CN105701506B - A kind of improved method based on transfinite learning machine and rarefaction representation classification - Google Patents
A kind of improved method based on transfinite learning machine and rarefaction representation classification Download PDFInfo
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Abstract
The invention discloses a kind of improved methods based on transfinite learning machine and rarefaction representation classification.Steps are as follows by the present invention: 1, hidden node parameter is randomly generated；2, hidden node output matrix is calculated, 3, according to the size relation of L and N, the output weight of connection hidden node and output neuron is calculated using different formula4, the output vector of inquiry picture y is calculated；5, to the maximum ο in ELM output vector οfWith second largest value οsDifference judged, if difference is greater than the set value, find out maximum value in output vector it is corresponding index be inquiry picture generic；Otherwise 6 are entered step；6, using training sample corresponding to k maximum value in output vector ο, constructor dictionary calculates the linear expression coefficient of picture y using coefficient restructing algorithm, calculates residual error and the classification according to corresponding to residual error determines the affiliated class of inquiry picture.Calculation amount of the present invention will greatly reduce, and realize higher discrimination, can also substantially reduce computation complexity.
Description
Technical field
The invention belongs to image classification field more particularly to a kind of improvement based on transfinite learning machine and rarefaction representation classification
Method.
Background technique
Image classification, that is, input picture is integrated into a certain specific classification automatically attracted it is more and more extensive
Concern, especially because it is in security system, medical diagnosis, the application of the multiple fields such as human-computer interaction.At past several years, from
Some technologies that machine learning develops also produce very big influence in image classification field.In fact, almost mentioning in the past
Each method out has its advantages and disadvantage.One inevitable problem is exactly computation complexity and classification accuracy
Compromise.In other words, that is, one kind can not be designed in all applications in efficiency and discrimination all the best ways.
In order to solve this problem, mixed system is come into being, that is, to form one the advantages of be integrated with various distinct methods
The significantly more efficient method of kind.
One vital factor of successful image classification system is exactly classifier.One good classifier of design is not
Can because of some other factor, such as different feature extracting methods and be affected.In the past few decades, artificial neuron
Network is benefited significantly since input parameter can arbitrarily be arranged, and not only pace of learning is than very fast, and achieves preferably
Generalization Capability.Among them, the learning machine (Extreme Learning Machine, ELM) that transfinites widely is paid close attention to and is ground
Study carefully.Why so welcome the learning machine (ELM) that transfinites is, is because it has quick pace of learning, the ability handled in real time
With the measurability of neural network.In addition to the learning machine that transfinites (ELM), another is also concerned with by research institution based on sparse
The classification (Sparse Representation based Classification, SRC) of expression.Rarefaction representation classifies (SRC)
Most it is initially the sparse performance in order to study human vision neuron, found it in recognition of face, machine vision and direction later
Estimation etc. also has good performance.Rarefaction representation classification (SRC) be to try to find out from of a sort samples pictures it
Between connection and the rarefaction representation coefficient of picture to be checked is set up by linear regression.Although ELM and SRC each have prominent
Out the advantages of, but they there are still some drawbacks the development for limiting them in practical applications.Experiment shows ELM
It practises speed quickly, cannot preferably handle noise, although SRC can preferably handle noise but paid very big meter
Calculate cost.It is additionally noted that a good classifier of design not only needs to show higher discrimination, but also
Need faster recognition efficiency.Since the learning machine that transfinites (ELM) and rarefaction representation classification (SRC) have their own advantages, then designing
A kind of hybrid classifer is exactly reasonable.Experiment shows that ELM-SRC does very well in terms of discrimination than the learning machine (ELM) that transfinites,
Computation complexity is also reduced than rarefaction representation classification (SRC), but due to having used complete dictionary, transfinite learning machine with it is sparse
Presentation class (ELM-SRC) computation complexity is still very high.
Artificial neural network (Artificial Neural Networks) is also referred to as neural network (NNs), it is one
Kind imitates animal nerve network behavior feature, carries out the algorithm mathematics model of distributed parallel information processing.This network relies on
The complexity of system, by adjusting relationship interconnected between internal great deal of nodes, to achieve the purpose that handle information.
Artificial neural network is a kind of mathematical model of structure progress information processing that application couples similar to cerebral nerve cynapse.In work
Journey and academia are also often directly referred to as neural network.Each neuron for constituting feedforward network receives previous stage input, and exports
To next stage, no feedback can be indicated with a directed acyclic graph.The node of figure is divided into two classes, i.e. input node and computing unit.
Each computing unit can have any input, but only one is exported, and export may be coupled to it is any other it is multiple other
The input of node.Feedforward neural network is generally divided into different layers, and i-th layer of input is only associated with (i-1)-th layer of output, defeated
Enter with output node due to can be connected with the external world, is directly protected from environmental, referred to as visible layer, and other middle layers then claim
For hidden layer.Single hidden layer feedforward neural networks (Single-hidden Layer Feedforword neural Networks,
SLFNs) as the term suggests being exactly the feedforward neural network that hidden layer only has one layer.For N number of any different sample (xi,ti), wherein
xi=[xi1,xi2,…xin]T, ti=[ti1,ti2,…,tin]T, the standard Single hidden layer feedforward neural networks with M hidden node
(SLFNs) for, mathematical model isWherein wiBe input node and
The weight of hidden node, βiIt is the weight between hidden node and output node, biIt is hidden layer deviation, g (x) is activation primitive.
Single hidden layer feedforward neural networks (SLFNs) with M hidden node can be approached with zero error, it is meant thatNamelyN number of equation above can also be write as H β=T, wherein
H is hidden layer output matrix.Experiment shows that N can be accurately obtained by randomly selecting input weight and hidden layer deviation
A different observation.It turns out that not only pace of learning is fast for Single hidden layer feedforward neural networks (SLFNs), but also have preferable
Generalization Capability.
Summary of the invention
The purpose of the present invention is being directed to existing method, provide a kind of based on transfinite learning machine and sparse table
Show the improved method of classification.This method is a kind of based on learning machine and rarefaction representation classification (the Extreme Learning of transfiniting
Machine-Sparse Representation based Classification, ELM-SRC) it improved adaptively transfinites
Habit machine and rarefaction representation classification (Extreme Learning Machine and Adaptive Sparse
Representation based Classification, EA-SRC) algorithm.To achieve the goals above, the present invention uses
Following scheme.
The technical solution adopted by the present invention to solve the technical problems includes the following steps:
Hidden node parameter (w is randomly generated in step 1i,bi), i=1,2 ..., L, wherein wiIt is i-th of hidden layer section of connection
The input weight of point and input neuron, biIt is the deviation of i-th of hidden node, L is hidden node number.
Step 2 calculates hidden node output matrix H (w1,…wL,x1,…,xN,b1,…bi,…,bL), and
Wherein w is the input weight for connecting hidden node and inputting neuron, and x is training sample input, and N is training sample
Number, biIt is the deviation of i-th of hidden node, g () indicates activation primitive.
Step 3, according to the size relation of L and N, different formula is respectively adopted and calculates connection hidden node and output mind
Output weight through member
Step 4, the output vector for calculating inquiry picture y
Step 5, to the maximum o in ELM output vector ofWith second largest value osDifference judged, and find out output to
The corresponding index of maximum value is inquiry picture generic in amount.
If the maximum o in ELM output vector ofWith second largest value osDifference be greater than preset threshold value σ, i.e. of-
os> σ then directlys adopt the learning machine that transfinites (ELM) trained neural network, finds out the corresponding rope of maximum value in output vector
Draw as inquiry picture generic.
If the maximum o in output vectorfWith second largest value osDifference be less than our preset threshold values, i.e. of-os
< σ, then it is assumed that the noise that picture includes is higher, is classified using rarefaction representation sorting algorithm.
In the step 3, if the size of L and N be L≤N, i.e., hidden node number be less than or equal to sample number, then for
Raising computational efficiency carries out singular value decomposition to hidden node output matrix, specific:
3-1. singular value decomposition H=UDVT, wherein D=diag { d1,…di,…dNIt is diagonal matrix, diIt is the of matrix H
I singular value, then HHT=VD2VT.Wherein U is n rank unitary matrice matrix, and V is n rank unitary matrice.And UUT=UTU=I, VVT=
VTV=I.
3-2. sets the upper limit λ of adjusting parameter λmaxWith lower limit λmin, in λi∈[λmin,λmax] in range, calculate separately
Every layer of decomposition square HAT of orthogonal intersection cast shadow matrix HAT outr, HATr=HV (D2+λnI)-1VTHT, wherein HAT=HH+=H (HTH)- 1HT。
3-3. is in λi∈[λmin,λmax] the corresponding mean square deviation of the different adjusting parameter λ of the interior calculating of rangeIt calculates public
Formula are as follows:
Wherein tjIt is desired output, and ojIt is actual output.
The calculated Minimum Mean Square Error of 3-4.Corresponding λ, i.e. λopt.Preferable generalization can be obtained at this time
Can, and can also maximize classification boundaries.
3-5. calculates the output weight of connection hidden node and output neuron
In the step 3, if the size of L and N is L > N, i.e. hidden node number is greater than sample number, then in order to improve
Computational efficiency carries out singular value decomposition to hidden node output matrix, specific:
3-6. singular value decomposition H=UDVT, wherein D=diag { d1,…di,…dNIt is diagonal matrix, diIt is the of matrix H
I singular value, then HHT=UD2UT, and UUT=UTU=I, VVT=VTV=I.
3-7. sets the upper limit λ of adjusting parameter λmaxWith lower limit λmin, in λi∈[λmin,λmax] in range, calculate separately
Every layer of decomposition square HAT of orthogonal intersection cast shadow matrix HAT outr=HHTU(D2+λiΙ)-1UT, wherein HAT=HH+=H (HTH)-1HT；
3-8. is in λi∈[λmin,λmax] in range, calculate the corresponding mean square deviation of different adjusting parameter λIt calculates
Formula are as follows:
Wherein tjIt is desired output, and ojIt is actual output.
The calculated Minimum Mean Square Error of 3-9.Corresponding λ, i.e. λopt.Preferable generalization can be obtained at this time
Can, and can also maximize classification boundaries.
3-10. calculates the output weight of connection hidden node and output neuron
Rarefaction representation sorting algorithm described in step 5 establishes adaptive son first with k maximum value preceding in output vector o
Then dictionary reconstructs the rarefaction representation coefficient of training sample, find out corresponding residual error, and it is corresponding finally to find out minimum value in residual error
Index be the classification that belongs to of picture, it is specific:
Classification corresponding to preceding k maximum value in output vector o is found out first, it is then maximum with first k in output vector o
It is worth corresponding vector and establishes adaptive sub- dictionary vectorWherein m (i) ∈ { 1,2 ... m }.
Then rarefaction representation coefficient is reconstructed, formula is as follows,Wherein τ is adjustment
Coefficient.
Finally calculate corresponding residual error
Wherein AdIt is the training sample of d class；It is the corresponding rarefaction representation coefficient of d class sample.
The present invention has the beneficial effect that:
It is this based on transfinite learning machine and rarefaction representation classification (ELM-SRC) it is improved it is adaptive transfinite learning machine with it is sparse
The algorithm of presentation class (EA-SRC) not only discrimination with higher, but also faster pace of learning, greatly reduces calculating
Complexity.
Detailed description of the invention
Fig. 1 is flow diagram of the present invention；
Fig. 2 is Single hidden layer feedforward neural networks schematic diagram of the present invention.
Specific embodiment
Improvements of the invention are verified below with reference to specific experiment, are described below only as demonstration and explanation, and
It is intended that the present invention is limited in any way.
As depicted in figs. 1 and 2, any one database is chosen, L hidden node ginseng is randomly generated by random function first
Number (wi,bi), i=1,2 ..., L, wherein wiIt is the input weight for connecting i-th of hidden node and input neuron, biIt is i-th
The deviation of a hidden node, L are hidden node numbers.Calculate hidden layer output matrix
(1) if hidden node number is less than sample number, i.e. L≤N.In order to improve computational efficiency, to hidden layer input matrix
Carry out singular value decomposition, it is assumed that H=UDVT, wherein D=diag { d1,…di,…dNIt is diagonal matrix, diIt is i-th of matrix H
Singular value, then HHT=VD2VT, and VVT=VTV=I.The upper limit λ of adjusting parameter λ has been previously setmaxWith lower limit λmin, in λi
∈[λmin,λmax] in range, calculate separately out every layer of decomposition square HAT of HAT matrixr=HV (D2+λoptI)-1VTHT, wherein HAT
=HH+=H (HTH)-1HT.In λi∈[λmin,λmax] in range, calculate the corresponding mean square deviation of different adjusting parameter λ
Calculation formula wherein tjIt is desired output, and ojIt is actual output.It returns
Calculated Minimum Mean Square Error corresponding λ, i.e. λ in above formulaopt.Preferable Generalization Capability can be obtained at this time, and can also be most
Bigization classification boundaries.Then the output weight calculation formula for calculating connection hidden node and output neuron is as follows
(2) if hidden node number is less than sample number, i.e. L >=N.Singular value decomposition is carried out to hidden layer input matrix, it is false
If H=UDVT, wherein D=diag { d1,…di,…dNIt is diagonal matrix, diIt is i-th of singular value of matrix H, then HHT=
UD2UT, and UUT=UTU=I.The upper limit λ of adjusting parameter λ has been previously setmaxWith lower limit λmin, in λi∈[λmin,λmax] range
It is interior, calculate separately out every layer of decomposition square HAT of HAT matrixr=HHTU(D2+λoptΙ)-1UT, wherein HAT=HH+=H (HTH)-1HT,
The corresponding mean square deviation of different adjusting parameter λ, calculation formula are calculated againWherein tj
It is desired output, and ojIt is actual output.Then calculated Minimum Mean Square Error corresponding λ, i.e. λ in above formula is returnedopt。
Preferable Generalization Capability can be obtained at this time, and can also maximize classification boundaries.Calculate connection hidden node and output
The output weight of neuron
Then output vector is calculatedIf inquired in the output vector o of picture
Maximum and the difference of second largest value are greater than the threshold value being previously set, i.e. of-os> σ directlys adopt the learning machine that transfinites (ELM) and has trained
Good neural network, the corresponding index of maximum value is inquiry picture generic in output vector.If ELM output vector o
Middle maximum and the difference of second largest value are less than the threshold value being previously set, i.e. of-osIt is a most to find out preceding k in output vector o first by < σ
The corresponding index of big value, wherein d ∈ { 1,2 ... m }, then with the corresponding vector foundation of k maximum value preceding in output vector o
Adaptive sub- dictionary vectorThe rarefaction representation coefficient calculation formula of reconstruct is as follows,Wherein τ is regulation coefficient.For d=1, d < m finds out corresponding A respectivelydWithCalculate corresponding residual errorFind out the corresponding classification y of residual error minimum value, as picture
Generic.
Claims (2)
1. a kind of improved method based on transfinite learning machine and rarefaction representation classification, it is characterised in that include the following steps:
Hidden node parameter (w is randomly generated in step 1i,bi), i=1,2 ..., L, wherein wiBe i-th hidden node of connection and
Input the input weight of neuron, biIt is the deviation of i-th of hidden node, L is hidden node number；
Step 2 calculates hidden node output matrix H (w1,…wL,x1,…,xN,b1,…bi,…,bL), and
Wherein w is the input weight for connecting hidden node and inputting neuron, x1..., xNIt is training sample input, N is trained sample
This number, biIt is the deviation of i-th of hidden node, g () indicates activation primitive；
Step 3, according to the size relation of L and N, different formula is respectively adopted and calculates connection hidden node and output neuron
Output weight
Step 4, the output vector for calculating inquiry picture y
Step 5, to the maximum ο in ELM output vector οfWith second largest value οsDifference judged, and find out in output vector
The corresponding index of maximum value is inquiry picture generic；
If the maximum ο in ELM output vector οfWith second largest value οsDifference be greater than preset threshold value σ, i.e. οf-οs> σ,
The learning machine that transfinites (ELM) trained neural network is then directlyed adopt, finds out the corresponding index of maximum value in output vector i.e.
To inquire picture generic；
If the maximum ο in output vectorfWith second largest value οsDifference be less than our preset threshold values, i.e. οf-οs< σ,
The noise for then thinking that picture includes is higher, is classified using rarefaction representation sorting algorithm；
In the step 3, if the size of L and N be L <=N, i.e., hidden node number be less than or equal to sample number, then in order to
Computational efficiency is improved, singular value decomposition is carried out to hidden node output matrix, specific:
3-1. singular value decomposition H=UDVT, wherein D=diag { d1,…di,…dNIt is diagonal matrix, diIt is i-th of matrix H
Singular value, then HHT=VD2VT；Wherein U is n rank unitary matrice, and V is n rank unitary matrice；And UUT=UTU=I, VVT=VTV=I；
3-2. sets the upper limit λ of adjusting parameter λmaxWith lower limit λmin, in λi∈[λmin,λmax] in range, calculate separately out orthogonal
Every layer of decomposition square HAT of projection matrix HATr, HATr=HV (D2+λnI)-1VTHT, wherein HAT=HH+=H (HTH)-1HT；
3-3. is in λi∈[λmin,λmax] the corresponding statistics mean square error of the different adjusting parameter λ of the interior calculating of range, calculation formula are as follows:
Wherein tjIt is desired output, and οjIt is actual output；
The calculated minimum statistics mean square error of 3-4.Corresponding λ, i.e. λopt；Preferable generalization can be obtained at this time
Can, and can also maximize classification boundaries；
3-5. calculates the output weight of connection hidden node and output neuron
In the step 3, if the size of L and N is L > N, i.e. hidden node number is greater than sample number, then counts to improve
Efficiency is calculated, singular value decomposition is carried out to hidden node output matrix, specific:
3-6. singular value decomposition H=UDVT, wherein D=diag { d1,…di,…dNIt is diagonal matrix, diIt is i-th of matrix H
Singular value, then HHT=UD2UT, and UUT=UTU=I, VVT=VTV=I；
3-7. sets the upper limit λ of adjusting parameter λmaxWith lower limit λmin, in λi∈[λmin,λmax] in range, calculate separately out orthogonal
Every layer of decomposition square HAT of projection matrix HATr=HHTU(D2+λiI)-1UT, wherein HAT=HH+=H (HTH)-1HT；
3-8. is in λi∈[λmin,λmax] in range, calculate the corresponding statistics mean square error of different adjusting parameter λIt calculates
Formula are as follows:
Wherein tjIt is desired output, and οjIt is actual output；
The calculated minimum statistics mean square error of 3-9.Corresponding λ, i.e. λopt；Preferable generalization can be obtained at this time
Can, and can also maximize classification boundaries；
3-10. calculates the output weight of connection hidden node and output neuron
2. a kind of improved method based on transfinite learning machine and rarefaction representation classification as described in claim 1, it is characterised in that
Rarefaction representation sorting algorithm described in step 5 establishes adaptive sub- dictionary first with k maximum value preceding in output vector ο, so
The rarefaction representation coefficient for reconstructing training sample afterwards, finds out corresponding residual error, finally finds out the corresponding index of minimum value in residual error
The as classification that belongs to of picture, specific:
Classification corresponding to preceding k maximum value in output vector ο is found out first, then with preceding k maximum value pair in output vector ο
The vector answered establishes adaptive sub- dictionary vectorWherein m (i) ∈ { 1,2 ... m }；
Then rarefaction representation coefficient is reconstructed, formula is as follows,Wherein τ is regulation coefficient；
Finally calculate corresponding residual error
Wherein AdIt is the training sample of d class；It is the corresponding rarefaction representation coefficient of d class sample.
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| CN107369147B (en) * | 2017-07-06 | 2020-12-25 | 江苏师范大学 | Image fusion method based on self-supervision learning |
| CN107820093B (en) * | 2017-11-15 | 2019-09-03 | 深圳大学 | Information detecting method, device and receiving device based on grouping energy differences |
| CN108470337A (en) * | 2018-04-02 | 2018-08-31 | 江门市中心医院 | A kind of sub- reality Lung neoplasm quantitative analysis method and system based on picture depth feature |
| CN109902644A (en) * | 2019-03-07 | 2019-06-18 | 北京海益同展信息科技有限公司 | Face identification method, device, equipment and computer-readable medium |
| CN109934295B (en) * | 2019-03-18 | 2022-04-22 | 重庆邮电大学 | Image classification and reconstruction method based on transfinite hidden feature learning model |
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