CN107085700A - A kind of face identification method being combined based on rarefaction representation with neural networks with single hidden layer technology - Google Patents
A kind of face identification method being combined based on rarefaction representation with neural networks with single hidden layer technology Download PDFInfo
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Abstract
The present invention relates to a kind of face identification method being combined based on rarefaction representation with neural networks with single hidden layer technology, the time-consuming longer or unstable classification performance defect of recognition methods is solved compared with prior art.The present invention comprises the following steps：The face scope of face is determined in man face image acquiring and detection, the test two field picture extracted from video；Image preprocessing, carries out eliminating illumination or the pretreatment of noise jamming to test two field picture；Feature extraction, face characteristic extraction is carried out to test two field picture；Classification and Identification, by the face characteristic information extracted, scans for classification and matching with the feature templates that are stored in database, obtains final classification recognition result.Sparse representation method is combined by the present invention with Single hidden layer feedforward neural networks, is realized while very fast recognition speed is possessed, and keeps good Classification and Identification performance.
Description
Technical field
It is specifically a kind of to be based on rarefaction representation and neural networks with single hidden layer the present invention relates to image identification technical field
The face identification method that technology is combined.
Background technology
As one of most successful application in the fields such as image procossing, pattern-recognition, recognition of face is due to without identification object
Coordinate, can be received much concern the features such as remote concealed operation, identification process close friend.Except pure significance of scientific research, in business and hold
Also there are many applications in method, such as supervision, safety, communication and man-machine interaction.By the research of 30 years, various faces
Recognition methods is proposed in succession by researcher.
With the rise of compressive sensing theory, as the rarefaction representation of its core technology, data analysis can be not only reduced
With the cost of processing, and the compression efficiency of data can be improved, thus the method based on rarefaction representation is due to its outstanding point
Direction of scientific rersearch, is absorbed in is based on one after another by class performance and the extensive concern that researcher is received to noise and the robustness blocked
In the research of the recognition of face of rarefaction representation, realize that the more precision of recognition of face improves face recognition technology, but this method
Often more take.
Single hidden layer feedforward neural networks eliminate continuous iteration to obtain compared to traditional neural network learning training method
Best Generalization Capability, but the classification of this method are realized in the redundant and complicated process of optimized parameter, pursuit with most fast pace of learning
Performance is more unstable.
Therefore, how rarefaction representation is combined with Single hidden layer feedforward neural networks, set using the advantage of its own
Count out a kind of face identification method and have become the technical problem for being badly in need of solving.
The content of the invention
The invention aims to solve, recognition methods in the prior art is time-consuming longer or unstable classification performance to be lacked
Fall into and above-mentioned ask solved with the face identification method that neural networks with single hidden layer technology is combined based on rarefaction representation there is provided a kind of
Topic.
To achieve these goals, technical scheme is as follows：
A kind of face identification method being combined based on rarefaction representation with neural networks with single hidden layer technology, including following step
Suddenly：
The face scope of face is determined in man face image acquiring and detection, the test two field picture extracted from video；
Image preprocessing, carries out eliminating illumination or the pretreatment of noise jamming to test two field picture；
Feature extraction, face characteristic extraction is carried out to test two field picture；
Classification and Identification, by the face characteristic information extracted, classification is scanned for the feature templates that are stored in database
Matching, obtains final classification recognition result.
Described Classification and Identification comprises the following steps：
Sample training is carried out to training set；
Test sample classification is carried out to the face characteristic information for testing two field picture.
Described comprises the following steps to training set progress sample training：
Calculate rarefaction representation coefficient xi, make it as the input sample of neural networks with single hidden layer；
Random generation input weight wiWith deviation bi；
Calculate hidden layer output matrix H；
Calculate optimal output weights
Wherein H+=(HTH)-1HT；
Wherein,For optimal output weights, H+For hidden layer output matrix H Moore-Penrose generalized inverse matrix；
Export the optimal output weights of neural networks with single hidden layer
Described calculates rarefaction representation coefficient xiComprise the following steps：
Training set A is obtained from database, training set A includes common c facial images of n different objects,
Wherein：C images are divided into n groups, and each object includes niIndividual face sample image, n is object number, niTo be each
The sample image quantity of object；
I-th group of facial image in training set A is defined as Ai,
Wherein, ai,j∈RD×1Represent in i-th group j-th of face sample image (j=1,2 ..., ni) D that is constituted
Dimensional vector；
C training sample image of n group is linked successively, c=n1+n2+...+nn,
Base or excessively complete dictionary A are constituted,
A=[A1,A2,…An]；
If images to be recognized y belongs to the i-th group objects, A is usediIn face sample image linear expression y,
Wherein, xiIt is y in AiOn expression coefficient,
Images to be recognized y is as follows in the linear expression of all training samples：
Y=Ax ∈ RD
Wherein, sparse coefficient vector
Sparse coefficient vector x is solved under packet and local sensitive constraint, it is expressed as minimization problem：
Wherein, λ is the regulation parameter for weighing local susceptibility and grouping sparsity,For point multiplication operation,
p∈Rn×1For local restriction vector, its similitude to test sample and around it between training sample enters row constraint,
It is expressed as follows：
Wherein, η is normal number parameter, dk(y,ai) it is core Euclidean distance, it is expressed as follows：
Wherein, gaussian kernel function is as follows：
σ is the standard error parameter of Gaussian kernel.
The described hidden layer output matrix H that calculates comprises the following steps：
Make { (xi,ti)|xi∈Rd,ti∈Rm, i=1 ..., N } it is the training set containing N number of different samples；
Wherein：Input sample xi=(xi1,xi2,...,xid)T, expectation target output label vector ti=(ti1,ti2,...,
tim)T；Possess L hidden node (general L ＜ ＜ N) and activation primitive is g (wi,bi, neural networks with single hidden layer unified model x)
It is expressed as follows:
Wherein, wi=(wi1,wi2,...,wid)TFor i-th of hidden node of connection and the input weights of input layer, bi
It is the deviation of i-th of hidden node, βi=(βi1,βi2,...,βim)TIt is i-th of hidden node of connection and output node layer
Export weights, wi·xjRepresent wiAnd xjInner product, g (wi,bi, x) it is Sigmoid functions or RBF functions；
The unified model of neural networks with single hidden layer is written as matrix form：
H β=T
Wherein,
Wherein, H is the hidden layer output matrix of neutral net, and i-th in matrix H to be classified as correspondence on i-th of hidden node defeated
Enter x1,x2,...,xNOutput vector.
The face characteristic information of described pair of test two field picture carries out test sample classification and comprised the following steps：
Input test sample y and the optimal output weights of neural networks with single hidden layer in training airplane
Processing formula is minimized using sparse coefficient vector x sparse coding is carried out to y, obtain the corresponding rarefaction representation systems of y
Number
WillAs the input sample of neural networks with single hidden layer, classified using neural networks with single hidden layer, by judging most
Small residual error method obtains final classification result, and its formula is as follows：
Output category result class label t.
Beneficial effect
A kind of face identification method being combined based on rarefaction representation with neural networks with single hidden layer technology of the present invention, with showing
There is technology compared to sparse representation method is combined with Single hidden layer feedforward neural networks, realize and possessing very fast recognition speed
Meanwhile, keep good Classification and Identification performance.
The present invention obtains facial image under recognition of face framework using sparse representation method has the sparse table of identification
Show coefficient, the double constraints of local susceptibility and grouping sparsity are carried out in sparse coding, neural networks with single hidden layer pair is used
Facial image sample carries out effective classification and identification.The perfect neural networks with single hidden layer for possessing very fast pace of learning of the present invention
When applied to classification due to noise-sensitive so that the relatively low deficiency of accuracy, compared to the identity of neural networks with single hidden layer
Can, relatively significantly it is improved；Though sparse representation method classification performance is preferably and to the more robust such as illumination, noise, carry out
More taken during image classification, the present invention also effectively improves this problem so that the image classification time is substantially reduced.
Brief description of the drawings
Fig. 1 is method precedence diagram of the invention；
Fig. 2 is the algorithm logic figure of neural networks with single hidden layer in the prior art.
Embodiment
To make to have a better understanding and awareness to architectural feature of the invention and the effect reached, to preferably
Embodiment and accompanying drawing coordinate detailed description, are described as follows：
Recognition of face is：Face characteristic to be identified and obtained skin detection are compared, and according to two
Similarity degree between person is judged the identity information of face.As shown in figure 1, of the present invention a kind of based on rarefaction representation
The face identification method being combined with neural networks with single hidden layer technology, it comprises the following steps：
The first step, man face image acquiring is determined with detection in the test two field picture extracted using conventional method from video
The face scope of face.Video is obtained, video is divided with frame, is positioned from the image of every frame and marks off face substantially
Face scope, that is, carry out the detection of facial image, face determined in test image or the two field picture extracted from video
Approximate location.Generally in video, it is necessary to which multiple image is used to trace detection face part.
Second step, image preprocessing carries out eliminating the pre- of illumination or noise jamming using conventional method to test two field picture
Processing.Image preprocessing step is used to eliminate illumination or noise jamming, obtains preferable standard faces image, is to extract Shandong in the later stage
The face characteristic of rod provides strong ensure.
3rd step, feature extraction carries out face characteristic extraction using conventional method to test two field picture.Also referred to as face table
Levy, be that some features for being directed to face are carried out, be also the process that feature modeling is carried out to face.
4th step, Classification and Identification.By the face characteristic information extracted, searched with the feature templates that are stored in database
Rope classification and matching, obtains final classification recognition result.By what is stored in face characteristic information, with database obtained from extraction
Feature templates scan for classification and matching, can be by setting a threshold value, when similarity exceedes this threshold value, then classification
With obtained result output, final classification can also be obtained using the method for least residual herein by judging minimum residual method
As a result.It is comprised the following steps that：
(1) training process, sample training is carried out to training set.It is dilute with being grouped that local susceptibility is carried out for training sample set
The sparse coding under property double constraints is dredged, the rarefaction representation coefficient of resulting training sample is regard as neural networks with single hidden layer
Input sample, and substitute into neutral net and be trained, in network training, the input weights and deviation in activation primitive are equal
Randomly select, realize the Optimal Learning performance of the neutral net by constantly adjusting hidden node number, namely obtain optimal
Export weights.It comprises the following steps：
A, calculate rarefaction representation coefficient xi, make it as the input sample of neural networks with single hidden layer.
Here, the grouping sparsity method for expressing with internal structural is considered first, and relative to the number of sparse coding
According to openness, data locality preferably can enter row constraint to the similitude data, thus the present invention will enter to sparse coding
The double constraints of row local susceptibility and grouping sparsity so that the internal structural information of test sample and training dictionary is filled
Divide and utilize, so as to obtain more efficiently rarefaction representation coefficient.
First, training set A is obtained from database, training set A includes common c facial images of n different objects.Its
In：C images are divided into n groups, and each object includes niIndividual face sample image.Because a people there may be multiple different angles
Facial image, that is to say, that the multiple face samples of people correspondence, n is then object number (number or face number), niIt is then
The sample image quantity (sample image corresponding to everyone) of each object.
I-th group of facial image in training set A is defined as Ai,
Wherein, ai,j∈RD×1Represent in i-th group j-th of face sample image (j=1,2 ..., ni) D that is constituted
Dimensional vector, the D dimensional vectors are to be sequentially connected in series acquisition to the pixel brightness value that face sample image is respectively arranged.
Secondly, c training sample image of n group is linked successively, c=n1+n2+...+nn, constitute base or excessively complete word
Allusion quotation A, excessively complete dictionary can be by the atom linear expression in the dictionary, A by the vector of any one identical dimensional1In have n1It is individual
Sample, A2In have n2Individual sample, similarly, AnIn have nnIndividual sample.
A=[A1,A2,…An]。
Again, if images to be recognized y belongs to the i-th group objects, A is usediIn face sample image linear expression y,
Wherein, x is madeiIt is y in AiOn expression coefficient,X hereiniFor illustrating y
Can be completely with i-th group of dictionary AiLinear expression, herein and need not be solved, and that really solve is following x.
Then images to be recognized y is as follows in the linear expression of all training samples：
Y=Ax ∈ RD
Wherein, sparse coefficient vector
Here, assume that y belongs to i-th group before, therefore y can be only with i-th group of dictionary linear expression, because A is by each
Packet composition A=[A1,A2,…An], the non-zero value part in wherein x is A in corresponding AiThe part at place, and other parts are
0。
Finally, sparse coefficient vector x is solved under packet and local sensitive constraint, it can be expressed as minimum and ask
Topic：
Wherein, λ is the regulation parameter for weighing local susceptibility and grouping sparsity,For point multiplication operation,
p∈Rn×1For local restriction vector, its similitude to test sample and around it between training sample enters row constraint,
It is expressed as follows：
Wherein, η is normal number parameter, dk(y,ai) it is core Euclidean distance, it is expressed as follows：
Wherein, gaussian kernel function is as follows：
σ is the standard error parameter of Gaussian kernel.
B, random generation input weight wiWith deviation bi, wiAnd biInitialized with random value, generally take 0~1 it
Between white noise random value.
C, hidden layer output matrix H is calculated, its calculation procedure is as follows：
A) { (x is madei,ti)|xi∈Rd,ti∈Rm, i=1 ..., N } it is the training set containing N number of different samples；
Wherein：Input sample xi=(xi1,xi2,...,xid)T, expectation target output label vector ti=(ti1,ti2,...,
tim)T。
B) as shown in Fig. 2 c possesses L hidden node (general L ＜ ＜ N) and activation primitive is g (wi,bi,x)
Neural networks with single hidden layer unified model be expressed as follows:
Wherein, wi=(wi1,wi2,...,wid)TFor i-th of hidden node of connection and the input weights of input layer, bi
It is the deviation of i-th of hidden node, βi=(βi1,βi2,...,βim)TIt is i-th of hidden node of connection and output node layer
Export weights, wi·xjRepresent wiAnd xjInner product, g (wi,bi, x) it is Sigmoid functions or RBF functions.
C) unified model of neural networks with single hidden layer is written as matrix form：
H β=T
Wherein,
Wherein, H is the hidden layer output matrix of neutral net, and i-th in matrix H to be classified as correspondence on i-th of hidden node defeated
Enter x1,x2,...,xNOutput vector.
D, the optimal output weights of calculating
Wherein H+=(HTH)-1HT；
Wherein,For optimal output weights, H+For hidden layer output matrix H Moore-Penrose generalized inverse matrix.
E, the output optimal output weights of neural networks with single hidden layer
(2) test process, test sample classification is carried out to the face characteristic information for testing two field picture.Test sample is carried out
Local susceptibility and the sparse coding under grouping sparsity double constraints, obtain the rarefaction representation system corresponding to the test sample
Number, and as the input sample of neural networks with single hidden layer, training set is carried out to instruct in sample training step while will pass through
Optimal output weights obtained by practicingIt is updated among the network, using differentiating that minimal error obtained corresponding to test sample
Class label, that is, obtain final classification result, completes the identification of face.It is comprised the following steps that：
A, input test sample y and the optimal output weights of neural networks with single hidden layer in training airplane
B, using sparse coefficient vector x minimize processing formula to y carry out sparse coding, obtain the corresponding rarefaction representations of y
CoefficientLocal susceptibility and the sparse coding under grouping sparsity double constraints are carried out to test sample y, the test is obtained
Rarefaction representation coefficient corresponding to sample y
C, generalAs the input sample of neural networks with single hidden layer, classified using neural networks with single hidden layer, by judging
Least residual method obtains final classification result, and its formula is as follows：
D, output category result class label t, complete classification, different faces are identified from test sample y.
The present invention compensate for possessing the neural networks with single hidden layer of very fast pace of learning when applied to classification due to noise
It is sensitive thus accuracy is relatively low and classification performance is preferable；Sparse representation method to the more robust such as illumination, noise but more consumes
When deficiency.The method that the present invention is provided is realized while very fast recognition speed is possessed, and keeps preferable Classification and Identification performance.
General principle, principal character and the advantages of the present invention of the present invention has been shown and described above.The technology of the industry
Personnel are it should be appreciated that the present invention is not limited to the above embodiments, and that described in above-described embodiment and specification is the present invention
Principle, various changes and modifications of the present invention are possible without departing from the spirit and scope of the present invention, these change and
Improvement is both fallen within the range of claimed invention.The protection domain of application claims by appended claims and its
Equivalent is defined.
Claims (6)
1. a kind of face identification method being combined based on rarefaction representation with neural networks with single hidden layer technology, it is characterised in that bag
Include following steps：
11) the face scope of face is determined in man face image acquiring and detection, the test two field picture extracted from video；
12) image preprocessing, carries out eliminating illumination or the pretreatment of noise jamming to test two field picture；
13) feature extraction, face characteristic extraction is carried out to test two field picture；
14) Classification and Identification, by the face characteristic information extracted, classification is scanned for the feature templates that are stored in database
Match somebody with somebody, obtain final classification recognition result.
2. a kind of recognition of face being combined based on rarefaction representation with neural networks with single hidden layer technology according to claim 1
Method, it is characterised in that described Classification and Identification comprises the following steps：
21) sample training is carried out to training set；
22) test sample classification is carried out to the face characteristic information for testing two field picture.
3. a kind of recognition of face being combined based on rarefaction representation with neural networks with single hidden layer technology according to claim 2
Method, it is characterised in that described to comprise the following steps to training set progress sample training：
31) rarefaction representation coefficient x is calculatedi, make it as the input sample of neural networks with single hidden layer；
32) random generation input weight wiWith deviation bi；
33) hidden layer output matrix H is calculated；
34) optimal output weights are calculated
Wherein H+=(HTH)-1HT；
Wherein,For optimal output weights, H+For hidden layer output matrix H Moore-Penrose generalized inverse matrix；
35) the optimal output weights of neural networks with single hidden layer are exported
4. a kind of recognition of face being combined based on rarefaction representation with neural networks with single hidden layer technology according to claim 3
Method, it is characterised in that described calculates rarefaction representation coefficient xiComprise the following steps：
41) training set A is obtained from database, training set A includes common c facial images of n different objects,
Wherein：C images are divided into n groups, and each object includes niIndividual face sample image, n is object number, niFor each object
Sample image quantity；
I-th group of facial image in training set A is defined as Ai,
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<mi>k</mi>
<mrow>
<mo>(</mo>
<mi>y</mi>
<mo>,</mo>
<msub>
<mi>a</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>k</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>a</mi>
<mi>i</mi>
</msub>
<mo>,</mo>
<msub>
<mi>a</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</msqrt>
<mo>,</mo>
</mrow>
Wherein, gaussian kernel function is as follows：
<mrow>
<mi>k</mi>
<mrow>
<mo>(</mo>
<mi>y</mi>
<mo>,</mo>
<msub>
<mi>a</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>exp</mi>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<mo>-</mo>
<msup>
<mrow>
<mo>|</mo>
<mrow>
<mi>y</mi>
<mo>-</mo>
<msub>
<mi>a</mi>
<mi>i</mi>
</msub>
</mrow>
<mo>|</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<mn>2</mn>
<msup>
<mi>&sigma;</mi>
<mn>2</mn>
</msup>
</mrow>
</mfrac>
<mo>)</mo>
</mrow>
</mrow>
σ is the standard error parameter of Gaussian kernel.
5. a kind of recognition of face being combined based on rarefaction representation with neural networks with single hidden layer technology according to claim 3
Method, it is characterised in that the described hidden layer output matrix H that calculates comprises the following steps：
51) { (x is madei,ti)|xi∈Rd,ti∈Rm, i=1 ..., N } it is the training set containing N number of different samples；
Wherein：Input sample xi=(xi1,xi2,...,xid)T, expectation target output label vector ti=(ti1,ti2,...,tim)T；
52) possess L hidden node and activation primitive is g (wi,bi, neural networks with single hidden layer unified model x) is expressed as follows:
<mrow>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>L</mi>
</munderover>
<msub>
<mi>&beta;</mi>
<mi>i</mi>
</msub>
<msub>
<mi>g</mi>
<mi>i</mi>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>x</mi>
<mi>j</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>L</mi>
</munderover>
<msub>
<mi>&beta;</mi>
<mi>i</mi>
</msub>
<msub>
<mi>g</mi>
<mi>i</mi>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>w</mi>
<mi>i</mi>
</msub>
<mo>&CenterDot;</mo>
<msub>
<mi>x</mi>
<mi>j</mi>
</msub>
<mo>+</mo>
<msub>
<mi>b</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msub>
<mi>t</mi>
<mi>j</mi>
</msub>
<mo>,</mo>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
<mo>,</mo>
<mn>2</mn>
<mo>,</mo>
<mo>...</mo>
<mo>,</mo>
<mi>N</mi>
<mo>,</mo>
</mrow>
Wherein, wi=(wi1,wi2,...,wid)TFor i-th of hidden node of connection and the input weights of input layer, biIt is i-th
The deviation of individual hidden node, βi=(βi1,βi2,...,βim)TIt is that the output for connecting i-th of hidden node and output node layer is weighed
Value, wi·xjRepresent wiAnd xjInner product, g (wi,bi, x) it is Sigmoid functions or RBF functions；
53) unified model of neural networks with single hidden layer is written as matrix form：
H β=T
Wherein,
<mrow>
<mi>&beta;</mi>
<mo>=</mo>
<msub>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<msubsup>
<mi>&beta;</mi>
<mn>1</mn>
<mi>T</mi>
</msubsup>
</mtd>
</mtr>
<mtr>
<mtd>
<msubsup>
<mi>&beta;</mi>
<mn>2</mn>
<mi>T</mi>
</msubsup>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<msubsup>
<mi>&beta;</mi>
<mi>L</mi>
<mi>T</mi>
</msubsup>
</mtd>
</mtr>
</mtable>
</mfenced>
<mrow>
<mi>L</mi>
<mo>&times;</mo>
<mi>m</mi>
</mrow>
</msub>
<mo>,</mo>
<mi>T</mi>
<mo>=</mo>
<msub>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<msubsup>
<mi>t</mi>
<mn>1</mn>
<mi>T</mi>
</msubsup>
</mtd>
</mtr>
<mtr>
<mtd>
<msubsup>
<mi>t</mi>
<mn>2</mn>
<mi>T</mi>
</msubsup>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<msubsup>
<mi>t</mi>
<mi>N</mi>
<mi>T</mi>
</msubsup>
</mtd>
</mtr>
</mtable>
</mfenced>
<mrow>
<mi>N</mi>
<mo>&times;</mo>
<mi>m</mi>
</mrow>
</msub>
<mo>,</mo>
</mrow>
Wherein, H is the hidden layer output matrix of neutral net, and i-th in matrix H is classified as correspondence input x on i-th of hidden node1,
x2,...,xNOutput vector.
6. a kind of recognition of face being combined based on rarefaction representation with neural networks with single hidden layer technology according to claim 2
Method, it is characterised in that the face characteristic information of described pair of test two field picture carries out test sample classification and comprised the following steps：
61) input test sample y and the optimal output weights of neural networks with single hidden layer in training airplane
62) minimize processing formula using sparse coefficient vector x and sparse coding is carried out to y, obtain the corresponding rarefaction representation coefficients of y
63) willAs the input sample of neural networks with single hidden layer, classified using neural networks with single hidden layer, by judging most
Small residual error method obtains final classification result, and its formula is as follows：
<mrow>
<munder>
<mrow>
<mi>m</mi>
<mi>i</mi>
<mi>n</mi>
</mrow>
<mi>t</mi>
</munder>
<mo>|</mo>
<mi>H</mi>
<mrow>
<mo>(</mo>
<mover>
<mi>x</mi>
<mo>&OverBar;</mo>
</mover>
<mo>)</mo>
</mrow>
<mover>
<mi>&beta;</mi>
<mo>^</mo>
</mover>
<mo>-</mo>
<mi>t</mi>
<mo>|</mo>
<mo>;</mo>
</mrow>
64) output category result class label t.
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