is characterized in that: the initial distribution state of each view of the multi-view data established according to S2 in step S3 is calculated The arrival probability matrix of the first transition state of each view of the multi-view data, the calculation formula is:

in

α is the restart probability determined according to prior knowledge, [Q ^t ] ⁽¹⁾ is the arrival probability matrix of the first transition state of the t-th view of the multi-view data in the initial distribution state. 5. the multi-view semi-supervised classification method of a kind of fast seed random walk according to claim 1, is characterized in that: described step S4 specifically comprises the following steps: Step S41: Iteratively calculate the arrival probability matrix of the multiple transition states of each view of the multi-view data, and the calculation formula is as follows: [Q ^t ] ^(k) = (1-α)[Q ^t ] ^(k-1) P ^t +α[Q ^t ] ⁽⁰⁾ for k≥2, Among them, [Q ^t ] ^(k) is the arrival probability matrix of the k-th transition state of the t-th view of the multi-view data; Step S42: Weighted summation is performed on the arrival probability matrices of all transition states of each view of the multi-view data to obtain the reward matrix of each view, and the calculation formula is as follows:

Among them, s is the number of transition steps determined according to prior knowledge, [R ^t ] ^(s) is the reward matrix of the t-th view of the multi-view data under the number of transition steps s, and γ is determined according to prior knowledge decay factor. 6. the multi-view semi-supervised classification method of a kind of fast seed random walk according to claim 1, is characterized in that: the reward matrix of each view of the multi-view data calculated according to S4 described in step S5 predicts every A category label for multi-view data used for testing. The specific calculation formula is as follows:

where V is the number of viewing angles of the multi-view data,

is the predicted label for the jth data point.

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