Regression Techniques versus Discriminative Methods for Face Recognition Vitomir ˇ Struc, France Miheliˇ c, Rok Gajˇ sek and Nikola Paveˇ si´ c Abstract— In the field of face recognition it is generally believed that ”state of the art” recognition rates can only be achieved when discriminative (e.g., linear or generalized discriminant analysis) rather than expressive (e.g., principal or kernel principal component analysis) methods are used for facial feature extraction. However, while being superior in terms of the recognition rates, the discriminative techniques still exhibit some shortcomings when compared to the expressive approaches. More specifically, they suffer from the so-called small sample size (SSS) problem which is regularly encountered in the field of face recognition and occurs when the sample dimensionality is larger than the number of available training samples per subject. In this type of problems, the discriminative techniques need modifications in order to be feasible, but even in their most elaborate forms require at least two training samples per subject. The expressive approaches, on the other hand, are not susceptible to the SSS problem and are thus applicable even in the most extreme case of the small sample size problem, i.e., when only one training sample per subject is available. Nevertheless, in this paper we will show that the recognition performance of the expressive methods can match (or in some cases surpass) that of the discriminative techniques if the ex- pressive feature extraction approaches are used as multivariate regression techniques with a pre-designed response matrix that encodes the class-membership of the training samples. The effectiveness of the regression techniques for face recognition is demonstrated in a series of experiments performed on the ORL database. Additionally a comparative assessment of the regression techniques and popular discriminative approaches is presented. I. INTRODUCTION Over the past decades, automatic face recognition has become a highly active research area, mainly due to the countless application possibilities in both the private as well as the public sector [1]. Automated face recognition systems offer a possible way of improving security in var- ious domains ranging from access control, e-commerce, e- banking, e-government and health monitoring applications to automated user-authentications at ATMs, borders and air- ports. Face recognition, being a sub-discipline of biometrics 1 , has several advantages when compared to the classically employed knowledge- (e.g., passwords, PINs) or token-based (e.g., ID cards) security schemes [2]. Passwords and PINs can be forgotten, ID cards can be lost or stolen. The human V. ˇ Struc, R. Gajˇ sek, F. Miheliˇ c and N. Paveˇ si´ c are all with the Faculty of Electrical Engineering, University of Ljubljana, Trˇ zaˇ ska 25, SI-1000 Ljubljana, Slovenia (vitomir.struc, rok.gajsek, france.mihelic,nikola.pavesic)@fe.uni-lj.si 1 The term biometrics refers to a scientific discipline which involves methods of automatically recognizing (verifying or identifying) people by their physical and/or behavioral characteristics. face, on the other hand, cannot be stolen nor forgotten and is, furthermore, unique for each individual. Clearly, it holds a great potential in serving as means for authentication and/or identification of people. Security schemes, however, are not the only applica- tion domain of face recognition systems. They are often found in conjunction with ambient intelligence (and smart house/home) applications where they are used for profile managing. For example, when a person enters a room or house, the face recognition system identifies the person and adjusts the environment (e.g., lighting conditions, music, etc.) in accordance with his/her personal profile. As we have seen, automated face recognition system are suitable for various applications, however, a number of shortcomings have to be sorted out to improve their performance. One of the major issues with face recognition systems is their performance under the lack of training data. While the existing face recognition techniques work well when a sufficient number of facial images is available for training, the majority of them suffers with their recognition performance when only a small number of images is at hand for training. However, as this is the case with many real-life applications (due to limited memory or processing resources as, for example, in many mobile devices) researchers have directed a considerable research effort towards developing algorithms that require only a small number of training images and still achieve high recognition rates. If we confine ourselves to the dominant face recogni- tion techniques, i.e., appearance-based methods, two main research trends in respect to the lack of training data can be identified: (i) researchers try to improve the performance of the expressive approaches, such as principal component analysis (PCA)[3] or kernel principal component analysis (KPCA)[4], which are feasible regardless of the number of available training images but usually result in an in- sufficient recognition performance, and (ii) researchers try to modify the discriminative approaches, such as linear discriminant analysis (LDA)[5] or generalized discriminant analysis (GDA)[6] which commonly ensure high recognition rates, but require a sufficient number of training images to be applicable. The problem where the sample dimensionality is larger than the number of available training samples per subject is usually referred to as the small sample size (SSS) problem. Several techniques were presented in the literature to cope with the lack of training data. Wu and Zhou [7], for example, tried to improve the performance of the PCA- based Eigenface technique and introduced a technique called