Low Rank Representation on Riemannian Manifold of Square Root Densities
This work addresses a domain-specific problem in computer vision by extending low rank representation to non-Euclidean manifolds, which is incremental as it adapts an existing method to a new geometric setting.
The paper tackled the problem of low rank representation for data on the manifold of square root densities by developing a novel algorithm that incorporates intrinsic geometric structure and geodesic distance, resulting in improved noise robustness and superior performance in classification and subspace clustering on computer vision datasets.
In this paper, we present a novel low rank representation (LRR) algorithm for data lying on the manifold of square root densities. Unlike traditional LRR methods which rely on the assumption that the data points are vectors in the Euclidean space, our new algorithm is designed to incorporate the intrinsic geometric structure and geodesic distance of the manifold. Experiments on several computer vision datasets showcase its noise robustness and superior performance on classification and subspace clustering compared to other state-of-the-art approaches.