In this paper, we propose a novel classification algorithm, called geometrical probability covering (GPC) algorithm, to improve classification ability. On the basis of geometrical properties of data, the proposed algorithm first forms extended prototypes through computing means of any two prototypes in the same class. Then Gaussian kernel is employed for covering the geometrical structure of da...

Given n uniformly and independently distributed points in a ball of unit volume in dimension d, it is well established that the length of several combinatorial optimization problems (including the minimum spanning tree (MST), the minimum matching (M), the traveling salesman problem (TSP), etc.) on these n points obeys laws of large numbers. It has been a long open conjecture that a central limi...

The Bertrand paradox question is: “Consider a unit-radius circle for which the length of a side of an inscribed equilateral triangle equals 3 . Determine the probability that the length of a ‘random’ chord of a unit-radius circle has length greater than 3 .” Bertrand derived three different ‘correct’ answers, the correctness depending on interpretation of the word, random. Here we employ geomet...