Vol.2, No.1, 49-53 (2010) Natural Science

http://dx.doi.org/10.4236/ns.2010.21007

Copyright © 2010 SciRes. OPEN ACCESS

Face recognition based on manifold learning and

Rényi entropy

Wen-Ming Cao, Ning Li

Intelligent Information Processing Key Laboratory, Shenzhen University, Shenzhen, China; wmcao@szu.edu.cn

Received 10 September 2009; revised 29 October 2009; accepted 9 November 2009.

ABSTRACT

Though manifold learning has been success-

fully applied in wide areas, such as data visu-

alization, dimension reduction and speech rec-

ognition; few researches have been done with

the combination of the information theory and

the geometrical learning. In this paper, we carry

out a bold exploration in this field, raise a new

approach on face recognition, the intrinsic

α-Rényi entropy of the face image attained from

manifold learning is used as the characteristic

measure during recognition. The new algorithm

is tested on ORL face database, and the ex-

periments obtain the satisfying results.

Keywords: Manifold Learning; Rényi Entropy; Face

Recognition

1. INTRODUCTION

Face recognition has becoming a research hotspot in the

fields of image processing, pattern recognition and arti-

ficial intelligence in recent years. Numerous research

papers appear on the famous international publications, a

great deal of capital and manpower is invested to this

research and its relevant application system develop-

ments. However, the performance of the face recognition

could be influenced by many factors, such as illumina-

tion, gesture, age, facial expressions, image resolution,

and noise, etc; which cause difficulties for the computer

processing of face recognition, and turn it into a chal-

lenging task at the same time.

The existing face recognition methods can be roughly

classified into two categories [1]: local feature based,

and global feature based. A local feature based method

symbolizes a human face with the extracted feature vec-

tors (eyes, nose, mouth, hair, and face contours), designs

certain kinds of classifiers to make recognition. On the

other hand, a global feature based method employs the

whole images as the input feature vectors, and then

low-dimensional features are extracted by some learning

algorithms. The main difference between the two cate-

gories lies in the way how the features are extracted. In a

local feature based method, features are designed com-

pletely by the algorithm designers; while in global fea-

ture based method, features are automatically extracted

or learned by some self-learning algorithms.

Local feature based or learning based methods can be

further divided into two classes: 1) statistical learning,

such as artificial neural networks (ANN) [2-4], support

vector machine (SVM) [5,6], and Boosting [7,8]; 2)

manifold learning(or dimensionality reduction), such as

linear methods like PCA [9,10], LDA [11,12], and

nonlinear methods like Isomap [13], LLE [14], Lapla-

cian Eigenmaps [15,16].

In recent years, nonlinear dimensionality reduction

(NLDR) methods have attracted great attentions due to

their capability to deal with nonlinear and curved data

[1]. All these algorithms rely on an assumption that the

image data lie on or close to a smooth low-dimensional

manifold in a high-dimensional input image space. A big

limitation of NLDR algorithms is the way how to esti-

mate the intrinsic dimension of the manifold. LLE and

Laplacian Eigenmaps do not give method to estimate the

intrinsic dimension; Isomap shows a simple way to es-

timate the intrinsic dimension by searching for the “el-

bow point” where the residual error decreases signifi-

cantly. However, for some real data, it is difficult to find

an obvious “elbow point” to indicate the intrinsic di-

mension.

The intrinsic dimensionality estimation of a data set is

a classical problem of pattern recognition. From the

math point, the intrinsic dimension of a manifold is the

dimension of the vector space that is homeomorphic to

local neighborhoods of the manifold; in other words,

intrinsic dimension describes how many “degrees of

freedom” are necessary to generate the observed data.

When the samples are drawn from a large population of

signals one can interpret them as realizations from a

multivariate distribution supported on the manifold. The

intrinsic entropy of random samples obtained from a

manifold is an information theoretic measure of the

complexity of this distribution. The entropy is a finite

value when the distribution satisfies the restriction of