Autoencoder-like Sparse Non-Negative Matrix Factorization with Structure Relationship Preservation | JoVE Visualize

Area of Science:

Data Mining
Machine Learning
Pattern Recognition

Background:

Traditional non-negative matrix factorization (NMF) methods in data mining offer interpretability but struggle with preserving data topology during dimensionality reduction.
Capturing complex relationships and higher-order structures in data remains a challenge for existing NMF algorithms.

Purpose of the Study:

To propose an advanced NMF algorithm, autoencoder-like sparse non-negative matrix factorization with structure relationship preservation (ASNMF-SRP), designed to overcome the limitations of traditional NMF.
To enhance the stability and representation capabilities of coefficient matrices in NMF by incorporating autoencoder principles.
To effectively preserve topological structure information and feature relationships within data during low-dimensional representation.

Main Methods:

A novel "decoder-encoder" co-optimization matrix factorization framework inspired by autoencoders is developed.
A preference-adjusted random walk strategy is employed to capture higher-order neighborhood relationships and encode multi-order topological structures via graph regularization.
The l2,1-norm is utilized to constrain feature correlations and preserve feature relationships, while sparse constraints are applied to the coefficient matrix.

Main Results:

Experimental results on eight public datasets demonstrate the effectiveness of the proposed ASNMF-SRP algorithm.
ASNMF-SRP consistently achieves favorable clustering performance compared to existing methods.
The method successfully preserves topological structures and feature relationships in low-dimensional representations.

Conclusions:

ASNMF-SRP offers a robust and effective approach for data clustering by integrating autoencoder principles and advanced structure preservation techniques.
The proposed method enhances NMF's ability to capture complex data topology, leading to improved clustering accuracy.
ASNMF-SRP represents a significant advancement in NMF-based clustering, particularly for datasets with intricate structural information.