A Class of Manifold Regularized Multiplicative Update Algorithms for Image Clustering.

Area of Science:

• Machine Learning
• Data Science
• Computer Vision

Background:

• Multiplicative update algorithms are crucial for information retrieval, image processing, and pattern recognition.
• Graph regularization in cost functions can cause data clustering errors by mapping different classes to the same subspace.

Purpose of the Study:

• To introduce an improved nonnegative matrix factorization (NMF) cost function.
• To develop novel graph regularized NMF algorithms with manifold structure regularization.

Main Methods:

• Development of extended multiplicative update algorithms based on an improved NMF cost function.
• Incorporation of manifold structure regularization to enhance data representation.

Main Results:

• The proposed algorithms efficiently minimize the rank of the data representation matrix during learning.
• Simulations confirm theoretical results, demonstrating convergence features and efficiency through basis images, reconstructed images, and clustering results.
• The algorithms achieve state-of-the-art performance in image clustering applications.

Conclusions:

• The novel graph regularized NMF algorithms effectively address data clustering errors introduced by standard graph regularization.
• The developed algorithms offer improved manifold structure regularization, leading to enhanced clustering accuracy and state-of-the-art performance.