Central Point Selection in Dimension Reduction Projection Simple-Map with Binary Quantization

Abstract

A Simple-Map (S-Map, for short), which is one of dimension reduction techniques applicable to any metric space, uses the distances between central points and objects as the coordinate values. S-Map with multiple central points is a projection to multidimensional $L_\infty$ space. In the previous researches for S-Map, the candidates for central points are randomly selected from data objects in database, and the summation of projective distances between sampled pairs of points is used as the scoring function to be maximized. We can improve the above method to select central points by using local search. The coordinate values of central points obtained after local search tend to be the maximum or the minimum ends of the space. By focusing on this tendency, in this paper, we propose a binary quantization to select central points divided into the maximum values and the minimum values based on whether the coordinate value of an object in database is greater than the threshold or not.

This work is partially supported by Grant-in-Aid for Scientific Research 24240021, 24300060, 25540137, 26280085, 26280090 and 26370281 from the Ministry of Education, Culture, Sports, Science and Technology, Japan.