Manifold Segmentation and Deep Convolutional Networks
Abstract
The manifold clustering problem has attracted interest in several areas of mathematics and its applications to science and engineering. For example, all images of a given face with same facial expression, obtained under different illuminations and facial positions, can be modeled as a set of vectors belonging to a low dimensional subspace living in a higher dimensional space. The motion segmentation problem is also a special case of subspace segmentation problem. Deep convolutional networks are multilayer neural networks that have linear convolution layers followed by a set of fully connected layers. Each layer receives input from the previous layer and reshapes the data through transformations. A set of filters are applied to the convolution layers and a training stage is used to determine the filter parameters. The filters are simply automatic feature extractors and deep convolutional networks are currently the state-of-the-art for object recognition. Even though various deep learning architectures have been applied to many high-dimensional problems, its mathematics and relationship to manifold clustering are not well-understood. The research goal of this project is to develop mathematical theory and efficient algorithms for robust deep learning integrated with manifold and subspace clustering}. The associated objectives are listed as: (1) Improve our existing subspace clustering theory and extend it to manifold clustering in more general sense. (2) Improve existing mathematical theory of deep convolution networks with enhanced manifold separation in feature spaces/layers. (3) Develop new algorithms for robust deep learning with manifold/subspace segmentation and apply them to computer vision, speech processing, and medical imaging. This project will complement and extend theory and techniques from machine learning, subspace clustering, manifold approximations, and sampling theory. The proposed research will generate interactions between certain areas of mathematics and computer science, such as non-linear approximation, optimization, probability theory, and algorithms. The PI holds two PhD degrees in Electrical Engineering and Mathematics and he is a full professor of Computer Science. The PI previously completed a basic research grant from the Department of Defense to develop theories and algorithms for solving subspace segmentation problem in its general sense. The proposed research focuses on mathematical understanding of deep convolutional networks and its relationship to subspace/manifold segmentation. It partially builds on our existing research but it develops new theory and techniques for development of robust deep convolutional networks. The proposed research is very recent and has numerous potential applications in the key DoD research areas. It is envisioned that TSU s position as an HBCU will enable research opportunities to be extended to many students, including underrepresented minority students.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jul 09, 2020
- Source ID
- W911NF2010284
Entities
People
- Ali Sekmen
Organizations
- Army Contracting Command
- Office of the Secretary of Defense
- Tennessee State University