CN106485286B - Matrix classification model based on local sensitivity discrimination - Google Patents

Matrix classification model based on local sensitivity discrimination Download PDF

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CN106485286B
CN106485286B CN201610923346.8A CN201610923346A CN106485286B CN 106485286 B CN106485286 B CN 106485286B CN 201610923346 A CN201610923346 A CN 201610923346A CN 106485286 B CN106485286 B CN 106485286B
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王喆
李冬冬
张国威
高大启
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East China University of Science and Technology
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Abstract

The invention provides a matrix classification model based on local sensitivity discrimination, and the first isFirstly, collecting a data set, and converting collected samples into a matrix mode; second, using training set to construct sub-graph in and between local classes
Figure 100004_DEST_PATH_IMAGE001
And
Figure 100004_DEST_PATH_IMAGE002
use of
Figure 625505DEST_PATH_IMAGE001
And
Figure 815178DEST_PATH_IMAGE002
constructing regularization terms
Figure 100004_DEST_PATH_IMAGE003
Then regularizing the terms
Figure 100004_DEST_PATH_IMAGE004
Introducing a matrix-mode-oriented classifier MatMHKS to generate a new matrix-mode-oriented classification model LSDMatMHKS, training the LSDMatMHKS by using a training set, and solving the optimal solution of the model LADMatMHKS by using a gradient descent method; then, testing an optimal solution by using the test set, and obtaining an optimal decision function; and finally, calculating the input unknown matrix mode by using the obtained optimal decision function, and classifying the unknown matrix mode according to the output result. Compared with the traditional classification technology, the method and the device have the advantages that local sensitive discrimination information is introduced, so that local patterns of the same type are close to each other as much as possible, and local patterns of different types are far away from each other as much as possible, and therefore the classification stability and the model learning capacity are improved.

Description

Matrix classification model based on local sensitivity discrimination
Technical Field
The invention relates to the field of pattern recognition, in particular to a method for a matrix learning machine model based on local sensitivity discrimination.
Background
Different from the traditional vectorization-oriented classifier design method, the matrix-mode-oriented classifier design method is a method capable of directly classifying the matrixed samples. In an actual experiment, the matrix pattern-oriented classifier design method can effectively improve the performance of the vectorization-oriented classifier design method. The reason is mainly shown in three aspects: firstly, the design method of the matrix-oriented pattern classifier can capture more structural information in a single sample, and the matrixing method requires relatively less storage space on the storage space of one pattern; secondly, the design method of the matrix-oriented pattern classifier avoids the operation of converting a single sample into a vector-form sample, and avoids high computational complexity caused by overhigh dimension to a certain extent; third, experiments and theories show that the design method of the vectorization-oriented classifier can be regarded as a special case of the design method of the matrix-mode-oriented classifier, namely, the method for solving the design method of the matrix-mode-oriented classifier is also suitable for the vectorization method.
The Matrix pattern Classifier design method only considers minimizing empirical errors and reducing generalized errors of the models and ignores locally sensitive discrimination information between the models, wherein a more typical linear algorithm is MatMHKS (Matrix-pattern-oriented Ho-Kashyap Classifier). At present, no one has mentioned a relevant method in a matrix pattern classifier design method to solve the defect. To address this deficiency, we propose a new regularization term
Figure DEST_PATH_IMAGE001
And adding local sensitive discrimination information for the design of the matrix pattern classifier. The design method of the new regularization term comes from local Sensitive Discriminant Analysis (Locality Sensitive Discriminant Analysis). Local sensitive discriminant analysis can capture local discriminant information and local geometric structures. We exploit this advantage of locality sensitive discriminant analysis to design a new regularization term
Figure DEST_PATH_IMAGE002
And local sensitive discrimination information is introduced for matrixing classification design, so that a new model for the classifier design of a matrix mode is generated. According to the idea of local sensitive discriminant analysis, two non-overlapping weighted neighbor subgraphs are constructed
Figure DEST_PATH_IMAGE003
And
Figure DEST_PATH_IMAGE004
. Wherein
Figure 579617DEST_PATH_IMAGE003
Is from the local connection relationship between matrix patterns of the same type,
Figure 496757DEST_PATH_IMAGE004
is to reflect the local connection relationship between different types of matrix patterns. We define class subgraphs in matrix mode
Figure 276494DEST_PATH_IMAGE003
Is composed of
Figure DEST_PATH_IMAGE005
And subgraph between classes
Figure 609387DEST_PATH_IMAGE004
Is composed of
Figure DEST_PATH_IMAGE006
To characterize intra-class patterns as close as possible and inter-class patterns as far apart.
Handle
Figure 423759DEST_PATH_IMAGE002
Introduced into the double-edge matrix type classifier MatMHKS, thereby generating a new classification algorithm lsdmathmks. The LSDMathMHKS can well capture local sensitive discrimination information, so that the classification accuracy of MatMHKS is improved, and the learning stability of the MatMHKS is also improved.
Disclosure of Invention
Aiming at the problem that the existing design method for the matrix pattern-oriented classifier does not consider local sensitive discrimination information between matrix patterns, the solution of the invention is to design a new regularization item on the frame of the original design method for the matrix pattern-oriented classifier to consider the local sensitive discrimination information, and the regularization item is modified into a regularization item suitable for the matrix patterns based on the advantages of local sensitive discrimination analysis, so as to generate a local sensitive discrimination matrix learning model. We applied this framework to our previous work MatMHKS and named LSDMatMHKS. And the LSDMathMHKS is solved by a gradient descent method, and the algorithm can effectively introduce local sensitive discrimination information and improve the accuracy of mode classification and the learning stability. As the model adopts the two-classification technology, the data set with the number of classes N can be converted into N (N-1)/2 two-classification problems, and it can be known that N (N-1)/2 models need to be trained.
The technical scheme adopted by the invention for solving the technical problems is as follows: firstly, a data set is collected, collected samples are converted into a matrix mode so that a later algorithm can process the data set, wherein the data set which is not numerical type is digitized, and the picture data set also needs dimension reduction processing by a traditional dimension reduction algorithm so as to remove noise. Second, using training set to construct sub-graph in and between local classes
Figure DEST_PATH_IMAGE007
And
Figure DEST_PATH_IMAGE008
use of
Figure 183905DEST_PATH_IMAGE007
And
Figure 450938DEST_PATH_IMAGE008
constructing regularization terms
Figure 649838DEST_PATH_IMAGE002
. Then regularizing term
Figure 318717DEST_PATH_IMAGE002
Introducing a matrix-oriented mode classifier MatMHKS to generate a new matrix-oriented mode classification model LSDMatMHKS, training the LSDMatMHKS by using a training set, and solving the model LADMatMHKS to obtain the optimal solution by using a gradient descent method. And then testing the optimal solution by using the test set, and obtaining an optimal decision function. Finally, the obtained optimal decision function is used for calculating the input unknown matrix mode, and the unknown matrix mode is divided according to the output resultAnd (4) class.
The technical scheme adopted by the invention can be further perfected. Within and between said constructed local classes
Figure 249764DEST_PATH_IMAGE007
And
Figure 4093DEST_PATH_IMAGE008
the method of (1) is to construct a local sensitivity weight matrix
Figure DEST_PATH_IMAGE009
And
Figure DEST_PATH_IMAGE010
then is reused
Figure 678788DEST_PATH_IMAGE009
And
Figure 202173DEST_PATH_IMAGE010
to construct a local matrix pattern discriminant relationship, wherein
Figure 632017DEST_PATH_IMAGE009
And
Figure 873643DEST_PATH_IMAGE010
is determined by a neighbor method. Constructing regularization terms in said training module
Figure DEST_PATH_IMAGE011
The method for making the local intra-class as close as possible and the local inter-class as far as possible from the expression form is that the distance between the patterns in the local intra-class is minimized and the distance between the patterns in the local inter-class is maximized. This method is a classification model of matrix patterns, i.e. the method for vector patterns can be handled as well.
The invention has the beneficial effects that: finding out the local sensitive discrimination relation between the matrix modes by defining a weight matrix of the local sensitive discrimination relation of the matrix modes; by introducing the local sensitive discrimination information, the local patterns of the same type are close to each other as much as possible, and the local sensitive information is introduced into the traditional matrix-mode-oriented classification model, so that the classification accuracy is improved; meanwhile, the overfitting problem of the small sample is improved to a certain extent, and the classification stability and the learning capacity of the model are improved; and the method can directly process whether the image data set or the vector data set.
Drawings
FIG. 1 is a system framework of a local sensitivity discriminant matrix learning machine model according to the present invention.
Detailed Description
The invention will be further described with reference to the following figures and examples: the method of the invention is divided into four steps.
The first step is as follows: and (5) data set acquisition transformation.
Firstly, processing an acquired data set, digitizing the data set if the data set is not digitized, and reducing the dimension of the image data set by using a classical future algorithm after digitizing the image data set so as to facilitate subsequent processing; second converting the acquired data set into a matrix pattern, e.g.
Figure DEST_PATH_IMAGE012
Converting it into matrix mode
Figure DEST_PATH_IMAGE013
Wherein
Figure DEST_PATH_IMAGE014
。
The second step is that: and (5) training a model.
1) First, a regularization term is constructed
Figure 24133DEST_PATH_IMAGE002
Assume a two-class matrix pattern of
Figure DEST_PATH_IMAGE015
. The local sensitivity weight matrix is defined by using the training set as follows：
Figure DEST_PATH_IMAGE016
(1)
Figure DEST_PATH_IMAGE017
(2)
Constructing intra-class and inter-class subgraphs
Figure 605287DEST_PATH_IMAGE005
And
Figure 940453DEST_PATH_IMAGE006
we define
Figure 669375DEST_PATH_IMAGE005
And
Figure 748189DEST_PATH_IMAGE006
as follows:
Figure DEST_PATH_IMAGE018
(3)
Figure DEST_PATH_IMAGE019
(4)
so the regularization term defined in the matrix pattern
Figure 198498DEST_PATH_IMAGE002
As follows:
Figure DEST_PATH_IMAGE020
(5)
wherein
Figure DEST_PATH_IMAGE021
To control
Figure 907828DEST_PATH_IMAGE005
And
Figure 858467DEST_PATH_IMAGE006
the relationship between them can be known
Figure 740972DEST_PATH_IMAGE005
And
Figure 31139DEST_PATH_IMAGE006
including locally sensitive discrimination information.
2) The conventional matrixing method has a common minimum structural risk frame, and the minimum structural branch frame is as follows:
Figure DEST_PATH_IMAGE022
(6)
wherein
Figure DEST_PATH_IMAGE023
Is a risk term for the experience that,
Figure DEST_PATH_IMAGE024
is a regularization term that aims to control the smoothness and computational complexity of the entire framework. Regularization parameter
Figure DEST_PATH_IMAGE025
Is to balance
Figure 911370DEST_PATH_IMAGE023
And
Figure 286988DEST_PATH_IMAGE024
the relationship (2) of (c). We term regularization
Figure 707605DEST_PATH_IMAGE002
A new matrixing method framework can be obtained by introducing into (6), as shown in formula (7):
Figure DEST_PATH_IMAGE026
(7)
the first two items
Figure 180175DEST_PATH_IMAGE023
And
Figure 231307DEST_PATH_IMAGE024
as in the case of the formula (1),
Figure 156538DEST_PATH_IMAGE011
the same as the formula (5).
3) After introducing the new framework into matrix-oriented classifier MatMHKS, we can obtain LSDMatMHKS, and the objective function is shown in formula (8):
Figure DEST_PATH_IMAGE027
（8）
it is composed of
Figure DEST_PATH_IMAGE028
,
Figure DEST_PATH_IMAGE029
,
Figure DEST_PATH_IMAGE030
,
Figure DEST_PATH_IMAGE031
,
Figure DEST_PATH_IMAGE032
In order to be offset in the amount of the offset,
Figure DEST_PATH_IMAGE033
in the form of a matrix pattern, the matrix pattern,
Figure DEST_PATH_IMAGE034
for each matrix pattern class index, N is the total number of patterns.
4) Firstly, matrixing the formula (8), and then solving the optimal weight vector of the LSDMatMHKS model by using a gradient descent method
Figure DEST_PATH_IMAGE035
And
Figure DEST_PATH_IMAGE036
respectively to the pair of formula (8)
Figure DEST_PATH_IMAGE037
And
Figure DEST_PATH_IMAGE038
derivation of the deviation, i.e.
Figure DEST_PATH_IMAGE039
And
Figure DEST_PATH_IMAGE040
then respectively order
Figure DEST_PATH_IMAGE041
And
Figure DEST_PATH_IMAGE042
to find a weight vector
Figure 66332DEST_PATH_IMAGE037
And
Figure 127829DEST_PATH_IMAGE038
. The weight vector obtained
Figure 412180DEST_PATH_IMAGE037
And
Figure 762389DEST_PATH_IMAGE038
as shown in formulas (9) and (10):
Figure DEST_PATH_IMAGE043
（9）
Figure DEST_PATH_IMAGE044
（10）
wherein
Figure DEST_PATH_IMAGE045
，
Figure DEST_PATH_IMAGE046
，
Figure DEST_PATH_IMAGE047
,
Figure DEST_PATH_IMAGE048
，
And the calculation formula of the iteration termination condition is as follows:
Figure DEST_PATH_IMAGE049
（11）
wherein
Figure DEST_PATH_IMAGE050
，
Figure DEST_PATH_IMAGE051
。
Third, model testing
And after the model is optimized in the second step to obtain the weight vector, testing the obtained weight vector by using the test set to select an optimal decision function.
The fourth step, prediction
And selecting an optimal decision function through the third step to identify the unknown mode. Assume a pattern of unknown classes as
Figure DEST_PATH_IMAGE052
Then the decision function is as follows:
Figure DEST_PATH_IMAGE053
（12）
wherein
Figure DEST_PATH_IMAGE054
Are classified.
Hereinbefore, specific embodiments of the present invention are described with reference to the drawings. It will be understood by those skilled in the art that various changes and substitutions may be made to the specific embodiments of the invention without departing from the spirit and scope of the invention. Such modifications and substitutions are intended to be included within the scope of the present invention as defined by the appended claims.
Results of the experiment
To verify the effectiveness and feasibility of our proposed method, we collected 4 vector data sets from UCI, KEEL, and also collected image data sets Coil-20 and Yale, for a total of 6 data sets to verify our algorithm. The selected data set is shown in table 1, and the dimensions, the number of categories, the scale of the training set and the scale of the test set of the data set are given in table 1. The data sets are divided into a training set and a test set, wherein the proportion of the training set to the test set in each data set is 0.5, and 5 rounds of Monte Carlo cross validation are adopted to obtain the classification accuracy. The setting of the model parameters is set by experiment and manual experience, wherein locally sensitive parameter values
Figure DEST_PATH_IMAGE055
Regularization term parameter values
Figure DEST_PATH_IMAGE056
And
Figure DEST_PATH_IMAGE057
initializing boundary vectors
Figure DEST_PATH_IMAGE058
Weight vector
Figure DEST_PATH_IMAGE059
Maximum number of iterations
Figure DEST_PATH_IMAGE060
Minimum stopping error
Figure DEST_PATH_IMAGE061
Iteration step size
Figure DEST_PATH_IMAGE062
。
TABLE 1 data set
Figure DEST_PATH_IMAGE063
The parameter settings of the comparison algorithm are as follows:
the original algorithm MatMHKS and the modified algorithm LSDMatMHKS involved use the same parameter settings to facilitate the comparison. The parameters for MatMHKS were set as: regularization term parameter values
Figure DEST_PATH_IMAGE064
Initializing boundary vectors
Figure DEST_PATH_IMAGE065
Weight vector
Figure DEST_PATH_IMAGE066
Maximum number of iterations
Figure DEST_PATH_IMAGE067
Minimum stopping error
Figure DEST_PATH_IMAGE068
Iteration step size
Figure 419417DEST_PATH_IMAGE062
。
The results of the experiment are shown in table 2. From the experimental results, the accuracy and the standard deviation of the accuracy of the LSDMatMHKS are better than that of MatMHKS. This verifies the effectiveness and feasibility of our proposed method.
Table 2 data set accuracy (%)
Figure DEST_PATH_IMAGE069
Remarking: the above experimental data are all from the environments of Inter Xeon CPU E5-24072.20 GHZ, 16G RAMDDR3, Windows Server 2012 and Matlab.

Claims (2)

1. A matrix classification model based on local sensitivity discrimination is characterized in that: the method comprises the following specific steps:
1) firstly, collecting a data set: converting the collected samples into a matrix pattern so that the subsequent algorithm can process the samples, wherein the data set which is not numerical type is digitized, and the picture data set also needs to be subjected to dimension reduction processing by using a traditional dimension reduction algorithm so as to remove noise;
2) secondly, constructing partial intra-class and partial inter-class subgraphs A (f) and B (f) by using the training set, and constructing a regularization term R by using A (f) and B (f)LSDEta a (f) - (1-eta) b (f), wherein eta e [0,1]To control the relationship between A (f) and B (f);
3) then the regularization term RLSDIntroducing matrix-mode-oriented classifier MatMHKS to generate a matrix-mode-oriented classification model LSDMatMHKS considering the intra-class relation and the inter-class relation simultaneously, training the LSDMatMHKS by using a training set, and solving the model LSDMatMHKS to obtain the optimal solution by using a gradient descent method, wherein the target function of the LSDMatMHKS is
Figure FDA0002576563800000011
Wherein,
Figure FDA0002576563800000012
v0b is not less than 0 and is offset, i, j is the number of the basic model, biIs the offset of the ith base model, AiFor the augmented matrix mode, c, η are hyper-parameters,
Figure FDA0002576563800000013
in the form of a matrix pattern, the matrix pattern,
Figure FDA0002576563800000014
for each matrix pattern class index, N is the total number of patterns, Ww,ijAnd Wb,ijRespectively a local intra-class matrix and a local inter-class matrix,
Figure FDA0002576563800000015
4) then, testing an optimal solution by using the test set, and obtaining an optimal decision function;
5) and finally, calculating the input unknown matrix mode by using the obtained optimal decision function, and classifying the unknown matrix mode according to the output result.
2. The matrix classification model based on locality sensitive discriminant as claimed in claim 1, wherein: the partial intra-class and partial inter-class subgraphs A (f) and B (f) are obtained by passing through a partial sensitivity weight matrix WwAnd WbIs shown in (a) wherein W iswAnd WbRespectively refer to the intra-local-class weight matrix and the inter-local-class weight matrix, WwAnd WbThe calculation of (2) is carried out by using a nearest neighbor method to obtain a current matrix mode
Figure FDA0002576563800000021
Nearest neighbor, namely, calculating the Euclidean distance between each sample and other samples, selecting the point with the nearest distance as the nearest neighbor point, and if the mode in the neighbor and the current mode belong to the same class, making the weight matrix W at the momentwThe element value of the corresponding position of (1) is 1, otherwise, it is 0; if the modes in the neighborhood and the current mode belong to different classes, the weight matrix W at the moment is orderedbThe element value of the corresponding position of (1) is 1, otherwise it is 0.
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