Adaptive Neighborhood Select Based on Local Linearity for Nonlinear Dimensionality Reduction

Authors:
Yubin Zhan;Jianping Yin;Xinwang Liu;Guomin Zhang
Affiliations:
Computer School, National University of Defense Technology, Changsha, China;Computer School, National University of Defense Technology, Changsha, China;Computer School, National University of Defense Technology, Changsha, China;Computer School, National University of Defense Technology, Changsha, China
Venue:
ISICA '09 Proceedings of the 4th International Symposium on Advances in Computation and Intelligence
Year:
2009

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Abstract

Neighborhood selection plays an important role in manifold learning algorithm. This paper proposes an Adaptive Neighborhood Select algorithm based on Local Linearity(ANSLL). Given manifold dimensionality d as a priori knowledge, ANSLL algorithm constructs neighborhood based on two principles: 1. data points in the same neighborhood should approximately lie on a d -dimensional linear subspace; 2. each neighborhood should be as large as possible. And in ASNLL algorithm PCA technique is exploited to measure the linearity of finite data points set. Moreover, we present an improved method of constructing neighborhood graph, which can improve the accuracy of geodesic distance estimate for isometric embedding. Experiments on both synthetic data sets and real data sets show that ANSLL algorithm can adaptively construct neighborhood according to local curvature of data manifold and then improve the performance of most manifold algorithms, such as ISOMAP and LLE.