Regularized Locality Preserving Projections with Two-Dimensional Discretized Laplacian Smoothing

Cai, Deng; He, Xiaofei; Han, Jiawei

Permalink

https://hdl.handle.net/2142/11231 Copy

Description

Title

Regularized Locality Preserving Projections with Two-Dimensional Discretized Laplacian Smoothing

Author(s)

• Cai, Deng
• He, Xiaofei
• Han, Jiawei

Issue Date

2006-07

Keyword(s)

computer science

Abstract

A novel approach to linear dimensionality reduction is introduced that is based on Locality Preserving Projections (LPP) with a discretized Laplacian smoothing term. The choice of penalty allows us to incorporate prior information that some features may be correlated. For example, an n_1 \times n_2 image represented in the plane is intrinsically a matrix. The pixels spatially close to each other may be correlated. Even though we have n_1 \times n_2 pixels per image, this spatial correlation suggests the real number of freedom is far less. However, most of the previous methods consider an image as a vector in \mathbb{R}^{n_1 \times n_2}. They do not take advantage of the spatial correlation in the image, and the pixels are considered as independent pieces of information. In this paper, we introduce a Regularized LPP model using a Laplacian penalty to constrain the coefficients to be spatially smooth. By preserving the local geometrical structure of the image space, we can obtain a linear subspace which is optimal for image representation in the sense of local isometry. Recognition, clustering and retrieval can be then performed in the image subspace. Experimental results on face representation and recognition demonstrate the effectiveness of our method.

Type of Resource

text

Permalink

http://hdl.handle.net/2142/11231

Copyright and License Information

You are granted permission for the non-commercial reproduction, distribution, display, and performance of this technical report in any format, BUT this permission is only for a period of 45 (forty-five) days from the most recent time that you verified that this technical report is still available from the University of Illinois at Urbana-Champaign Computer Science Department under terms that include this permission. All other rights are reserved by the author(s).

Owning Collections