A regularization framework for robust dimensionality reduction with applications to image reconstruction and feature extraction

Authors:
Zhizheng Liang;Youfu Li
Affiliations:
School of Computer Science and Technology, China University of Mining and Technology, China;Department of Manufacturing Engineering and Engineering Management, City University of Hong Kong, Hong Kong
Venue:
Pattern Recognition
Year:
2010

Citing 24
Cited 3

Introduction to statistical pattern recognition (2nd ed.)

Introduction to statistical pattern recognition (2nd ed.)
Constrained Restoration and the Recovery of Discontinuities

IEEE Transactions on Pattern Analysis and Machine Intelligence
Eigenfaces vs. Fisherfaces: Recognition Using Class Specific Linear Projection

IEEE Transactions on Pattern Analysis and Machine Intelligence
Minimizers of Cost-Functions Involving Nonsmooth Data-Fidelity Terms. Application to the Processing of Outliers

SIAM Journal on Numerical Analysis
Robust Factorization

IEEE Transactions on Pattern Analysis and Machine Intelligence
Solving the Small Sample Size Problem of LDA

ICPR '02 Proceedings of the 16 th International Conference on Pattern Recognition (ICPR'02) Volume 3 - Volume 3
Linear Dimensionality Reduction via a Heteroscedastic Extension of LDA: The Chernoff Criterion

IEEE Transactions on Pattern Analysis and Machine Intelligence
Discriminative Common Vectors for Face Recognition

IEEE Transactions on Pattern Analysis and Machine Intelligence
Face Recognition Using Laplacianfaces

IEEE Transactions on Pattern Analysis and Machine Intelligence
A Two-Stage Linear Discriminant Analysis via QR-Decomposition

IEEE Transactions on Pattern Analysis and Machine Intelligence
Robust L" Norm Factorization in the Presence of Outliers and Missing Data by Alternative Convex Programming

CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 1 - Volume 01
Graph Embedding: A General Framework for Dimensionality Reduction

CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
Characterization of a Family of Algorithms for Generalized Discriminant Analysis on Undersampled Problems

The Journal of Machine Learning Research
Analysis of Half-Quadratic Minimization Methods for Signal and Image Recovery

SIAM Journal on Scientific Computing
R1-PCA: rotational invariant L1-norm principal component analysis for robust subspace factorization

ICML '06 Proceedings of the 23rd international conference on Machine learning
Graph Embedding and Extensions: A General Framework for Dimensionality Reduction

IEEE Transactions on Pattern Analysis and Machine Intelligence
A study on three linear discriminant analysis based methods in small sample size problem

Pattern Recognition
Discriminant Subspace Analysis: A Fukunaga-Koontz Approach

IEEE Transactions on Pattern Analysis and Machine Intelligence
A Trust Region Direct Constrained Minimization Algorithm for the Kohn-Sham Equation

SIAM Journal on Scientific Computing
Principal Component Analysis Based on L1-Norm Maximization

IEEE Transactions on Pattern Analysis and Machine Intelligence
Efficient Reconstruction of Piecewise Constant Images Using Nonsmooth Nonconvex Minimization

SIAM Journal on Imaging Sciences
An optimization criterion for generalized discriminant analysis on undersampled problems

IEEE Transactions on Pattern Analysis and Machine Intelligence
Generalizing discriminant analysis using the generalized singular value decomposition

IEEE Transactions on Pattern Analysis and Machine Intelligence
Efficient and robust feature extraction by maximum margin criterion

IEEE Transactions on Neural Networks

A semi-supervised approach for dimensionality reduction with distributional similarity

Neurocomputing
Adaptive weighted learning for linear regression problems via Kullback-Leibler divergence

Pattern Recognition
Feature extraction based on Lp-norm generalized principal component analysis

Pattern Recognition Letters

Quantified Score

Hi-index	0.01

Visualization

Abstract

Dimensionality reduction has many applications in pattern recognition, machine learning and computer vision. In this paper, we develop a general regularization framework for dimensionality reduction by allowing the use of different functions in the cost function. This is especially important as we can achieve robustness in the presence of outliers. It is shown that optimizing the regularized cost function is equivalent to solving a nonlinear eigenvalue problem under certain conditions, which can be handled by the self-consistent field (SCF) iteration. Moreover, this regularization framework is applicable in unsupervised or supervised learning by defining the regularization term which provides some types of prior knowledge of projected samples or projected vectors. It is also noted that some linear projection methods can be obtained from this framework by choosing different functions and imposing different constraints. Finally, we show some applications of our framework by various data sets including handwritten characters, face images, UCI data, and gene expression data.