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