A Fast Linear Separability Test by Projection of Positive Points on Subspaces

Yogananda, AP and Narasimha Murthy, M and Gopal, Lakshmi (2007) A Fast Linear Separability Test by Projection of Positive Points on Subspaces. In: ICML '07 Proceedings of the 24th international conference on Machine learning, June 20-24, 2007, New York, NY.

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Abstract

A geometric and non parametric procedure for testing if two finite set of points are linearly separable is proposed. The Linear Separability Test is equivalent to a test that determines if a strictly positive point h > 0 exists in the range of a matrix A (related to the points in the two finite sets). The algorithm proposed in the paper iteratively checks if a strictly positive point exists in a subspace by projecting a strictly positive vector with equal co-ordinates (p), on the subspace. At the end of each iteration, the subspace is reduced to a lower dimensional subspace. The test is completed within r ≤ min(n, d + 1) steps, for both linearly separable and non separable problems (r is the rank of A, n is the number of points and d is the dimension of the space containing the points). The worst case time complexity of the algorithm is O(nr3) and space complexity of the algorithm is O(nd). A small review of some of the prominent algorithms and their time complexities is included. The worst case computational complexity of our algorithm is lower than the worst case computational complexity of Simplex, Perceptron, Support Vector Machine and Convex Hull Algorithms, if d<n2/3.

Item Type:	Conference Paper
Publisher:	ACM Press
Additional Information:	Copyright of this article belongs to ACM Press.
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation
Date Deposited:	17 Oct 2011 09:43
Last Modified:	17 Oct 2011 09:43
URI:	http://eprints.iisc.ac.in/id/eprint/41487

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