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Cone algorithm: an extension of the perceptron algorithm

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1 Author(s)
Wan, S.J. ; Dept. of Comput. Sci., Regina Univ., Sask., Canada

The perceptron convergence theorem played an important role in the early development of machine learning. Mathematically, the perceptron learning algorithm is an iterative procedure for finding a separating hyperplane for a finite set of linearly separable vectors, or equivalently, for finding a separating hyperplane for a finite set of linearly contained vectors. In this paper, the author shows that the perceptron algorithm can be extended to a more general algorithm, called the cone algorithm, for finding a covering cone for a finite set of linearly contained vectors. A proof of the convergence of the cone algorithm is given. The relationship between the cone algorithm and other related algorithms is discussed. The equivalence of the problem of finding a covering cone for a set of linearly contained vectors and the problem of finding a solution cone for a system of homogeneous linear inequalities is established

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Systems, Man and Cybernetics, IEEE Transactions on  (Volume:24 ,  Issue: 10 )