Improved Spectral Clustering Using Adaptive Mahalanobis Distance

In this paper, we consider the manifold clustering problem. In manifold clustering, data are sampled from multiple manifolds and the goal is to partition the data accordingly. Spectral clustering algorithms have been developed to solve this problem, but they tend to fail when the underlying manifolds are very close to each other and/or they intersect. We propose an improvement to spectral clustering algorithms using adaptive neighborhoods computed using Mahalanobis distance. We show the effectiveness of this approach on some artificial data. We further incorporate the modification into recent related algorithms and compare the results on datasets in motion segmentation, handwritten digit recognition, and object rotation.