Notification:
We are currently experiencing intermittent issues impacting performance. We apologize for the inconvenience.
By Topic

Sparsity in unions of subspaces for classification and clustering of high-dimensional data

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

2 Author(s)
Elhamifar, E. ; Dept. of Electr. & Comput. Eng., Johns Hopkins Univ., Baltimore, MD, USA ; Vidal, R.

In many problems in signal/image processing, machine learning and computer vision, data in multiple classes lie in multiple low-dimensional subspaces of a high-dimensional ambient space. We consider the two problems of classification and clustering of data in a union subspaces using sparse representation techniques. We use the idea that the collection of data forms a self-expressive dictionary in which a new data point can write itself as a linear combination of points from the same class/subspace. First, we consider the classification problem where the training data in each class form a few groups of the dictionary and correspond to a few subspaces. We formulate the classification problem as finding a few active subspaces in the union of subspaces using two classes of convex optimization programs. We investigate conditions under which the proposed optimization programs recover the desired solution. Next, we consider the clustering problem, where the goal is to cluster the data in a union of subspaces so that data points in each cluster correspond to points in the same subspace. We propose a convex optimization program based on sparse representation and use its solution to infer the clustering of data using spectral clustering. We investigate conditions under which the proposed convex program successfully finds a sparse representation of each point as a linear combination of points from the same subspace. We demonstrate the efficacy of the proposed classification and clustering algorithms through synthetic and real experiments.

Published in:

Communication, Control, and Computing (Allerton), 2011 49th Annual Allerton Conference on

Date of Conference:

28-30 Sept. 2011