Dynamic Neighborhood Selection for Nonlinear Dimensionality Reduction

Neighborhood construction is a necessary and important step in nonlinear dimensionality reduction algorithm. In this paper. we first summarize the two principles for neighborhood construction via analyzing existing nonlinear dimensionality reduction algorithms: 1) data points in the same neighborhood should approximately lie on a low dimensional linear subspace; and 2) each neighborhood should be as large as possible. Then a dynamic neighborhood selection algorithm based on this two principles is proposed in this paper. The proposed method exploits PCA technique to measure the linearity of a finite points set. Moreover, for isometric embedding, we present an improved method or constructing neighborhood graph, which can improve the accuracy of geodesic distance estimation. Experiments on both synthetic data sets and real data sets show that our method can construct neighborhood according to local curvature of data manifold and then improve the performance of most manifold algorithms, such as ISOMAP and LLE.