CN109389217A - Learning method based on Jim Glassman core - Google Patents
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Abstract
The present invention provides a kind of learning methods based on Jim Glassman core, comprising the following steps: for each point in Grassmann manifold, multiple leading role's degree vectors between the point and another point are obtained using sub-space analysis method；For each of the multiple leading role's degree vector, construction portion Jim Glassman core, wherein the part Jim Glassman core is the nuclear matrix that the product of cosine function and respective weights based on each leading role's degree vector is constituted；The part Jim Glassman core is combined, whole Jim Glassman core is obtained；Using core target alignment method, learn the respective weights in the whole Jim Glassman core.Present invention firstly provides the weight coefficients for learning above-mentioned whole Jim Glassman core with core target alignment method, and since core objective matrix is using the matrix of data tag information construction, learning obtained weight coefficient has optimal identification.
Description
Technical field
The present invention relates to machine learning field more particularly to a kind of learning methods based on Jim Glassman core.
Background technique
With the outburst of deep learning, neural network becomes hot spot concerned by people again.Traditional data analysis is to abide by
From Euclidean space it is assumed that the vector of i.e. expression data, is a point on dimensional Euclidean Space, the distance between point-to-point can
To be indicated with Euclidean distance.Data analysing method in recent years indicates that the point in most higher dimensional spaces is really low embedded in one
Tie up the point in manifold.And manifold at this moment, from global angle no longer defer to Euclidean space it is assumed that only each put office
Portion space meets the requirement of Euclidean space.Grassmann manifold is a kind of special manifold, and the original representation of data is square
Battle array, rather than general vector.The present invention is exactly to propose a kind of differentiation core study side on the basis of Grassmann manifold analysis
Method.Its research belongs to machine learning and the field of data mining.Technology relevant with its includes that Grassmann manifold analysis and lattice are drawn
This graceful discriminant analysis.
Grassmann manifold G (m, D) is m- dimensional linear subspace RDSet.One in such Grassmann manifold
Point can be indicated with the orthogonal matrix of a D × m.
In general Grassmann manifold analysis, the distance measure of two point A and B is using the most short geodesic distance between two o'clock
From i.e. dG(A, B)=| | Θ | |2=(Σi(θi)2)1/2.Wherein Θ=[θ1,θ2,...,θd] it is using two matrixes of A and B as son
Leading role's degree vector when space between two sub-spaces.Wherein each leading role's degree 0 to 90 degree between and θ1<θ2<...<
θd.Or other distances based on leading role's degree vector are used, such as mapping distance (Projection distance) dproj(A,B)
With
Binet-Cauchy distance dBC(A,B)。
dproj(A, B)=(Σi(sinθi)2)1/2=1/2 | | AA'-BB'| |F 2 (1)
dBC(A, B)=(1- Πi(cosθi)2)1/2=1- (det (A'B))2 (2)
In terms of Jim Glassman core angle, for mapping distance (Projection distance) dproj(A, B) and Binet-
Cauchy distance dBC(A, B), presently, there are two kinds of nuclear matrix, i.e. KprojAnd KBC, they can be defined as follows:
Kproj(A, B)=tr (AA'BB')=| | AB'| |F 2 (3)
KBC(A, B)=(det (A'B))2 (4)
Jim Glassman discriminant analysis is that core linear discriminant analysis method is used for Jim Glassman kernel function.Linear discriminant analysis
Core concept be that is found by a kind of combination α Φ, makes feature after reconfiguring by original training data character representation Φ
In space, class scatter SBBecome larger and divergence S in classWBecome smaller.By geo-nuclear tracin4, following target can be established by kernel function K
Function:
Wherein K be training data feature nuclear matrix, 1NIt is complete 1 vector that a length is N, V is pair of a piecemeal
Angle battle array, wherein c-th piece is one 1Nc1'Nc/ Nc, and δ2INTo make to calculate the stable regular factor.α is combination system to be estimated
Number.
Grassmann manifold is a kind of special manifold structure, each data point in the manifold with a matrix rather than
Vector indicates.In the distance put on calculating Grassmann manifold at present, leading role usually is obtained using subspace analysis method
Vector is spent, carries out subsequent analysis on this basis.Presently, there are the distance measure based on leading role's degree, such as mapping distance
(Projection distance)dproj(A, B) and Binet-Cauchy distance dBC(A, B) is all directly by each leading role's degree
The influence of component bring is handled according to identical weight, and in formula (1) and (2), overall estimating is each leading role's degree
θpSine or cosine function and.
The problem of handling in this way is, the weight of each main angle component has been previously set, and can not be according to different
Using being adjusted, different types of data cannot be well adapted for.
Summary of the invention
The invention proposes the concepts of part Jim Glassman core, and assume the weighted of each leading role's degree, are made
Whole Jim Glassman core is obtained for unknown parameter to be learned, by way of core target alignment, estimation obtains weighted value.
The present invention provides a kind of learning methods based on Jim Glassman core, comprising the following steps: (a) is directed to Jim Glassman
Each point in manifold obtains multiple leading role's degree vectors between the point and another point using sub-space analysis method；(b) for institute
State each of multiple leading role's degree vectors, construction portion Jim Glassman core；(c) group is carried out to the part Jim Glassman core
It closes, obtains whole Jim Glassman core；(d) core target alignment method is utilized, the respective weights in the whole Jim Glassman core are learnt.
The present invention proposes that partitive case is drawn using the cosine function of leading role's degree to analyze the effect of each main angle component
This graceful core KpConcept, and assume the weighted of each leading role's degree, obtained as unknown parameter to be learned whole
Body Jim Glassman core Kμ, by way of core target alignment, estimation obtains weighted value, and this method is expanded to non-linear
Situation.
The present invention proposes the concept of part Jim Glassman core for the first time, only related with leading role's degree.And whole lattice
Relationship between the graceful kernel function in Lars and part Jim Glassman core is
Kμ(A, B)=Σpμpcos(θp) (6)
Wherein μ=[μ1,μ2,μp,...,μd] it is unknown weight to be learned.
The present invention uses core target alignment method to learn the weight coefficient of above-mentioned whole Jim Glassman core for the first time, due to core mesh
Mark matrix is the matrix constructed using data tag information, therefore the weight coefficient that study obtains has optimal identification.
In the present invention, whole Jim Glassman core is using core target alignment method, and adjusting parameter makes the target of itself and construction
Nuclear matrix reaches consistent and determining.Since core objective matrix is learnt using the matrix of data tag information construction
The weight coefficient arrived has optimal identification.
Detailed description of the invention
Fig. 1 is the flow chart of the learning method of the invention based on Jim Glassman core.
Fig. 2 is the flow chart of the first embodiment of learning method of the invention.
Fig. 3 is the flow chart of the second embodiment of learning method of the invention.
Specific embodiment
Technical solution in order to enable those skilled in the art to better understand the present invention, with reference to the accompanying drawing and specific embodiment party
The learning method provided by the invention based on Jim Glassman core is described in detail in formula.In the drawings, for identical or
The comparable constituent element of person, marks identical label.It is below only the best of the learning method of the invention based on Jim Glassman core
Embodiment, the present invention are not limited in following structures.
Illustrate the learning method of the invention based on Jim Glassman core referring to Fig. 1.
As shown in Figure 1, the learning method of the invention based on Jim Glassman core is the following steps are included: be directed to Jim Glassman stream
Each point in shape obtains multiple leading role's degree vectors (S100) between the point and another point using sub-space analysis method；For
Each of multiple leading role's degree vectors, construction portion Jim Glassman core (S102), wherein part Jim Glassman core is each
The cosine function of leading role's degree vector and the product of respective weights；Part Jim Glassman core is combined, whole Jim Glassman is obtained
Core (S104)；Using core target alignment method, learn the respective weights (S106) in whole Jim Glassman core.
The whole Jim Glassman kernel function that the present invention constructs are as follows:
To part Jim Glassman core KpCentralization is carried out, following matrix is obtained
Pass through the part Jim Glassman core of centralizationAvailable centralization entirety Jim Glassman core
The selection principle of whole Jim Glassman nuclear parameter μ is that following objective functions is made to reach maximum:
Target nuclear matrix KTIt is as follows:
KT=YYT (10)
Wherein Y is the label vector of N number of data point, constructs as follows, Y=[y1,...,yi,...,yN]T, yiIt is one long
Degree is the binary vector of classification number, such as yiCorresponding sample XiFor c-th of class label, then yi=[0 ... 0,1,0 ...],
Wherein 1 position occurred is c.
Formula (7) indicates the linear combination relationship between whole Jim Glassman core and part Jim Glassman core, and the present invention is into one
Step is by the linear combination relational extensions of (7) to nonlinear combination, i.e., its nonlinear combination relationship is
After also passing through centralization, estimated using weight of the core target alignment method to nonlinear weight.
The learning method of the invention based on Jim Glassman core is illustrated below with reference to embodiment one and two.
[first embodiment]
Assuming that { X1,...,Xi,...,XNIt is N number of point in Grassmann manifold, wherein each point XiIt is all a square
Battle array, rather than a vector.The present invention constructs the part Jim Glassman core about this N number of point, by part Jim Glassman core
Linear and nonlinear is carried out to combine to form whole Jim Glassman nuclear matrix Kμ, by core target alignment method, estimate parameter μ.
First embodiment is whole Jim Glassman nuclear matrix K in linear combinationμEstimate parameter μ process.It is detailed referring to Fig. 2
Describe bright specific steps in detail.
Step 1: by the point X in each Grassmann manifoldiOrthogonalization process；
Step 2: calculating section Jim Glassman core: Kp(Xi,Xj)=cos (θp), wherein θpFor XiAnd XjBetween p-th of master
Angle.It can be obtained by SVD singular value decomposition, and process is as follows:
XiXj T=Ucos (Θ) VT (12)
Wherein cos (Θ)=diag (cos (θ1),...,cos(θp),...,cos(θd)) (13)
Step 3: part Jim Glassman nuclear matrix centralization:
And
Λ=I-11T/N (15)
Wherein I is unit diagonal matrix, and 1 is complete 1 vector, and N is the number of sample point.
Step 4: calculating target nuclear matrix KTIt is as follows:
KT=YYT (16)
Wherein Y is the label vector of N number of data point, constructs as follows, Y=[y1,...,yi,...,yN]T, yiIt is one long
Degree is the binary vector of classification number, such as yiCorresponding sample XiFor c-th of class label, then yi=[0 ... 0,1,0 ...],
Wherein 1 position occurred is c.
Step 5: the α vector that construction length is d is as follows:
WhereinIndicate two matrix F robenius inner products
Step 6: the Metzler matrix that construction size is d × d is as follows:
Step 7: full to the estimation of the parameter μ of entirety Jim Glassman nuclear matrix made of the Jim Glassman core linear combination of part
The majorized function in foot face:
Wherein
Its solution is
[second embodiment]
In the present invention, second embodiment is whole Jim Glassman nuclear matrix K in nonlinear combinationμEstimate the mistake of parameter μ
Journey.Specific steps are described in detail referring to Fig. 3.
Step 1: by the point X in each Grassmann manifoldiOrthogonalization process；
Step 2: calculating section Jim Glassman core: Kp(Xi,Xj)=cos (θp), wherein θpFor XiAnd XjBetween p-th of master
Angle.It can be obtained by SVD singular value decomposition, and process is as follows:
XiXj T=Ucos (Θ) VT (22)
Wherein
Cos (Θ)=diag (cos (θ1),...,cos(θp),...,cos(θd)] (23)
Step 3: carrying out nonlinear extensions to part Jim Glassman core, (here for expanding to second order, other high-orders expand
Open up similar), part Jim Glassman core set at this moment are as follows:
KS={ K1,…,Kd,Kd+1,…,KD}={ K1,…,Kd,K1·K1,…,K1·Kd,K2·K2,…,K2·Kd,
K3·K3,…,K3·Kd,…,Kd·Kd} (24)
At this moment the number of the graceful core in partitive case Lars is in set
Step 4: centralization is carried out to each in D part Jim Glassman nuclear matrix set after extension:
And
Λ=I-11T/N (26)
Wherein I is unit diagonal matrix, and 1 is complete 1 vector, and N is the number of sample point.
Step 5: calculating target nuclear matrix KTIt is as follows:
KT=YYT (27)
Wherein Y is the label vector of N number of data point, and construction is as follows,yiIt is one long
Degree is the binary vector of classification number, such as yiCorresponding sample XiFor c-th of class label, then yi=[0 ... 0,1,0 ...],
Wherein 1 position occurred is c.
Step 6: the α vector that construction length is D is as follows:
WhereinIndicate two matrix F robenius inner products.
Step 7: the Metzler matrix of construction D × D is as follows:
Step 8: to the parameter μ of entirety Jim Glassman nuclear matrix made of the Jim Glassman core set nonlinear combination of part
Estimation meets following majorized function
Wherein
Its solution is
Combine two embodiments that the principle of learning method of the invention is described in detail above.Below with reference to experiment
To illustrate the effect of this learning method.
In an experiment, the video data of movement is analyzed.
1) Grassmann manifold of initial data indicates.
In video data, video is separated into segment according to content, feature is extracted to the frame in each segment, it can be with
It is CNN feature or HOG feature, time pond then is carried out to each segment, each segment is indicated with a vector, this
Sample is indicated that is, each video is a point in Grassmann manifold by the video of several segments with a matrix.
2) learning process: the label Y=[y of known training data1,...,yi,...,yN] and training data { X1,...,
Xi,...,XN, seek the coefficient μ in whole Jim Glassman core.The study side according to the invention under linear and nonlinear situation
Method acquires weight vectors μ respectively.
3) obtain the whole Jim Glassman core of training data: the weight vectors μ obtained according to study acquires training data
Whole Jim Glassman core.
4) obtain the whole Jim Glassman core of test data: the weight vectors μ obtained according to study acquires test data
Whole Jim Glassman core.
5) Classification and Identification task is completed using LibSVM.Recognition result is in table 1.
Table 1
In table 1, YouTube, Penn Action, UCF50 and UCF101 be in the prior art action recognition using more
Database.Its initial data is the different video of length, by each representation of video shot at a point in Grassmann manifold,
Identifying system is constructed according to above-mentioned steps, the results are shown in Table 1 for discrimination.
The case where in table 1, " uniform " each weight of expression is identical, is 1.It is " linear " indicate to part Jim Glassman core into
The whole Jim Glassman nuclear matrix that row linear weighted function obtains.And (2) and (3) under nonlinear situation respectively indicate and draw partitive case
This graceful core carries out 2 ranks and the extension of 3 ranks.
In the following, illustrating the effect of learning method of the invention in conjunction with table 2-5.
Table 2 lists learning method of the invention (DGK) and performance comparison of other schemes on YouTube database.
As can be seen that the learning method of the invention based on part Jim Glassman core obtains higher precision compared to other schemes.
Table 2
Table 3 lists learning method of the invention (DGK) and performance pair of other schemes on Penn Action database
Than.As can be seen that the learning method of the invention based on part Jim Glassman core obtains higher essence compared to other schemes
Degree.
Table 3
Table 4 lists learning method of the invention (DGK) and performance comparison of other schemes on UCF50 database.It can
To find out, compared to other schemes, the learning method of the invention based on part Jim Glassman core obtains higher precision.
Table 4
Table 5 lists learning method of the invention (DGK) and performance comparison of other schemes on UCF101 database.It can
To find out, compared to other schemes, the learning method of the invention based on part Jim Glassman core obtains higher precision.
Table 5
The present invention utilizes the cosine function composition part Jim Glassman core of each leading role's degree, and utilizes core target alignment side
The weight coefficient of method the estimating part linear combination of Jim Glassman core and nonlinear combination, thus obtains whole Jim Glassman core.
Core objective matrix is substantially the nuclear matrix for utilizing label information to construct, and in core target alignment method, weight
Selection gist be that the whole Jim Glassman nuclear matrix generated and the degree of correlation of core objective matrix is made to reach maximum.It is namely each
A main angle component it is important whether (size of weight), be to be learnt by given training data, due to core target
Matrix inherently utilizes the label information of data to construct, therefore reaches by adjusting weight coefficient and have with core objective matrix
The whole Jim Glassman nuclear matrix of maximum relation degree has optimal identification.
Principle that embodiment of above is intended to be merely illustrative of the present and the illustrative embodiments used, however this hair
It is bright to be not limited thereto.For those skilled in the art, in the feelings for not departing from spirit and substance of the present invention
Under condition, various changes and modifications can be made therein.These variations and modifications are also considered as protection scope of the present invention.
Claims (8)
1. a kind of learning method based on Jim Glassman core, comprising the following steps:
(a) it for each point in Grassmann manifold, is obtained using sub-space analysis method multiple between the point and another point
Leading role's degree vector；
(b) for each of the multiple leading role's degree vector, construction portion Jim Glassman core, wherein the partitive case is drawn
This graceful core is the nuclear matrix of the product construction of cosine function and respective weights based on each leading role's degree vector；
(c) the part Jim Glassman core is combined, obtains whole Jim Glassman core；
(d) core target alignment method is utilized, the respective weights in the whole Jim Glassman core are learnt.
2. learning method according to claim 1, wherein step (b) the following steps are included:
(b1) orthogonalization process is carried out to each point in the Grassmann manifold；
(b2) centralization is carried out to the part Jim Glassman core；
(b3) target nuclear matrix is constructed.
3. learning method according to claim 2, wherein step (d) includes: the suitable weight of selection, makes the entirety
The degree of correlation of Jim Glassman core and the target nuclear matrix maximizes.
4. learning method according to claim 3, wherein step (c) includes: non-to part Jim Glassman core progress
Linear combination.
5. learning method according to claim 2, wherein the target nuclear matrix is
KT=YYT
Wherein Y is the label vector of N number of data point, Y=[y1,...,yi,...,yN]T, yiIt is two that a length is classification number
System vector.
6. learning method according to claim 3, wherein make the whole Jim Glassman core and the target nuclear matrix
It includes estimating the respective weights that the degree of correlation, which maximizes, is allowed to meet following majorized function:
Wherein
Centered on change after p-th of part Jim Glassman core
Its solution is
Metzler matrix is
α vector is as follows:
7. learning method according to claim 4, wherein make the whole Jim Glassman core and the target nuclear matrix
It includes estimating the respective weights that the degree of correlation, which maximizes, is allowed to meet following majorized function:
Wherein
After to former part nuclear matrix nonlinear extensions, then p-th of part Jim Glassman core after centralization is carried out, middle part
Collect after pyrene matrix nonlinear extensions and is combined into
KS={ K1,…,Kd,Kd+1,…,KD}
={ K1,…,Kd,K1·K1,…,K1·Kd,K2·K2,…,K2
·Kd,K3·K3,…,K3·Kd,…,Kd·Kd}
Its solution is
Metzler matrix is
α vector is as follows:
8. a kind of computer readable storage medium is stored with program, following step can be realized when described program is executed by processor
It is rapid:
(a) it for each point in Grassmann manifold, is obtained using sub-space analysis method multiple between the point and another point
Leading role's degree vector；
(b) for each of the multiple leading role's degree vector, construction portion Jim Glassman core, wherein the partitive case is drawn
This graceful core is the nuclear matrix of the product building of cosine function and respective weights based on each leading role's degree vector；
(c) the part Jim Glassman core is combined, obtains whole Jim Glassman core；
(d) core target alignment method is utilized, the respective weights in the whole Jim Glassman core are learnt.
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