moreadaptiveandupdatable:anonlinesparselearning...

Research ArticleMore Adaptive and Updatable An Online Sparse LearningMethod for Face Recognition

Qiaoling Han 12 Jianbo Su 3 and Yue Zhao 12

1School of Technology Beijing Forestry University Beijing 100083 China2Beijing Laboratory of Urban and Rural Ecological Environment Beijing Forestry University Beijing 100083 China3Department of Automation Shanghai Jiao Tong University and Key Laboratory of System Control and Information ProcessingMinistry of Education of China Shanghai 200240 China

Correspondence should be addressed to Yue Zhao zhaoyue0609126com

Received 24 June 2019 Accepted 24 August 2019 Published 13 October 2019

Academic Editor Sos S Agaian

Copyright copy 2019 Qiaoling Han et al is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

In the actual face recognition applications the sample sets are updated constantly However most of the face recognition modelswith learning strategy do not consider this fact and using a fixed training set to learn the face recognition models for once Besidesthat the testing samples are discarded after the testing process is completed Namely the training and testing processes areseparated and the later does not give a feedback to the former for better recognition results To attenuate these problems this paperproposed an online sparse learning method for face recognition It can update the salience evaluation vector in real time toconstruct a dynamical facial feature description model Also a strategy for updating the gallery set is proposed in this proposedmethod Both the dynamical facial feature description model and the gallery set are employed to recognize faces Experimentalresults show that the proposed method improves the face recognition accuracy comparing with the classical learning models andother state-of-the-art face recognition methods

1 Introduction

Face recognition is a significant gift that humans performeffortlessly and automatically in our daily lives According tothe wide applications of automatic face recognition such aspublic security and human-robot interaction it is anestablished field attracting great attention [1ndash3]

In 1973 Takeo Kanade presented the first face recog-nition system [4] After that there was a dormant period inautomatic face recognition until the work on a low-di-mensional face representation by Sirovich and Kirby de-rived using the K-L transform or principal componentanalysis (PCA) [5] It is the pioneering work of Turk andPentland that proposes a new facial feature descriptionmodel Eigenface [6 7] to recognize faces From then on anumber of face recognition and modeling systems have beendeveloped and deployed Some major state-of-the-artmethods of face recognition are as follows Ahonen et aldivide a face image into some regions and then extract local

binary patterns from these regions to recognize faces [8] toenhance the robustness to noise of LBP features Zhang et al[9] introduce a combination approach which employsmultiorientation and multiscale Gabor filtering to extendLBP to Local Gabor Binary Pattern (LGBP) they alsopropose a combination of the spatial histogram and theGabor phase information encoding scheme the Histogramof Gabor Phase Pattern (HGPP) [10] to reduce the di-mension of LGBP and suppress the intrapersonal variationwhitened PCA technique is applied on LGBP by Nguyenet al [11] and leads to very high recognition rate throughapplying the LBP-based structure on oriented magnitudesPatterns of Oriented Edge Magnitudes (POEM) is proposedby Vu and Caplier [12] followed by the whitened PCA toincrease the discriminative power and robustness for facerecognition to generate a more robust face descriptorMehta et al [13] propose a new approach for face recog-nition using directional and texture information from faceimages which improves the recognition results significantly

HindawiJournal of Electrical and Computer EngineeringVolume 2019 Article ID 8370835 7 pageshttpsdoiorg10115520198370835

Besides these single feature-based face recognition methodsrecently there are some fusion feature methods for morehigher face recognition accuracy Zou et al [14] adopt Bordacount method to combine different classifiers which aretrained with one type of features selected from LBP Gaborand Eigenface Tan and Triggs [15] fuse LBP and Gaborfeatures to recognize faces with the kernel discriminantcommon vector (DCV) method

Classical face recognition methods mentioned aboveemploy a training set to train the face recognitionmodel anda gallery set to be the prototype which the testing samplesmatched against during the recognition procedure Goodresults have been achieved of the classical methods howevertwo drawbacks are also found from these methods (1) efixed training sets and gallery sets could not adapt to thevariation of face images during testing especially in realapplications For example faces will gradually change withage (2) e testing sample is discarded after the recognitionprocedure which causes great loss of information containedin the testing set Namely the training and testing processesare separated and the latter does not give a feedback to theformer for better recognition results In order to attenuatethese problems an online sparse learning method is pro-posed in this paper which can accommodate itself to var-iation of the face images in the testing set or realapplications In addition the proposed method can updatethe facial feature description model in real time and ensurethe good sparsity of the facial features

2 Previous Works

In our previous work [16] we proposed a sparse learningmethod for salient facial feature description and a new facialfeature description model was obtained which is given by

Q q1 qj qm1113960 1113961

β1h1 βjhj βmhm1113960 1113961

⎡⎣ β1h1 βmhm1113980radicradicradicradicradicradic11139791113978radicradicradicradicradicradic1113981Q[1]

β(iminus 1)m+1h(iminus 1)m+1 βimhim1113980radicradicradicradicradicradicradicradicradicradicradicradic11139791113978radicradicradicradicradicradicradicradicradicradicradicradic1113981Q[i]

β(rminus 1)m+1h(rminus 1)m+1 βrmhrm1113980radicradicradicradicradicradicradicradicradicradicradicradic11139791113978radicradicradicradicradicradicradicradicradicradicradicradic1113981Q[r]

⎤⎦

(1)

where Q [q1 qj qm] is a sparse facial featurevector and H [[h1 hj hm] is a LBP feature vectorβ [β1 βj βm] is a salience evaluation vector for HQ[i] is a local sparse feature vector of the i minus th region in thefacial image

e method for obtaining β is described in detail in ourprevious work [16] and there are two limitations in thismethod (1) the training set is fixed for example it does notconsider the dynamic changes of the sample set (2) β isobtained by only once learning and there is no furtheradjustment for it us its adaptability and self-adjustmentability need to improve An online sparse learning method

for face recognition is presented in this paper to solve theseproblems

3 The Proposed Method

31 Online Sparse Learning With the method in our pre-vious work [16] the initial salience evaluation vector andfacial feature description model can be obtained and sup-pose they are β0 and Q0 Let T and G denote the testing setand gallery set respectively Now we propose an onlinesparse learning method to update β0 and Q0

Randomly select a sample from testing T and denote it astn Suppose the label of tn is Ln which can be computed withnearest neighbor model and gallery set G Take 1113957gn and 11139571113957gn todenote one nearest neighbor and next-nearest neighbor of twhich are obtained from the gallery set G with Ln

Region-based features (such as LBP and POEM) can beextracted from images t 1113957g and 11139571113957g which respectively are asfollows

H h1 hj hm1113960 1113961

1113957H 1113957h1 1113957hj 1113957hm1113960 1113961

11139571113957H 11139571113957h1

11139571113957hj 11139571113957hm1113876 1113877

(2)

A feature transformation is introduced to generate twoclasses of distance samples If two feature vectors are fromthe nearest neighbor couple the following transformationwill produce a positive sample

X+i f(H 1113957H)

h1 minus 1113957h11113872 1113873

2

h1 + 1113957h1

hj minus 1113957hj1113872 11138732

hj + 1113957hj

hM minus 1113957hM1113872 1113873

2

hM + 1113957hM

⎡⎢⎢⎢⎣ ⎤⎥⎥⎥⎦

x1 xj xM1113960 1113961

⎡⎣ x1 xm1113980radicradicradicradic11139791113978radicradicradicradic1113981Xi[1]

xm+1 x2m1113980radicradicradicradicradic11139791113978radicradicradicradicradic1113981Xi[2]

x(rminus 1)m+1 xrm1113980radicradicradicradicradicradicradic11139791113978radicradicradicradicradicradicradic1113981Xi[r]

⎤⎦

(3)

Also a negative sample can be generated by applying thesame transformation to the next-nearest neighbor couplenamely the transformation f(H 11139571113957H) will generate a negativesample Xminus

i We should know that the number of the nearestneighbors and next-nearest neighbors are both at least oneAll the positive and negative samples form the positive andnegative sample set X+ and Xminus respectively e samplematrix E consists ofX+ andXminus Label vector Y is obtained byassigning label ldquo1rdquo and ldquo0rdquo to the positive and negativesample respectively Let β denote the updated value of β0then we have

β β0 + Δβ (4)

where Δβ is the increment of β0e initial value of β0 is obtained by using the sample

matrix (which is learned from the training samples and

2 Journal of Electrical and Computer Engineering

different to E) and salience evaluation vector to fit the labelvector As β is the updated value of β0 it also have theproperty that it can fit the label vector cooperated with thesample matrix If we take one testing set tn and its nearestand next-nearest neighbors as the training samples we canuse E and β to fit Y en we arrive at

Y Eβ (5)

Plug equation (4) into equation (5) we have

Y minus Eβ0 Eβ (6)

A linear system is obtained by substituting Y minus Eβ0 withYprime which is given by

Yprime Eβ

E X+

Xminus1113890 1113891

⎧⎪⎪⎨

⎪⎪⎩(7)

A visual expression in Figure 1 is afforded to betterunderstand the facial feature transformation equation (3)and the theory for constructing the linear system

As the number of samples in E is much smaller than thedimensionality of the sample it cannot get an ununiquesolution for Δβ Here the structured sparse representation isintroduced [17ndash21] to overcome this problem Simulta-neously this strategy leads to the sparsity at both the groupand individual levels By dividing the sample matrix E andthe salience evaluation Δβ into r region we have

E ⎡⎣ e1 em1113980radicradicradicradic11139791113978radicradicradicradic1113981E[1]

em+1 e2m1113980radicradicradicradicradic11139791113978radicradicradicradicradic1113981E[2]

e(rminus 1)m+1 erm1113980radicradicradicradicradicradicradic11139791113978radicradicradicradicradicradicradic1113981E[r]

⎤⎦

β ⎡⎣β1 βm1113980radicradicradicradicradicradic11139791113978radicradicradicradicradicradic1113981βT[1]

βm+1 β2m1113980radicradicradicradicradicradicradic11139791113978radicradicradicradicradicradicradic1113981βT[2]

β(rminus 1)m+1 βrm1113980radicradicradicradicradicradicradicradicradic11139791113978radicradicradicradicradicradicradicradicradic1113981βT[r]

⎤⎦

T

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(8)

where em is the mth column of E en an optimizationproblem is constructed to solve Δβ as follows

argminΔβϵRM

Yprime1113944r

l1E[l]Δβ[l]

2

2

+ λ1113944r

l1Δβ[l] (9)

st βi ge 0 i 1 2 M (10)

where E[l] is the lth group columns of E and β[l] is thecorresponding salience evaluation vector of E[l] middot2 is theEuclidean norm λ is a complexity parameter which has apositive value and controls the amount of shrinkage namelythe larger the value of λ is the greater the amount ofshrinkage could be

When Δβ is obtained β can be computed with equation(4) en we use β to construct the facial feature description

model Q (in equation (1)) β0 and Q0 can be updated with βand Q respectively ese steps are performed iteratively

A summary of the online sparse learning algorithm isgiven in Algorithm 1

To better understand the online sparse learning algo-rithm a framework of the essential procedures of this al-gorithm is presented in Figure 2 Also a detailed descriptionof the online sparse learning algorithm is summarized inAlgorithm 2 With the update of the testing sample theonline sparse learning procedures are performed continu-ously More importantly the time cost of the online sparselearning algorithm is very low which ensures it can beperformed in real time

32 Criterion of Label Correctness is subsection presentsone comprehensive criterion for judging the correctness ofthe testing sample label Ln As we employ the nearestneighbor model to assign a label for the testing sample athreshold for the nearest neighbor distance is used to de-termine whether the label is correct For improving theaccuracy of the judgement further the next-nearestneighbor distance is also employed to these judgementprocedures Suppose the distance between two elements ofany one nearest neighbor couple (t 1113957g) is computed which isD(H 1113957H) Also D(H 1113957H) is used to denote the distancebetween two elements of any one next-nearest neighborcouple (t 1113957g) With the nearest neighbor distance and next-nearest neighbor distance one comprehensive criterion forjudging the correctness of the testing sample label is pro-posed as follows

Rule 1 (criterion of label correctness) If D(H 1113957H) andD(H 11139571113957H) satisfy

D(H 1113957H)leTN

D(H 1113957H)

D(H 11139571113957H)geTNN

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(11)

Ln the label of tn is correct where TN and TNN are re-spectively two thresholds for D(H 1113957H) and D(H 11139571113957H) whichare set manually according to the experience

33 Gallery Set Update Strategy In this research a dynamicgallery set is taken as the input of the online sparse learningalgorithm If the label of the testing sample is right thefollowing strategy is used to update the gallery set (Algo-rithm 2)

4 Experiments

In this section the performance of the proposed method isdemonstrated on the FERETdatabase [22] We first comparethe proposed method with the classical learning models PCA[23] and WPCA [24] using LBP and POEM features en alot of state-of-the-art face recognition results obtained on

Journal of Electrical and Computer Engineering 3

this database are shown to evaluate the performance of theproposed method Overall recognition rate (ORR) isdefined as the ratio that the number of images correctlyrecognized to the total number of images in the whole facedataset which is a comprehensive criterion for evaluatingthe performance of the face recognition method

41 Data Description FERET database is a famous databasefor face recognition It has 14051 grayscale images repre-senting 1199 individualsese images contain variations inlighting facial expressions and time e ways of selectingthe gallery and probe sets are the same to the FERETevaluation protocol [22] Namely fa (1196 images) is used asthe gallery set while fb (1195 images) fc (194 images) dupI

(722 images) and dupII (234 images) are used as the probesets Note that the original training set comes from twotraining sets the standard FERET training set (736 images)and subfc training set (194 images) [8] All the images arecropped to 130times150 pixels for LBP feature extraction and96times 96 for POEM feature extraction

Extended Yale B face database consists of 38 subjectsand each subject has approximately 64 frontal view imagesunder various lighting conditions All image data used in theexperiments are manually aligned cropped and then resizedto 168times192 pixels e database is divided into five subsetson the angle between the light direction gallery set (38images) S1 (225 images) S2 (456 images) S3 (455 images)S4 (526 images) and S5 (714 images) We random select 500images for training set

Region-based features


Distance vector

Distance vector

Distance matrix

Testing sample

Testing sample

Nearest neighbor

Next-nearestneighbor

Labels

Salience evaluation vector

Transformation

E

E[1] E[r]β[r]

β ∆β

β[1]

Y

+

∆β[r]

∆β[1]X+

Xndash

H[1] = [h1 hm]

H[1] = [h1 hm]

f(H[1] H[1])

=

0

1

Figure 1 Visual expression of facial feature transformation and theory for constructing the linear system

Test set Gallery set

Select onetest sample

Facial feature description model

Feature vector ofthe test sample

Feature vector ofgallery samples

Classification model

Is the labelcorrect

Online sparselearning

Gallery setupdate strategy

Update the salienceevaluation vector

No Yes

Figure 2 e framework of online sparse learning algorithm


42 Results e comparison results between the proposedmethod and other learning methods for face recognition onFERETdatabase are shown in Tables 1 and 2 From these twotables we can see that the proposed method achieves thehighest recognition accuracy in most of the subsets (exceptsubset fb) By considering the comprehensive criterion ofORR the proposed method (946 with LBP features and954 with POEM features) is significantly better than theother two methods which indicates that the online sparselearning strategy has great advantages than PCA model andWPCA model

Comparing the corresponding results of the samemethodin Tables 1 and 2 we find that the results obtained usingPOEM features (954) are better than the results obtainedusing LBP features (946) It indicates that POEM featuresare much discriminative than LBP features e proposedmethods obtained significantly better results than other twolearning methods PCA and WPCA both with LBP andPOEM which shows that the proposed method has bettergeneralization ability among different region-based features

We also compare the performance of the proposedmethod with other state-of-the-art methods and summa-rize the results in Table 3 is table shows that the per-formance of the proposed method is much better than thatof other state-of-the-art methods on the comprehensivecriterion ORR More importantly the proposed methodgains 100 accuracy on the subset dupII and much higherrecognition rate than other methods on the subset dupIBecause dupI and dupII were respectively taken withinone year of gallery image and at least one year apart which

Initialization(1) Obtain gallery set G testing set tn and its label Ln(2) Set the initial value for P (the maximal number of the pictures of each person in the gallery set)

Update gallery set(3) In gallery set G find the class that the testing sample belongs to using Ln(4) Obtain the number of the pictures in this class and suppose it is Cn(5) If Cn P remove the picture in the second place from the class and put tn in the last place If Cn ltP put tn in the last place directly

ALGORITHM 2 Gallery set update strategy

Table 1 Comparison results of different learning methods withLBP features

ModelRecognition rate () on the

subset ORR ()fb fc dupI dupII

PCA 883 314 553 376 683WPCA 985 840 794 700 886Proposed model 958 964 902 1000 946

Initialization(1) Obtain gallery set G testing set T initial salience evaluation vector β0 and facial feature description model Q0(2) Set the initial value for the number of iterations n 1(3) Set the initial value for the sign vector (each element denotes whether the label of the testing sample is correct ldquo1rdquo denotes ldquorightrdquo

and ldquominus 1rdquo denotes ldquowrongrdquo) SV 1(4) Randomly select a testing sample tn from T

Iteration(5) while the number of the consecutive testing sample labeled incorrectly klt 5 do(6) Q Q0(7) Compute the facial feature vector fn for tn with equation (1)(8) Compute the label Ln for tn with fn G and the nearest neighbor model(9) Judge the correctness of Ln according the criterion in Section 32 if Ln is correct then update G according the gallery set update

strategy in Section 33 if Ln is incorrect then repeat steps (4)sim(8)(10) Construct the nearest neighbor set N and next-nearest neighbor set NN find the nearest neighbor samples of tn from G and all

the nearest neighbor samples form set N similarly the next-nearest neighbor set NN is obtained(11) Construct positive and negative sample set X+ and Xminus according to equation (7)(12) Solve the optimization problem equations (9)sim(10) to obtain Δβ(13) Compute the salience evaluation vector β with equation (4)(14) Compute Q with equation (1)(15) Update β0 β0⟵ β

(16) Update Q0 Q0⟵Q

(17) n n+ 1(18) k is equal to the number of element ldquominus 1rdquo in vector [SV (n minus 4) SV (n minus 3) SV (n minus 2) SV (n minus 1) SV (n)](19) end while

ALGORITHM 1 Online sparse learning algorithm


means the proposed method is much more robust tovariations in time and age

5 Conclusions

Face recognition is the main task for person identificationis paper proposes an online sparse learning method forface recognition e initial salience evaluation vector in afacial feature description model is obtained from our pre-vious work en an online sparse learning method isproposed to learn the increment of the salience evaluationvector with one testing sample and the current gallery sete salience evaluation vector is updated by adding theinitial salience evaluation vector to its increment Also agallery set update strategy is presented in this paper whichachieves the dynamical update of the gallery set e pro-posed method can update the facial feature descriptionmodel in real time and ensure the good sparsity of the facialfeatures In addition it considers the dynamical changing ofthe sample set to generalize the ability of the proposedmethod for good face recognition results Experimentalresults show that the proposed method improves the facerecognition accuracy comparing with the methods of PCAand WPCA

Data Availability

Previously reported FERET database PCA learning modeland WPCA learning model were used to support this studyand are available at DOI 101109CVPR1997609311 DOI101016S1077-3142(03)00077-8 and DOI 101016jpat-cog200912004 ese prior studies and datasets are cited atrelevant places within the text as references [21ndash23]

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this paper

Authorsrsquo Contributions

Jianbo Su contributed to conceptualization and data cura-tion Qiaoling Han was involved in methodology and wrotethe original draft and Yue Zhao reviewed and edited themanuscript

Acknowledgments

is work was supported in part by the Fundamental Re-search Funds for the Central Universities (2019ZY12) and inpart by the NSF of China under the grant nos 61533012 and91748120

References

[1] S Elisabetta and F Carlo ldquoDesign and implementation of amulti-modal biometric system for company access controlrdquoAlgorithms vol 10 pp 61ndash71 2017

[2] C Lu W Liu X Liu and S An ldquoDouble sides 2DPCA forface recognitionrdquo in Proceedings of the International Con-ference on Intelligent Computing pp 446ndash459 SpringerShangai China September 2008

[3] F Liu Y Ding F Xu and Q Ye ldquoLearning low-rank reg-ularized generic representation with block-sparse structurefor single sample face recognitionrdquo IEEE Access vol 7pp 30573ndash30587 2019

[4] T Kanade Picture processing system by computer complex andrecognition of human faces PhD dissertation Kyoto Uni-versity Kyoto Japan 1973

[5] L Sirovich and M Kirby ldquoLow-dimensional procedure forthe characterization of human facesrdquo Journal of the OpticalSociety of America A vol 4 no 3 pp 519ndash524 1987

[6] M Turk and A Pentland ldquoFace recognition using eigenfacesrdquoin Proceedings of the IEEE International Cofference onComputer Vision and Pattern Recognition (CVPR) pp 586ndash591 IEEE Columbus OH USA 1991

[7] M Turk and A Pentland ldquoEigenfaces for recognitionrdquoJournal of Cognitive Neuroscience vol 3 no 1 pp 71ndash861991

[8] T Ahonen A Hadid and M Pietikainen ldquoFace descriptionwith local binary patterns application to face recognitionrdquoIEEE Transactions on Pattern Analysis and Machine In-telligence vol 28 no 12 pp 2037ndash2041 2006

[9] W Zhang S Shan W Gao X Chen and H Zhang ldquoLocalgabor binary pattern histogram sequence (lgbphs) a novelnon-statistical model for face representation and recogni-tionrdquo in Proceedings of the IEEE International Conference onComputer Vision ICCV-95 vol 1 pp 786ndash791 IEEE BeijingChina October 2005

[10] B Zhang S Shan X Chen andW Gao ldquoHistogram of gaborphase patterns (HGPP) a novel object representation ap-proach for face recognitionrdquo IEEE Transactions on ImageProcessing vol 16 no 1 pp 57ndash68 2007

[11] H V Nguyen L Bai and L Shen ldquoLocal gabor binary patternwhitened PCA a novel approach for face recognition from

Table 2 Comparison results of different face recognition methodswith POEM features

ModelRecognition rate () on the subset ORR

()fb fc dupI dupIIPCA 974 959 778 769 892WPCA 982 902 816 812 906Proposedmodel 977 902 915 1000 954


ModelRecognition rate ()

on the subset ORR()

fb fc dupI dupIIZhang et al [9] 980 970 740 710 878Zhang et al [10] 975 995 795 778 902Mehta et al [13] 982 964 839 748 913Nguyen et al [11] 981 990 838 816 921Zou et al [14] 995 995 850 795 930Tan and Triggs [15] 980 980 900 850 942Proposed method 977 902 915 100 954


single image per personrdquo in Advances in Biometricspp 269ndash278 Springer Berlin Germany 2009

[12] N-S Vu and A Caplier ldquoEnhanced patterns of oriented edgemagnitudes for face recognition and image matchingrdquo IEEETransactions on Image Processing vol 21 no 3 pp 1352ndash1365 2012

[13] R Mehta J Yuan and K Egiazarian ldquoFace recognition usingscale-adaptive directional and textural featuresrdquo PatternRecognition vol 47 no 5 pp 1846ndash1858 2014

[14] J Zou Q Ji and G Nagy ldquoA comparative study of localmatching approach for face recognitionrdquo IEEE Transactionson Image Processing vol 16 no 10 pp 2617ndash2628 2007

[15] X Tan and B Triggs ldquoFusing gabor and LBP feature sets forkernel-based face recognitionrdquo in Analysis and Modeling ofFaces and Gestures pp 235ndash249 Springer Berlin Germany2007

[16] Y Zhao and J Su ldquoSparse learning for salient facial featuredescriptionrdquo in Proceedings of the IEEE International Con-ference on Robotics and Automation (ICRA) pp 5565ndash5570IEEE Hong Kong China May-June 2014

[17] M Stojnic F Parvaresh and B Hassibi ldquoOn the re-construction of block-sparse signals with an optimal numberof measurementsrdquo IEEE Transactions on Signal Processingvol 57 no 8 pp 3075ndash3085 2009

[18] Z Liu D Jiang Y Li Y Cao M Wang and Y Xu ldquoAu-tomatic face recognition based on sparse representation andextended transfer learningrdquo IEEE Access vol 7 pp 2387ndash2395 2019

[19] J Friedman T Hastie and R Tibshirani ldquoA note on thegroup lasso and a sparse group lassordquo 2010 httparxivorgabs10010736

[20] Y Xu Z Li J Yang and D Zhang ldquoA survey of dictionarylearning algorithms for face recognitionrdquo IEEE Access vol 5pp 8502ndash8514 2017

[21] H Qiu D S Pham S Venkatesh J Lai and W Liu ldquoIn-novative sparse representation algorithms for robust facerecognitionrdquo International Journal of Innovative ComputingInformation amp Control vol 7 no 10 pp 5645ndash5667 2011

[22] P J Phillips H Moon S A Rizvi and P J Rauss ldquoeFERET evaluation methodology for face-recognition algo-rithmsrdquo IEEE Transactions on Pattern Analysis and MachineIntelligence vol 22 no 10 pp 1090ndash1104 2000

[23] B A Draper K Baek M S Bartlett and J R BeveridgeldquoRecognizing faces with PCA and ICArdquo Computer Vision andImage Understanding vol 91 no 1-2 pp 115ndash137 2003

[24] W Deng J Hu J Guo W Cai and D Feng ldquoRobust ac-curate and efficient face recognition from a single trainingimage a uniform pursuit approachrdquo Pattern Recognitionvol 43 no 5 pp 1748ndash1762 2010


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Besides these single feature-based face recognition methodsrecently there are some fusion feature methods for morehigher face recognition accuracy Zou et al [14] adopt Bordacount method to combine different classifiers which aretrained with one type of features selected from LBP Gaborand Eigenface Tan and Triggs [15] fuse LBP and Gaborfeatures to recognize faces with the kernel discriminantcommon vector (DCV) method

Classical face recognition methods mentioned aboveemploy a training set to train the face recognitionmodel anda gallery set to be the prototype which the testing samplesmatched against during the recognition procedure Goodresults have been achieved of the classical methods howevertwo drawbacks are also found from these methods (1) efixed training sets and gallery sets could not adapt to thevariation of face images during testing especially in realapplications For example faces will gradually change withage (2) e testing sample is discarded after the recognitionprocedure which causes great loss of information containedin the testing set Namely the training and testing processesare separated and the latter does not give a feedback to theformer for better recognition results In order to attenuatethese problems an online sparse learning method is pro-posed in this paper which can accommodate itself to var-iation of the face images in the testing set or realapplications In addition the proposed method can updatethe facial feature description model in real time and ensurethe good sparsity of the facial features

2 Previous Works

In our previous work [16] we proposed a sparse learningmethod for salient facial feature description and a new facialfeature description model was obtained which is given by

Q q1 qj qm1113960 1113961

β1h1 βjhj βmhm1113960 1113961

⎡⎣ β1h1 βmhm1113980radicradicradicradicradicradic11139791113978radicradicradicradicradicradic1113981Q[1]

β(iminus 1)m+1h(iminus 1)m+1 βimhim1113980radicradicradicradicradicradicradicradicradicradicradicradic11139791113978radicradicradicradicradicradicradicradicradicradicradicradic1113981Q[i]

β(rminus 1)m+1h(rminus 1)m+1 βrmhrm1113980radicradicradicradicradicradicradicradicradicradicradicradic11139791113978radicradicradicradicradicradicradicradicradicradicradicradic1113981Q[r]

⎤⎦

(1)

where Q [q1 qj qm] is a sparse facial featurevector and H [[h1 hj hm] is a LBP feature vectorβ [β1 βj βm] is a salience evaluation vector for HQ[i] is a local sparse feature vector of the i minus th region in thefacial image

e method for obtaining β is described in detail in ourprevious work [16] and there are two limitations in thismethod (1) the training set is fixed for example it does notconsider the dynamic changes of the sample set (2) β isobtained by only once learning and there is no furtheradjustment for it us its adaptability and self-adjustmentability need to improve An online sparse learning method

for face recognition is presented in this paper to solve theseproblems

3 The Proposed Method

31 Online Sparse Learning With the method in our pre-vious work [16] the initial salience evaluation vector andfacial feature description model can be obtained and sup-pose they are β0 and Q0 Let T and G denote the testing setand gallery set respectively Now we propose an onlinesparse learning method to update β0 and Q0

Randomly select a sample from testing T and denote it astn Suppose the label of tn is Ln which can be computed withnearest neighbor model and gallery set G Take 1113957gn and 11139571113957gn todenote one nearest neighbor and next-nearest neighbor of twhich are obtained from the gallery set G with Ln

Region-based features (such as LBP and POEM) can beextracted from images t 1113957g and 11139571113957g which respectively are asfollows

H h1 hj hm1113960 1113961

1113957H 1113957h1 1113957hj 1113957hm1113960 1113961

11139571113957H 11139571113957h1

11139571113957hj 11139571113957hm1113876 1113877

(2)

A feature transformation is introduced to generate twoclasses of distance samples If two feature vectors are fromthe nearest neighbor couple the following transformationwill produce a positive sample

X+i f(H 1113957H)

h1 minus 1113957h11113872 1113873

2

h1 + 1113957h1

hj minus 1113957hj1113872 11138732

hj + 1113957hj

hM minus 1113957hM1113872 1113873

2

hM + 1113957hM

⎡⎢⎢⎢⎣ ⎤⎥⎥⎥⎦

x1 xj xM1113960 1113961

⎡⎣ x1 xm1113980radicradicradicradic11139791113978radicradicradicradic1113981Xi[1]

xm+1 x2m1113980radicradicradicradicradic11139791113978radicradicradicradicradic1113981Xi[2]

x(rminus 1)m+1 xrm1113980radicradicradicradicradicradicradic11139791113978radicradicradicradicradicradicradic1113981Xi[r]

⎤⎦

(3)

Also a negative sample can be generated by applying thesame transformation to the next-nearest neighbor couplenamely the transformation f(H 11139571113957H) will generate a negativesample Xminus

i We should know that the number of the nearestneighbors and next-nearest neighbors are both at least oneAll the positive and negative samples form the positive andnegative sample set X+ and Xminus respectively e samplematrix E consists ofX+ andXminus Label vector Y is obtained byassigning label ldquo1rdquo and ldquo0rdquo to the positive and negativesample respectively Let β denote the updated value of β0then we have

β β0 + Δβ (4)

where Δβ is the increment of β0e initial value of β0 is obtained by using the sample

matrix (which is learned from the training samples and



Y Eβ (5)




Yprime Eβ

E X+

Xminus1113890 1113891

⎧⎪⎪⎨

⎪⎪⎩(7)






⎤⎦




⎤⎦

T

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(8)


argminΔβϵRM

Yprime1113944r

l1E[l]Δβ[l]

2

2

+ λ1113944r

l1Δβ[l] (9)

st βi ge 0 i 1 2 M (10)








D(H 1113957H)leTN

D(H 1113957H)

D(H 11139571113957H)geTNN

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(11)



4 Experiments









Distance vector

Distance vector

Distance matrix

Testing sample

Testing sample

Nearest neighbor


Labels


Transformation

E

E[1] E[r]β[r]

β ∆β

β[1]

Y

+

∆β[r]

∆β[1]X+

Xndash

H[1] = [h1 hm]

H[1] = [h1 hm]

f(H[1] H[1])

=

0

1








Is the labelcorrect




No Yes























5 Conclusions


Data Availability






Acknowledgments


References

















on the subset ORR()




















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Y Eβ (5)




Yprime Eβ

E X+

Xminus1113890 1113891

⎧⎪⎪⎨

⎪⎪⎩(7)






⎤⎦




⎤⎦

T

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(8)


argminΔβϵRM

Yprime1113944r

l1E[l]Δβ[l]

2

2

+ λ1113944r

l1Δβ[l] (9)

st βi ge 0 i 1 2 M (10)








D(H 1113957H)leTN

D(H 1113957H)

D(H 11139571113957H)geTNN

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(11)



4 Experiments









Distance vector

Distance vector

Distance matrix

Testing sample

Testing sample

Nearest neighbor


Labels


Transformation

E

E[1] E[r]β[r]

β ∆β

β[1]

Y

+

∆β[r]

∆β[1]X+

Xndash

H[1] = [h1 hm]

H[1] = [h1 hm]

f(H[1] H[1])

=

0

1








Is the labelcorrect




No Yes























5 Conclusions


Data Availability






Acknowledgments


References

















on the subset ORR()




















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia








Distance vector

Distance vector

Distance matrix

Testing sample

Testing sample

Nearest neighbor


Labels


Transformation

E

E[1] E[r]β[r]

β ∆β

β[1]

Y

+

∆β[r]

∆β[1]X+

Xndash

H[1] = [h1 hm]

H[1] = [h1 hm]

f(H[1] H[1])

=

0

1








Is the labelcorrect




No Yes























5 Conclusions


Data Availability






Acknowledgments


References

















on the subset ORR()




















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






















5 Conclusions


Data Availability






Acknowledgments


References

















on the subset ORR()




















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


moreadaptiveandupdatable:anonlinesparselearning...

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