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.
