in this paper, a chaotic particle swarm optimization with mutation-based classifier particle swarm optimization is proposed to classifypatterns of different classes in the feature space. the introduced mutation operators and chaotic sequences allows us to overcomethe problem of early convergence into a local minima associated with particle swarm optimization algorithms. that is, the mutationope...

Abstract Problems such as data compression, pattern recognition and artificial intelligence often deal with a large sample observations of an unknown object. An effective method is proposed to fit hyperplanes points in each hypercubic subregion the original sample. Corresponding set affine linear manifolds, locally fitted optimally approximate object sense least squares their perpendicular dist...

It is proved that the collection of blocks of an affine 1-design that yields a linear orthogonal array is a union of parallel classes of hyperplanes in a finite affine space. In particular, for every prime power q and every m ≥ 2 there exists a unique (up to equivalence) complete linear orthogonal array of strength two associated with the classical design of points and hyperplanes in AG(m, q).

We study the S-integral points on the complement of a union of hyperplanes in projective space, where S is a finite set of places of a number field k. In the classical case where S consists of the set of archimedean places of k, we completely characterize, in terms of the hyperplanes and the field k, when the (S-)integral points are not Zariski-dense.

We propose a recursive algorithm for clustering trajectories lying in multiple moving hyperplanes. Starting from a given or random initial condition, we use normalized gradient descent to update the coefficients of a time varying polynomial whose degree is the number of hyperplanes and whose derivatives at a trajectory give an estimate of the vector normal to the hyperplane containing that traj...

In [11] all locally subquadrangular hyperplanes of finite symplectic and Hermitian dual polar spaces were determined with the aid of counting arguments and divisibility properties of integers. In the present note we extend this classification to the infinite case. We prove that symplectic dual polar spaces and certain Hermitian dual polar spaces cannot have locally subquadrangular hyperplanes i...

Decision table describing n objects in terms of k classification attributes and one decision attribute can be seen as a collection of n points in k-dimensional space. Each point is classified either as positive or negative. The goal of this paper is to present an efficient strategy for constructing possibly the smallest number of hyperplanes so each area surrounded by them contains a group of p...

A celebrated technique for finding near neighbors for the angular distance involves using a set of random hyperplanes to partition the space into hash regions [Charikar, STOC 2002]. Experiments later showed that using a set of orthogonal hyperplanes, thereby partitioning the space into the Voronoi regions induced by a hypercube, leads to even better results [Terasawa and Tanaka, WADS 2007]. How...