Least square projection: a fast high-precision multidimensional projection technique and its application to document mapping

摘要

A new technique, least square projection (LSP), is proposed for projecting a set of points in a high-dimensional space to a low-dimensional one. The authors claim that it encompasses good features of both linear and nonlinear projection methods. The method is based on defining a set of control points; for instance, it uses the k-medoids method and takes the medoids as control points. The clustering also gives neighborhood relationships, used to construct a matrix that represents a neighborhood graph. A linear system is then defined using the control points and the graph matrix, and this system is solved in the least squares sense, giving the projected coordinates. The algorithm description might have been made somewhat more precise.