Cone algorithm: an extension of the perceptron algorithm
S.J. Wan · IEEE Transactions on Systems Man and Cybernetics · 1994
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.>