Kernel Spectral Curvature Clustering (KSCC)

Multi-manifold modeling is increasingly used in segmentation and data representation tasks in computer vision and related fields. While the general problem, modeling data by mixtures of manifolds, is very challenging, several approaches exist for modeling data by mixtures of affine subspaces (which is often referred to as hybrid linear modeling). We translate some important instances of multi-manifold modeling to hybrid linear modeling in embedded spaces, without explicitly performing the embedding but applying the kernel trick. The resulting algorithm, Kernel Spectral Curvature Clustering, uses kernels at two levels - both as an implicit embedding method to linearize nonflat manifolds and as a principled method to convert a multiway affinity problem into a spectral clustering one. We demonstrate the effectiveness of the method by comparing it with other state-of-the-art methods on both synthetic data and a real-world problem of segmenting multiple motions from two perspective camera views.Comment: accepted to 2009 ICCV Workshop on Dynamical Visio

Piecewise Linear Manifold Clustering

This work studies the application of topological analysis to non-linear manifold clustering. A novel method, that exploits the data clustering structure, allows to generate a topological representation of the point dataset. An analysis of topological construction under different simulated conditions is performed to explore the capabilities and limitations of the method, and demonstrated statistically significant improvements in performance. Furthermore, we introduce a new information-theoretical validation measure for clustering, that exploits geometrical properties of clusters to estimate clustering compressibility, for evaluation of the clustering goodness-of-fit without any prior information about true class assignments. We show how the new validation measure, when used as regularization criteria, allows creation of clusters that are more informative. A final contribution is a new metaclustering technique that allows to create a model-based clustering beyond point and linear shaped structures. Driven by topological structure and our information-theoretical criteria, this technique provides structured view of the data on new comprehensive and interpretation level. Improvements of our clustering approach are demonstrated on a variety of synthetic and real datasets, including image and climatological data