A fast linear separability test by projection of positive points on subspaces

A geometric and non parametric procedure for testing if two nite 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 nite 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 ...

• Type: Conference
• Year: 2007
• Where: ICML
• Authors: A. P. Yogananda, M. Narasimha Murty, Lakshmi Gopal
• Keywords: Case Computational Complexity, Case Time Complexity, ICML 2007, Lower Dimensional Subspace, Machine Learning