Robust Multiple Manifolds Structure Learning

TL;DR

This paper introduces a robust method for learning multiple manifold structures in data, combining local tangent space estimation with a novel clustering approach to improve accuracy in complex datasets.

Contribution

The paper proposes a new robust multiple manifolds structure learning scheme that integrates local tangent space estimation with a curved-level similarity based clustering method.

Findings

Higher clustering accuracy on synthetic and real datasets

Effective in human motion segmentation tasks

Promising results in motion flow learning from videos

Abstract

We present a robust multiple manifolds structure learning (RMMSL) scheme to robustly estimate data structures under the multiple low intrinsic dimensional manifolds assumption. In the local learning stage, RMMSL efficiently estimates local tangent space by weighted low-rank matrix factorization. In the global learning stage, we propose a robust manifold clustering method based on local structure learning results. The proposed clustering method is designed to get the flattest manifolds clusters by introducing a novel curved-level similarity function. Our approach is evaluated and compared to state-of-the-art methods on synthetic data, handwritten digit images, human motion capture data and motorbike videos. We demonstrate the effectiveness of the proposed approach, which yields higher clustering accuracy, and produces promising results for challenging tasks of human motion segmentation and motion flow learning from videos.