Unsupervised Segmentation of Non-Intersecting Manifolds

Abstract

Manifold learning has been an important research area as from literature it is evident that patterns in most real-life data sets can be embedded in low-dimensional space while maintaining the original structure of high-dimensional space. This work concentrates on one of the major research areas of manifold learning, which is the segregation of manifolds where more than one non-intersecting manifolds are present. The proposed method presents a solution to the problem by detecting the number of manifolds in a dataset using the Laplacian graph matrix and segregate the manifolds using agglomerative clustering. Eventually, locally linear embedding has been used for dimensionality reduction of every individual manifold in such a way that manifolds remain segregated and also holds the original global structure. The proposed method achieves finer results when applied on benchmark synthetic data sets SCurve, SwissRoll, Helix and real-life datasets COIL-20, optical digit recognition, att_faces, extended Yale Face Database B. While the state of the art methods fails to detect the number of manifolds in a dataset, the proposed method not only eclipses the performance of them but also carry the separable structure in the lower dimensional space.