Kernel Spectral Curvature Clustering (KSCC)

TL;DR

Kernel Spectral Curvature Clustering (KSCC) is a novel method that uses kernel tricks and spectral clustering to segment data lying on multiple manifolds, effectively handling complex multi-manifold modeling tasks.

Contribution

The paper introduces KSCC, a new algorithm that applies kernels at two levels for multi-manifold segmentation without explicit embedding, advancing hybrid linear modeling techniques.

Findings

KSCC outperforms existing methods on synthetic data.

KSCC effectively segments multiple motions in real-world scenarios.

The method efficiently handles nonflat manifolds in embedded spaces.

Abstract

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.