Neural computing: theory and practice
Neural computing: theory and practice
An algorithm for solving linear programming programs in O(n3L) operations
Progress in Mathematical Programming Interior-point and related methods
The quickhull algorithm for convex hulls
ACM Transactions on Mathematical Software (TOMS)
Making large-scale support vector machine learning practical
Advances in kernel methods
An introduction to support Vector Machines: and other kernel-based learning methods
An introduction to support Vector Machines: and other kernel-based learning methods
Pattern Classification (2nd Edition)
Pattern Classification (2nd Edition)
Core Vector Machines: Fast SVM Training on Very Large Data Sets
The Journal of Machine Learning Research
The linear separability problem: some testing methods
IEEE Transactions on Neural Networks
On the Foundations of Noise-free Selective Classification
The Journal of Machine Learning Research
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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 d2/3.