Low-Rank Representation with Empirical Kernel Space Embedding of Manifolds

Area of Science:

• Machine Learning
• Data Science
• Computer Vision

Background:

• Existing Low-Rank Representation (LRR) methods struggle with suboptimal classification accuracy due to direct application of Euclidean algorithms on manifold data.
• Non-linear data structures often hinder effective low-dimensional manifold representation and classification.

Purpose of the Study:

• To develop an unsupervised low-rank projection learning method that enhances classification accuracy for manifold data.
• To improve the representation of low-dimensional manifolds by enabling linear separability of non-linear data.

Main Methods:

• Introduced Low-Rank Representation with Empirical Kernel Space Embedding of Manifolds (LRR-EKM).
• Utilized empirical kernel mapping to project samples into the Reproduced Kernel Hilbert Space (RKHS).
• Incorporated row sparsity and manifold structure preserving constraints on the projection matrix.

Main Results:

• LRR-EKM achieved superior performance compared to state-of-the-art methods across various real-world datasets.
• The method demonstrated improved low-dimensional manifold representations and enhanced feature selection.
• Empirical kernel mapping facilitated linear separability of non-linearly structured samples.

Conclusions:

• LRR-EKM effectively addresses limitations of traditional LRR methods for manifold data.
• The proposed method offers enhanced classification accuracy, interpretability, and preserves original data structure.
• The publicly available code facilitates further research and application.