Dimensionality Reduction by Weighted Connections between Neighborhoods

Abstract

Dimensionality reduction is the transformation of high-dimensional data into a meaningful representation of reduced dimensionality. This paper introduces a dimensionality reduction technique by weighted connections between neighborhoods to improve $K$-Isomap method, attempting to preserve perfectly the relationships between neighborhoods in the process of dimensionality reduction. The validity of the proposal is tested by three typical examples which are widely employed in the algorithms based on manifold. The experimental results show that the local topology nature of dataset is preserved well while transforming dataset in high-dimensional space into a new dataset in low-dimensionality by the proposed method.