Independent Comparative Study of PCA, ICA, and …

1 Independent Comparative Study of PCA, ICA, and LDAon the FERET Data SetKresimir Delac, Mislav Grgic, Sonja GrgicUniversity of Zagreb, FER, Unska 3/XII, Zagreb, CroatiaReceived 28 December 2004; accepted 27 February 2006 ABSTRACT:Face recognition is one of the most successful applica-tions of image analysis and understanding and has gained muchattention in recent years. Various algorithms were proposed andresearch groups across the world reported different and often contra-dictory results when comparing them. The aim of this paper is topresent an Independent , Comparative Study of three most popularappearance-based face recognition projection methods (PCA, ICA,and LDA) in completely equal working conditions regarding prepro-cessing and algorithm implementation. We are motivated by the lackof direct and detailed Independent comparisons of all possible algo-rithm implementations ( , all projection metric combinations) inavailable literature.

2 For consistency with other studies, FERET dataset is used with its standard tests (gallery and probe sets). Our resultsshow that no particular projection metric combination is the bestacross all standard FERET tests and the choice of appropriate projec-tion metric combination can only be made for a specific task. Ourresults are compared to other available studies and some discrepan-cies are pointed out. As an additional contribution, we also introduceour new idea of hypothesis testing across all ranks when comparingperformance Wiley Periodicals, Inc. Int J ImagingSyst Technol, 15, 252 260, 2005; Published online in Wiley InterScience( ). DOI words:face recognition; PCA; ICA; LDA; FERET; subspaceanalysis methodsI. INTRODUCTIONOver the last ten years or so, face recognition has become a populararea of research in computer vision and one of the most successfulapplications of image analysis and understanding.

3 Because of thenature of the problem, not only computer science researchers areinterested in it, but also neuroscientists and psychologists. It is thegeneral opinion that advances in computer vision research will pro-vide useful insights to neuroscientists and psychologists into howhuman brain works, and vice versa. A general statement of the facerecognition problem can be formulated as follows (Zhao et al.,2003): Given still or video images of a scene, identify or verify oneor more persons in the scene using a stored database of faces. A sur-vey of face recognition techniques has been given by Zhao et al.,(2003). In general, face recognition techniques can be divided intotwo groups based on the face representation they , which uses holistic texture features and isapplied to either whole-face or specific regions in a faceimage; , which uses geometric facial features (mouth,eyes, brows, cheeks etc.)

4 And geometric relationships many approaches to the problem of face recognition,appearance-based subspace analysis, although one of the oldest,still gives the most promising results. Subspace analysis is done byprojecting an image into a lower dimensional space (subspace)and after that recognition is performed by measuring the dis-tances between known images and the image to be recognized. Themost challenging part of such a system is finding an this paper, three most popular appearance-based subspaceprojection methods for face recognition will be presented, and theywill be combined with four common distance metrics. Projectionmethods to be presented are: Principal Component Analysis (PCA), Independent Component Analysis (ICA), and Linear DiscriminantAnalysis (LDA). PCA (Turk and Pentland, 1991) finds a set of themost representative projection vectors such that the projected sam-ples retain most information about original samples.

5 ICA (Bartlettet al., 2002; Draper et al., 2003) captures both second and higher-order statistics and projects the input data onto the basis vectors thatare as statistically Independent as possible. LDA (Belhumeur et al.,1996; Zhao et al., 1998) uses the class information and finds a set ofvectors that maximize the between-class scatter while minimizingthe within-class scatter. Distance metrics used are L1 (City block),L2 (Euclidean), cosine and Mahalanobis aim of this paper is to provide an Independent , comparativestudy of these three projection methods and their accompanied dis-tance metrics in completely equal working conditions. In order toperform a fair comparison, same preprocessed images are the inputinto all algorithms and the number of dimensions to be retained ischosen following the standard recommendations. For consistencyCorrespondence to:K.

6 Delac; E-mail: Wiley Periodicals, other studies, FERET data set (Phillips et al., 2000), with itsstandard test sets, is used for comparisons. This research is motivatedby the lack of direct and detailed comparisons of these three projec-tion methods. They are rarely compared in a single paper and almostnever are all possible implementations considered ( , all projec-tion metric combinations). It is interesting to notice that the findingsof other research groups are often contradictory on this subject andthis is another important reason for performing a Study of this example, Liu and Wechsler (1999) and Bartlett et al. (2002)claim that ICA outperforms PCA, while Baek et al. (2002) claim thatPCA is better. Moghaddam (2002) states that there is no significantdifference. Beveridge et al. (2001a) claim that in their tests LDA per-formed uniformly worse than PCA, Martinez and Kak (2001) statethat LDA is better for some tasks, and Belhumeur et al.

7 (1996) andNavarrete and Ruiz-del-Solar (2002) claim that LDA outperformsPCA on all tasks in their tests (for more than two samples per class intraining phase). All these results are in most cases given only for oneor two projection metric combinations for a specific projectionmethod, and in some cases using nonstandard databases or somehybrid test sets derived from a standard rest of this paper is organized as follows: Section II gives abrief description of the algorithms to be compared, Section IIIreports the details of methodology, Section IV presents the resultsand compares our results to results of other research groups andSection V concludes the ALGORITHMSEven though projection methods and metrics used in this work arealready well known, we will include a brief description for the sakeof completeness. All three projection methods are so calledsub-space analysis methods.

8 A 2D imageGwithmrows andncolumnscan be viewed as a vector (after concatenating its rows or columns)inNdimensional image space (RN m n). Since space derived thisway is highly dimensional, recognition in it is unfeasible. There-fore, recognition algorithms usually derive lower dimensionalspaces to do the actual recognition while retaining as much infor-mation (energy) from the original images as possible. We will fur-ther clarify this on the example from this research: the originalFERET images (after preprocessing) are the size of 60 50 pixels,thus the image space dimensionality isRN 60 50 3000. It will beshown that projection methods presented here will yieldR270(R224for LDA) subspace in which the recognition will be done and inthese 270 dimensions of original information (energy) isretained. An example of building a general subspace appearance-based face recognition system can be seen in Figure 1.

9 Training ofthe subspace system can be seen in the left part of the figure and theprocedure for projecting gallery images onto a subspace (projectionmatrixWT) can be seen in the right part of the figure;Xis a matrixcontaining the images expressed as vectors in its columns,xmean mean image (as a vector),~X matrix containing mean-subtractedimages in its columns,WT projection matrix,xg gallery image(as a vector). During the training phase, the projection matrix (con-taining the basis vectors of the subspace) is calculated and then thegallery images (the images of known persons) are projected ontothat subspace and their projections are stored in a database. Later,in the matching phase (Fig. 2), new image is normalized, mean-sub-tracted, projected onto the same subspace as the gallery image wasand its projection is then compared to stored gallery projections(thenearest neighboris determined by calculating the distancesdfrom a probe image projection to all gallery images projections andthen choosing the minimum distance as a similarity measure).

10 Theidentity of the most similar gallery image is then chosen to be theFigure illustration of general sub-space appearance-based face recog-nition matching phase of ageneral subspace face 15, 252 260 (2005)253result of recognition and the unknown probe image is identified. Itis important to mention that a general face recognition system canwork in two modes: (1) theidentification modewhere the input tothe system is an unknown face and the system reports back thedetermined identity (our case) and (2) theverification modewherethe system needs to confirm or reject the claimed identity of theinput face. All our experiments are conducted for the identificationmode and the general illustration of the systems shown in Figures 1and 2 illustrates our Principal Component Analysis (PCA).In our experimentswe implemented Principal Component Analysis (PCA) procedureas described by Turk and Pentland (1991).