Relational multimanifold coclustering.

Area of Science:

• Machine Learning
• Data Mining
• Dimensionality Reduction

Background:

• Coclustering simultaneously groups samples and features, leveraging dual relations.
• Estimating intrinsic data manifolds in Euclidean space is challenging.
• Existing methods struggle to accurately approximate complex data structures.

Purpose of the Study:

• To enhance coclustering performance using manifold ensemble learning.
• To develop a novel algorithm for approximating intrinsic sample and feature manifolds.
• To address the challenge of data residing on submanifolds.

Main Methods:

• Developed relational multimanifold coclustering based on symmetric nonnegative matrix trifactorization.
• Incorporated intertype relationships and intratype information via affinity matrices.
• Optimized objective function using multiplicative rules and explored entropic mirror descent and coordinate descent algorithms.

Main Results:

• The proposed algorithm effectively approximates intrinsic manifolds for both sample and feature spaces.
• Demonstrated superior performance compared to existing coclustering methods.
• Achieved significant improvements in coclustering accuracy on document, image, and gene expression datasets.

Conclusions:

• Relational multimanifold coclustering offers a powerful approach for complex data analysis.
• Manifold ensemble learning is effective for improving coclustering on submanifold data.
• The novel algorithm provides a robust solution for simultaneous sample and feature grouping.