Unsupervised learning of low rank subspace projection using graph embedding

Abstract

Subspace learning has often been explored for various applications such as dimensionality reduction, denoising, clustering and feature extraction among others. However, low rank subspace learning for clustering as well as efficient feature extraction is still a challenging problem. In this thesis, we aim to study a low rank projection algorithm which uses graph embedding. Projection based learning has been widely explored in the field of image processing. We analyse the method via preserving the (local) neighbourhood relationship among data by incorporating graph embedding. Along with being able to explore the inter data relationship, the projection technique is robust to noise and outliers by learning a robust low-rank subspace projection. Aiming to strengthen the clustering performance, we also apply a co-clustering technique to take advantage of the co-occuring cluster structure among sample points and its features via a novel bipartite graph learning technique. In this project, we formulate this as a multi-objective convex optimization problem and theoretically provide an iterative approach by using a novel alternating direction method of multipliers (ADMM) to efficiently solve the optimization problem in polynomial time. We demonstrate the application of the projection matrix in image and text classification and clustering.