Semi-supervised classification in stratified spaces by considering non-interior points using Laplacian behavior

Abstract

Manifold-based semi-supervised classifiers have attracted increasing interest in recent years. However, they suffer from over learning of locality and cannot be applied to the point cloud sampled from a stratified space. This problem is resolved in this paper by using the fact that the smoothness assumption must be satisfied with the interior points of the manifolds and may be violated in the non-interior points. Distinction of interior and non-interior points is based on the behavior of graph Laplacian in the ϵ-neighborhood of the intersection points. First, this property was generalized to KNN graph representing the stratified space and then a new algorithm was proposed that penalizes the smoothness on the non-interior points of the manifolds by modifying the edge weights of the graph. Compared to some recent multi-manifold semi-supervised classifiers, the proposed method does not require neither knowing the dimensions of the manifolds nor large amount of unlabeled points to estimate the underling manifolds and does not assume similar properties for neighbors of all data points. Some experiments have been conducted in order to show that it improves the classification accuracy on a number of artificial and real benchmark data sets.