Doctoral Seminar: Kha Gia Quach

Speaker: Kha Gia Quach

Supervisor: Dr. T. D. Bui

Supervisory Committee:
Drs. E. J. Doedel, B. Jaumard, A. Ben Hamza

Title:  Non-convex Ip-norm Regularization and its Applications in Large Scale Data Analysis

Date: Thursday, March 17, 2016

Time: 10:15am

Place: EV 3.309

ABSTRACT

Compressive sensing, matrix rank optimization and Robust PCA-based matrix decomposition have an increasing number of non-convex approaches for optimizing the ideal l0-norm sparsity. In this research, we propose a novel online non-convex lp-norm based Robust PCA (OLP-RPCA) approach, where 0 < p < 1. OLP-RPCA is developed from the offline version LP-RPCA. Our LP-RPCA method uses a new objective function in the Alternating Direction Method of Multipliers (ADMM) framework to efficiently solve the Robust PCA problem. More importantly, our OLP-RPCA method can achieve real-time performance on large-scale data without parallelizing or implementing on a graphics processing unit. We mathematically and empirically show that our OLP-RPCA algorithm is linear in both the sample dimension and the number of samples.

The proposed approaches are successfully applied in various applications including image denoising, real-time background subtraction and video inpainting. For face modeling, it can remove unwanted factors, e.g. noise, shadows, darkness, etc., and produce better looking images, but it requires testing on the same subject appeared in training set.

Therefore, this research explores the idea of matrix decomposition to develop an extension on the existing generative models, namely Deep Appearance Models (DAMs). This extension can cope with occlusion and extreme poses when modeling facial images while relaxing constraints on the training set. This report presents the proposed OLP-RPCA and LP-RPCA approaches in depth and briefly discuss a robust extension of DAMs.