Evaluation of space partitioning data structures for nonlinear mapping

Abstract

Nonlinear mapping (Sammon mapping) is a nonlinear dimensionality reduction technique operating on the data structure preserving principle. Several possible space partitioning data structures (vp-trees, kd-trees and cluster trees) are applied in the paper to improve the efficiency of the nonlinear mapping algorithm. At the first step specified structures partition the input multidimensional space, at the second step space partitioning structure is used to build up the list of reference nodes used to approximate calculations. The further steps perform initialization and iterative refinement of the low-dimensional coordinates of objects in the output space using created lists of reference nodes. Analyzed space partitioning data structures are evaluated in terms of the data mapping error and runtime. The experiments are carried out on the well-known datasets.