CN109389127A - Structuring multiple view Hessian regularization sparse features selection method - Google Patents
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Abstract
The invention discloses a kind of structuring multiple view Hessian regularization sparse features selection methods, the following steps are included: the bottom visual signature of n original image of acquisition, obtain m view image eigenmatrix, if the feature selecting mapping matrix of X is variable G, construct the objective function of structuring multiple view Hessian regularization sparse features selection, the feature selecting mapping matrix G that X is calculated by iterative algorithm, according to gained feature selecting mapping matrix Gt, willDescending arrangement is carried out, ds before choosingFeature corresponding to X is as the character subset after feature selecting.The present invention is when carrying out semi-supervised feature selecting to multiple view data, not only consider the importance of each view, the importance of different characteristic under same view is also considered simultaneously, in addition, the performance of semi-supervised sparse features selection is further improved using multiple view Hessian regularization, therefore, the present invention has better feature selecting performance.
Description
Technical field
The invention belongs to semi-supervised sparse features selection technique fields, relate in particular to a kind of structuring multiple view
Hessian regularization sparse features selection method.
Background technique
In order to better understand, search for and image data of classifying, many visual signatures are suggested, such as shape feature, face
Color characteristic, textural characteristics etc..The feature of each type is all that image data is described from a certain particular space, and has
Specific physical significance and statistical property.For traditionally, the feature of each type can be counted as a view, therefore by
The data of different types of character representation are referred to as multiple view data.The effective information for how obtaining multiple view data, which becomes, works as
One research hotspot of preceding feature selecting analysis field.
A kind of most straightforward approach is exactly that multiple view data are directly concatenated into a long feature vector, this method letter
It is single, but this mode directly concatenated destroys the potential association between different views feature significantly, while also lacking physical solution
It releases.
In order to overcome the shortcomings of directly to concatenate multiple view data, in recent years, multiple view study is widely studied, and is applied to
Among feature selecting analysis.These methods can be effectively using the complementarity and relevance between different views feature, together
When think that all feature importance having the same under same view, all features under same view are endowed identical power
Weight.However in fact, the different characteristic under same view has different importance.
Therefore, it not only needs to consider the importance of each view when feature selecting, while needing to consider same
The importance of different characteristic under view, this further can select performance by lifting feature.Recently, there is a few thing to this progress
It attempts, Wang et al. proposes a group l1Norm (G1Norm), one is proposed based on the sparse regularization of co-ordinative constructionization based on this
The sparse Multimodal Learning method of supervision carry out heterogeneous feature integration, it is also proposed that non-supervisory more views of all features of integration
Figure learning model.
Ability is preferably inferred since Hessian regularization has than figure Laplace regularization, Hessian is just
Then changing has better semi-supervised learning ability.In recent years, the semi-supervised feature selection approach based on Hessian regularization is mentioned
Out, however, these semi-supervised feature selection approach do not have during constructing Hessian regularization when facing multiple view data
There are fine consideration multiple view data characteristics, has ignored the association between different views feature and complementary characteristic.
Summary of the invention
In view of the deficiencies of the prior art, the object of the present invention is to provide a kind of structuring multiple view Hessian regularization is dilute
Dredge feature selection approach.
For this purpose, technical scheme is as follows:
A kind of structuring multiple view Hessian regularization sparse features selection method, comprising the following steps:
1) the bottom visual signature for acquiring n original image, obtains m view image eigenmatrix, wherein
The m view image eigenmatrix are as follows:
In the formula (1), the dvFor v-th of view image characteristic dimension；The XvIt is special for v-th of view image
Matrix is levied, and
In the formula (2), x1 v,x2 v…,xl vThere is label figure for l under v-th of view in the n original image
The feature vector of picture, xl+1 v,…,xn vFor the features without label image of n-l under v-th of view in the n original image to
Amount；
In the step 1), the bottom visual signature includes: color correlogram, wavelet texture and edge direction histogram
Figure.
2) the feature selecting mapping matrix of the step 1) X is set as variable G, and:
In the formula (3), the c is the classification number of the label of the n original image；
Construct the objective function of structuring multiple view Hessian regularization sparse features selection:
In the formula (4):
For the sparse restriction of structuring multiple view, wherein λ and γ is regularization coefficient, the λ
Value range with γ is [10-5, 105]；For the G of the G1Norm,
For the l of the G2,1/2Matrix norm, gi'=[g1 i' … gc i']∈R1×c, 1≤i'≤d,
H is multiple view Hessian,
In formula (4) and (5), HvFor v-th of view Hessian；Variable F is the pre- mark of the n original image
Matrix is signed,For multiple view Hessian regularization；ηvIt is v-th in multiple view Hessian regularization
The weight of view Hessian；The ε is ηvIndex, ε > 1；
For loss function；
μ is regularization coefficient, and the value range of the μ is [10-5, 105]；
Y=[y1,y2…,yl,yl+1,…,yn]T∈{0,1}n×cFor the label matrix of the n original image；
Diagonal matrix U ∈ Rn×nFor the decision rule matrix determined according to the X, U=(Ui”i”)n×n, 1≤i "≤n, when 1
When≤i "≤l, diagonal element Ui”i”=∞, as l < i "≤n, diagonal element Ui”i”=1；
In the step 2), FvFor the prediction label matrix of v-th of view, Fv∈Rn×c。
3) the feature selecting mapping matrix G that the X is calculated by iterative algorithm, if GsFor the value of the G in the secondary iteration,
ηvsFor the η in the secondary iterationvValue, s=1,2 ... ..., t-1；If G1For random matrix and ηv1=1/m, by G1And ηv1As
Initial value substitutes into the iterative algorithm and is iterated calculating, until after the t-1 times iteration, corresponding to the t-1 times iteration
The value of objective function is poor less than 10 with the value of objective function corresponding to the t-2 times iteration-3When, iteration is completed；At this point, according to
(gi)tDetermine feature selecting mapping matrix GtThe feature selecting mapping matrix G of the as described X；Wherein,
The calculating process of each iterative algorithm are as follows:
By ηvsThe formula (5) are substituting to, the value H of the H in the secondary iteration is obtaineds,
By GsAnd HsIt substitutes into corresponding formula (6) and P is calculated in (7)sAnd Qs；
Ps=(Hs+U+μI)-1 (6)
Qs=UY+ μ XTGs (7)
F is calculated according to formula (8), (9) and (10)s、AsAnd Bs, FsFor the value of the F in the secondary iteration；
Fs=PsQs (8)
As=X (μ I- μ2Ps T)XT (9)
Bs=μ XPsUY (10)
Wherein, the I described in formula (6) is unit matrix；
It is (w that diagonal element, which is calculated, according to formula (11) and (12)i'i')sDiagonal matrix WsWith with j diagonal blocks
Block diagonal matrix (Di)s(1≤i≤c)；
Wherein,
In the formula (12), IjIt is the unit matrix that dimension is j*j；
By As、Bs、Ws(Di)sThe formula (13) are substituted into, (g is obtainedi)s+1；
(gi)s+1=(As+4λWs+γ(Di)s)-1Bs,1≤i≤c (13)
It calculates
4) according to feature selecting mapping matrix G obtained by step 3)t, will1≤i'≤d carries out descending arrangement, chooses
Preceding dsFeature corresponding to the X is as the character subset after feature selecting, whereinFor G obtained by step 3)t
Corresponding gi′。
Compared with the prior art, the invention proposes a kind of selections of structuring multiple view Hessian regularization sparse features
Method (Structured Multi-view Hessian sparse Feature Selection, SMHFS) faces multiple view
When data, this method, which is based on the sparse regularization of structuring multiple view, to be made not only to consider each during semi-supervised feature selecting
The importance of view, while considering the importance of different characteristic under same view.In addition, SMHFS is utilizing multiple view Hessian just
Then change and further improves the performance of semi-supervised sparse features selection.Experimental evaluation is the result shows that SMHFS is better than existing feature
Selection algorithm has better feature selecting performance.
Detailed description of the invention
Fig. 1 (a) is Average Accuracy mean value (Mean Average Precision, MAP) property on NUS-WIDE database
The curve that can change with the variation for having label data percentage；Fig. 1 (b) be on MSRA-MM database MAP performance with having
The variation of label data percentage and the curve changed；
Fig. 2 (a) is by proposing method SMHFS and method MLSFS performance with selection number of features on NUS-WIDE database
The variation of ds and the curve changed；Fig. 2 (b) by mentioned on MSRA-MM database method SMHFS and method MLSFS performance with
The curve for selecting the variation of number of features ds and changing；
Fig. 3 (a) is by proposing method SMHFS and method SMML and SFUS performance with selection feature on NUS-WIDE database
The variation of number ds and the curve changed；Fig. 3 (b) is by mentioning method SMHFS and method SMML and SFUS on MSRA-MM database
The curve that performance changes with the variation of selection number of features ds.
Specific embodiment
Structuring multiple view Hessian regularization sparse features selection method of the invention is carried out with reference to the accompanying drawing detailed
It describes in detail bright, comprising the following steps:
1) the bottom visual signature for acquiring n original image, obtains m view image eigenmatrix, wherein
The m view image eigenmatrix are as follows:
In the formula (1), the dvFor v-th of view image characteristic dimension；The XvIt is special for v-th of view image
Matrix is levied, and
In the formula (2), x1 v,x2 v…,xl vThere is label image for l under v-th of view in the n original image
Feature vector, xl+1 v,…,xn vFor n-l under v-th of view in the n original image feature vectors without label image；
In the step 1), the bottom visual signature includes: color correlogram, wavelet texture and edge direction histogram
Figure extracts these three bottom visual signatures, i.e., the wavelet texture of the color correlogram of 144 dimensions, 128 dimensions to each image pattern
The edge orientation histogram that (MSRA-MM database) is tieed up with 73 dimensions (NUS-WIDE database) or 75, therefore, in two images
The dimension d of the multi-view image feature set obtained on database is respectively 345 dimensions or 347 dimensions.
2) the feature selecting mapping matrix of the step 1) X is set as variable G, and:
In the formula (3), the c is the classification number of the label of the n original image；
Construct the objective function of structuring multiple view Hessian regularization sparse features selection:
In the formula (4):
(it is located at ‖ G ‖ for sparse limit of structuring multiple view2,1/2The 1/2 of the upper right corner is index), it should
The sparse restriction of structuring multiple view can guarantee the importance that each view is not only considered during feature selecting, simultaneously
The importance of different characteristic in each view is considered, to reach good feature selecting performance.
Wherein, λ and γ is regularization coefficient, and the value range of the λ and γ are [10-5, 105]；
For the G of the G1Norm,For the l of the G2, 1/2 matrix norm, gi'=[g1 i' … gc i']∈
R1×c, 1≤i'≤d, selection l2,1/2Matrix norm can guarantee the feature most identification chosen；
H is multiple view Hessian,
In corresponding formula (4) and (5), HvFor v-th of view Hessian；Variable F is the n original image
Prediction label matrix,For multiple view Hessian regularization, it is contemplated that between different views feature
Association and complementary characteristic, while there is better semi-supervised learning ability.ηvIt is v-th in multiple view Hessian regularization
The weight of view Hessian；The ε is ηvIndex, ε > 1；Parameter ε is introduced, guarantees that each view selects final feature
Specific contribution is selected.It is special that multiple view Hessian regularization can make full use of the complementary information between different views to be promoted
Sign selection performance, while Hessian regularization has preferably deduction ability than figure Laplace regularization, to have more preferable
Semi-supervised learning ability.
For loss function；
μ is regularization coefficient, and the value range of the μ is [10-5, 105]；
Y=[y1,y2…,yl,yl+1,…,yn]T∈{0,1}n×cFor the label matrix of the n original image；
Diagonal matrix U ∈ Rn×nFor the decision rule matrix determined according to the X, U=(Ui”i”)n×n, 1≤i "≤n, when 1
When≤i "≤l, diagonal element Ui”i”=∞, as l < i "≤n, diagonal element Ui”i”=1；Guarantee the label matrix of prediction
F is consistent with existing label matrix Y.(method of determining decision rule matrix is shown in: " Z.G.Ma, F.P.Nie, Y.Yang,
J.Uijlings,N.Sebe,and A.Hauptmann,“Discriminating joint feature analysis for
multimedia data understanding,”IEEE Trans.Multimedia,vol.14,no.6,pp.1662–
1672,Dec.2012.”)
In the step 2), FvFor the prediction label matrix of v-th of view, Fv∈Rn×c。
3) the feature selecting mapping matrix G that the X is calculated by iterative algorithm, if GsFor the value of the G in the secondary iteration,
ηvsFor the η in the secondary iterationvValue, s is the number of iterations, s=1,2 ... ..., t-1；If G1For random matrix and ηv1=1/m,
By G1And ηv1It is substituted into the iterative algorithm as initial value and is iterated calculating, until this is the t-1 times after the t-1 times iteration
The value of objective function corresponding to iteration is poor less than 10 with the value of objective function corresponding to the t-2 times iteration-3When, iteration is complete
At；At this point, according to (gi)tDetermine feature selecting mapping matrix GtThe feature selecting mapping matrix G of the as described X；Wherein,
The calculating process of each iterative algorithm are as follows:
By ηvsThe formula (5) are substituting to, the value H of the H in the secondary iteration is obtaineds,
By GsAnd HsIt substitutes into corresponding formula (6) and P is calculated in (7)sAnd Qs(PsAnd QsThe respectively P in the secondary iteration
With the value of Q)；
Ps=(Hs+U+μI)-1 (6)
Qs=UY+ μ XTGs (7)
F is calculated according to formula (8), (9) and (10)s、AsAnd Bs, FsFor the value of the F in the secondary iteration；
Fs=PsQs (8)
As=X (μ I- μ2Ps T)XT (9)
Bs=μ XPsUY (10)
Wherein, AsAnd BsRespectively in the secondary iteration A and B value, in the formula (6) I be unit matrix；
It is (w that diagonal element, which is calculated, according to formula (11) and (12)i'i')sDiagonal matrix WsWith with j diagonal blocks
Block diagonal matrix (Di)s(1≤i≤c)；
Wherein,
In the formula (12), IjIt is the unit matrix that dimension is j*j；
By As、Bs、Ws(Di)sThe formula (13) are substituted into, (g is obtainedi)s+1；
(gi)s+1=(As+4λWs+γ(Di)s)-1Bs,1≤i≤c (13)
It calculates
It 4), will according to feature selecting mapping matrix Gt obtained by step 3)1≤i'≤d carries out descending arrangement, chooses
Preceding dsFeature corresponding to the X is as the character subset after feature selecting, whereinFor G obtained by step 3)t
Corresponding gi′, ds is characterized selection number.(quotation " Z.G.Ma, F.P.Nie, Y.Yang, J.Uijlings, N.Sebe, and
A.Hauptmann,“Discriminating joint feature analysis for multimedia data
understanding,”IEEE Trans.Multimedia,vol.14,no.6,pp.1662–1672,Dec.2012.”)
The property of semi-supervised sparse features selection is carried out to verify the mentioned SMHFS algorithm of the present invention in face of multiple view data
Can, by it and other 4 kinds semi-supervised sparse features selection algorithm SMBLR (Sparse Multinomial Logistic
Regression via Bayesian L1Regularization, Bayes l1Regularization sparse polynomial logistic regression is calculated
Method), FSNM (Feature Selection via Joint l2,1- Norms Minimization combines l2,1Norm minimum
Feature selecting algorithm), FSLG (Feature Selection based on Graph Laplacian, based on figure Laplce
Semi-supervised sparse features selection algorithm), MLSFS (Multi-view Laplacian Sparse Feature Selection,
The semi-supervised feature selecting algorithm of multiple view Laplce) and 2 kinds of supervision feature selecting algorithm SFUS (Sub-Feature
Uncovering with Sparsity, the subcharacter discovery based on sparsity) and SMML (Sparse Multi-Modal
Learning, sparse Multimodal Learning) test and has compared.Wherein semi-supervised feature selecting algorithm SMBLR, FSNM, FSLG
It is directly to concatenate multiple view data to be when carrying out feature selecting to multiple view data with supervision feature selecting algorithm SFUS
One long feature vector；Semi-supervised feature selection approach MLSFS is considered not when carrying out feature selecting to multiple view data
With the complementary characteristic between view, each view is considered as a whole；Feature selection approach SMML is supervised to multiple view
The importance of different views and the importance of different characteristic under same view are considered when data carry out feature selecting simultaneously.
Experiment carries out on two image data bases NUS-WIDE and MSRA-MM, using three kinds of bottom multiple view features, i.e.,
Color correlogram, wavelet texture and edge orientation histogram.For semi-supervised feature selection approach, have shared by label data
Percentage is respectively 5%, 10%, 20%, 50%.In order to preferably assess the performance of feature selecting algorithm, 5 kinds of assessments are used
Criterion: bat mean value MAP, recall rate Recall, accurate rate Precision, MicroAUC and MacroAUC.In order to test
Characteristics of syndrome selects influence of the number to performance, and feature selecting number ds is respectively set as 100,150,200,250,300 and whole.
Regularization parameter μ, λ and γ are set separately in experiment are as follows: μ=10 on NUS-WIDE database, λ=100000, γ=1；
μ=1000 on MSRA-MM database, λ=100000, γ=1.Rule of thumb, parameter ε is set as 1010.Each experiment is equal
It does 10 times, takes average result as the final result of experiment.
Mentioned algorithm SMHFS and other 4 kinds semi-supervised sparse features algorithms are compared in experiment, comparison result is such as
Shown in Fig. 1, Tables 1 and 2.From comparison result it follows that no matter having how the percentage of label data changes, mentioned algorithm
SMHFS has best performance.
1 performance of table compares (NUS-WIDE database)
2 performance of table compares (MSRA-MM database)
In addition, SMHFS is compared with other 2 kinds of supervision feature selecting algorithm in experiment, set in SMHFS has at this time
Label data percentage is 100%, and the results are shown in Table 3.The experimental results showed that mentioned algorithm SMHFS is with best
Feature selecting performance.
3 performance of table compares
In summary, when facing multiple view data, mentioned algorithm SMHFS has better feature selecting performance, mainly returns
Because in following three points: firstly, SMHFS carries out feature choosing by the building sparse regularization of structuring multiple view, to multiple view data
The importance of different views and the importance of different characteristic under same view can be considered when selecting simultaneously；Secondly, more by constructing
View Hessian regularization considers the complementarity between different views, further improves the performance of semi-supervised feature selecting；Most
Afterwards, since SMHFS algorithm is based on l2,1/2Matrix norm, it can guarantee the feature most identification chosen.
In order to verify influence of the selection number of features ds to performance, ds is respectively set as 100,150,200,250,300
It is tested with whole.In addition also SMHFS algorithm and semi-supervised feature selection approach MLSFS are compared respectively, it will
SMHFS algorithm is compared with supervision feature selection approach SFUS and SMML.Experimental result is as shown in Figures 2 and 3, You Tuke
To obtain as drawn a conclusion:
1) when the number of features ds selected is 250, SMHFS has best performance；
2) for SMHFS algorithm compared with other algorithms, the performance of SMHFS is better than other algorithms.
Experimental result illustrates to mention again based on the sparse regularization of structuring multiple view and multiple view Hessian regularization
SMHFS algorithm can preferably carry out feature selecting when facing multiple view data, obtain good feature selecting performance.
The present invention constructs the sparse regularization of structuring multiple view, guarantees to consider simultaneously in feature selection process each
The importance of different characteristic under the importance of a view and same view, to obtain better feature selecting performance.Meanwhile
This method constructs multiple view Hessian regularization, can be good at using the complementarity between different views feature, in addition, phase
Than there is better semi-supervised learning performance in figure Laplace regularization.Therefore, when facing multiple view data, SMHFS can
Preferably realize semi-supervised sparse features selection.The experimental results showed that SMHFS method is better than traditional single view feature selecting
Method, the feature selection approach directly concatenated better than multiple view and relevant latest features selection method.
Illustrative description has been done to the present invention above, it should explanation, the case where not departing from core of the invention
Under, any simple deformation, modification or other skilled in the art can not spend the equivalent replacement of creative work equal
Fall into protection scope of the present invention.
Claims (5)
1. a kind of structuring multiple view Hessian regularization sparse features selection method, which comprises the following steps:
1) the bottom visual signature for acquiring n original image, obtains m view image eigenmatrix, wherein
The m view image eigenmatrix are as follows:
In the formula (1), the dvFor v-th of view image characteristic dimension；The XvFor v-th of view image feature square
Battle array, and
In the formula (2), x1 v,x2 v…,xl vThere is label image for l under v-th of view in the n original image
Feature vector, xl+1 v,…,xn vFor n-l under v-th of view in the n original image feature vectors without label image；
2) the feature selecting mapping matrix of the step 1) X is set as variable G, and:
In the formula (3), the c is the classification number of the label of the n original image；
Construct the objective function of structuring multiple view Hessian regularization sparse features selection:
In the formula (4):
For the sparse restriction of structuring multiple view, wherein λ and γ is regularization coefficient；
For the G of the G1Norm,For the l of the G2,1/2Matrix norm, gi'=[g1 i' … gc i']∈
R1×c, 1≤i'≤d,
H is multiple view Hessian,
In formula (4) and (5), HvFor v-th of view Hessian；Variable F is the prediction label square of the n original image
Battle array,For multiple view Hessian regularization；ηvFor v-th of view in multiple view Hessian regularization
Scheme the weight of Hessian；The ε is ηvIndex, ε > 1；
For loss function；
μ is regularization coefficient；
Y=[y1,y2…,yl,yl+1,…,yn]T∈{0,1}n×cFor the label matrix of the n original image；
Diagonal matrix U ∈ Rn×nFor the decision rule matrix determined according to the X, U=(Ui”i”)n×n, 1≤i "≤n, as 1≤i "
When≤l, diagonal element Ui”i”=∞, as l < i "≤n, diagonal element Ui”i”=1；
3) the feature selecting mapping matrix G that the X is calculated by iterative algorithm, if GsFor the value of the G in the secondary iteration, ηvsFor
The η in the secondary iterationvValue, s=1,2 ... ..., t-1；If G1For random matrix and ηv1=1/m, by G1And ηv1As initial
Value substitutes into the iterative algorithm and is iterated calculating, until after the t-1 times iteration, target corresponding to the t-1 times iteration
The value of function is poor less than 10 with the value of objective function corresponding to the t-2 times iteration-3When, iteration is completed；At this point, according to
(gi)tDetermine feature selecting mapping matrix GtThe feature selecting mapping matrix G of the as described X；Wherein,
The calculating process of each iterative algorithm are as follows:
By ηvsThe formula (5) are substituting to, the value H of the H in the secondary iteration is obtaineds,
By GsAnd HsIt substitutes into corresponding formula (6) and P is calculated in (7)sAnd Qs；
Ps=(Hs+U+μI)-1 (6)
Qs=UY+ μ XTGs (7)
F is calculated according to formula (8), (9) and (10)s、AsAnd Bs, FsFor the value of the F in the secondary iteration；
Fs=PsQs (8)
As=X (μ I- μ2Ps T)XT (9)
Bs=μ XPsUY (10)
Wherein, the I described in formula (6) is unit matrix；
It is (w that diagonal element, which is calculated, according to formula (11) and (12)i'i')sDiagonal matrix WsWith the block with j diagonal blocks
Diagonal matrix (Di)s(1≤i≤c)；
Wherein,
In the formula (12), IjIt is the unit matrix that dimension is j*j；
By As、Bs、Ws(Di)sThe formula (13) are substituted into, (g is obtainedi)s+1；
(gi)s+1=(As+4λWs+γ(Di)s)-1Bs,1≤i≤c (13)
It calculates
4) according to feature selecting mapping matrix G obtained by step 3)t, willDescending arrangement is carried out, before selection
DsFeature corresponding to the X is as the character subset after feature selecting, whereinFor step
3) gained GtCorresponding gi′。
2. structuring multiple view Hessian regularization sparse features selection method according to claim 1, feature exist
In in the step 1), the bottom visual signature includes: color correlogram, wavelet texture and edge orientation histogram.
3. structuring multiple view Hessian regularization sparse features selection method according to claim 1, feature exist
In the value range of the λ and γ are [10-5, 105]。
4. structuring multiple view Hessian regularization sparse features selection method according to claim 1, feature exist
In the value range of the μ is [10-5, 105]。
5. structuring multiple view Hessian regularization sparse features selection method according to claim 1, feature exist
In, in the step 2), FvFor the prediction label matrix of v-th of view, Fv∈Rn×c。
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| Application Number | Priority Date | Filing Date | Title |
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| CN110188825A (en) * | 2019-05-31 | 2019-08-30 | 山东师范大学 | Image clustering method, system, equipment and medium based on discrete multiple view cluster |
| CN111783816A (en) * | 2020-02-27 | 2020-10-16 | 北京沃东天骏信息技术有限公司 | Feature selection method and device, multimedia and network data dimension reduction method and equipment |
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