Auto-Contractive Maps: an artificial adaptive system for data mining. An application to Alzheimer disease

Area of Science:

• Computational neuroscience
• Machine learning
• Network analysis

Background:

• Traditional Artificial Neural Networks (ANNs) rely on random weight initialization and do not inherently possess topological properties.
• Analyzing complex diseases requires advanced methods to understand intricate factor structures.

Purpose of the Study:

• Introduce Auto-Contractive Maps (Auto-CM) as a new paradigm in Artificial Neural Networks.
• Present novel algorithms, the H Function and Maximally Regular Graph (MRG), for graph analysis.
• Apply Auto-CM and MRG to a real-world dataset for Alzheimer's disease research.

Main Methods:

• Auto-Contractive Maps (Auto-CM) learn without random initialization and exhibit data-driven space warping.
• The H Function quantifies global hubness in graphs, derived from Auto-CM weight matrices.
• Maximally Regular Graph (MRG) is an advancement over Minimum Spanning Trees (MST) for graph analysis.

Main Results:

• Auto-CM demonstrates unique learning dynamics, converging when output nodes become null.
• The H Function provides a measure of topological complexity for graphs.
• Application to the Nuns Study dataset revealed insights into Alzheimer's disease factors.

Conclusions:

• Auto-CM offers a novel framework for neural network design with distinct topological features.
• The H Function and MRG provide powerful tools for graph and network complexity analysis.
• This approach can help restructure the understanding of complex disease factors, exemplified by Alzheimer's disease research.