An application study of manifold learning-ranking techniques in face recognition A. Zagouras A. Macedonas Electronics Laboratory, Department of Physics Electronics Laboratory, Department of Physics University of Patras University of Patras 26500 Patras, Greece 26500 Patras, Greece thzagour@upatras.gr anmack@upatras.gr G. Economou S. Fotopoulos Electronics Laboratory, Department of Physic Electronics Laboratory, Department of Physics University of Patras University of Patras 26500 Patras, Greece 26500 Patras, Greece economou@physics.upatras.gr spiros@physics.upatras.gr Abstract-Locally Linear Embedding (LLE), Isometric reduction methods have been proposed, embedding the face Mapping (Isomap) are two relatively new nonlinear data to a low dimensional feature space while at the same time dimensionality reduction algorithms also used in face recognition preserving the main structure of the manifold. Recently some applications. Their main aim is to create a low-dimensional new extended dimensionality reduction algorithms have been embeddings of the original high-dimensional data, laying the face proposed [3], and used in clustering and classification of face data points on a 'face manifold'. In this work in order to test images [4,5]. Furthermore the combination of different their performance we applied LLE and Isomap in two face embedding techniques provides interesting results [6]. databases together with principal component analysis (PCA), On the manifold of the embedded space, similar face their linear counterpart, varying as parameters the (i) number embedding dimensions and (ii) the number of neighbours. imge ar pont ofalclnihorod h lsia Euclidean distance that is used as a similarity measure does Furthermore, at the final stage we used a data ranking not always follow the geometric properties of the manifold. algorithm, which ranks the data with respect to the intrinsic That leads us to another more efficient way of data ranking manifold structure and its geometric properties. Experimental which can exploit the intrinsic structure of the data and results indicate the superiority of the data ranking algorithm on enhance the face retrieval procedure. In this work, we study a face manifolds against the classical Euclidean distance measure. recently proposed data ranking algorithm [7] and apply it to Keywords-dimensionality reduction, manifold ranking, face the face recognition problem. recognition. In order to investigate the performance of data ranking Topic area-Signal and multimedia analysis. algorithm in face retrieval applications we applied LLE, Isomap and PCA on two faces databases. Using as guidance I. INTRODUCTION the best retrieval rate, we found the optimal embedding dimensionality and the required number of nearest neighbours Within the last several years, numerous algorithms have (LLE, Isomap) for each database. At the same time the been proposed for face recognition. It is accepted as a difficult different dimensionality reduction methods were tested. pattern recognition problem where illumination changes, facial expressions and head pose in face images are just some The remainder of this paper is organized as follows. In of the influencing factors that add to the complexity and are Section 2, we describe the basic concepts of the employed currently investigated in commercial and security face dimensionality reduction algorithms. Next, the data ranking recognition applications. algorithm is presented in Section 3. Section 4 presents the experimental results on AT&T [8] and Grimace [9] face A face image with N pixels can be considered as an a databases. Finally, the conclusions are given in Section 5. point in N-dimensional image space, and the variability of faces images can be represented by low-dimensional II. DIMENSIONALITY REDUCTION ALGORITHMS manifolds which are embedded in the high-dimensional image The intrinsic high dimensionality of data in many real life space. Dimensionality reduction is an important operation,n . 1- A' 11 -1-1I A - - -I I -I~~ applications as L.e in the case of ima2es and the fact onlv a few finding a suitable lower-dimensional space to represent, analyze~ ~~ an prcs th orgnldt.Frti ups,lna rojections are interesting has spJarked a great interest in the (PCA) an nolna (LL [1] Ismp[].imninlt research and developJment of manyt dimensionalityt reduction 1-4244-1274-9/07/$25.00 ©C2007 IEEE 445 MMSP 2007