Stochastic tensor space feature theory with applications to robust machine learning

TL;DR

This paper introduces a stochastic tensor space feature theory using multilevel orthogonal subspaces for robust machine learning, demonstrating significant accuracy improvements in Alzheimer's disease classification from blood tests.

Contribution

It develops a novel MOS Karhunen-Loeve feature framework based on stochastic tensor spaces for enhanced class separation and anomaly detection in machine learning.

Findings

Dramatic accuracy increase in Alzheimer's disease classification.

Effective detection of anomalous signal components.

Superior performance compared to popular ML methods.

Abstract

In this paper we develop a Multilevel Orthogonal Subspace (MOS) Karhunen-Loeve feature theory based on stochastic tensor spaces, for the construction of robust machine learning features. Training data are treated as instances of a random field within a relevant Bochner space. Our key observation is that separate machine learning classes can reside predominantly in mostly distinct subspaces. Using the Karhunen-Loeve expansion and a hierarchical expansion of the first (nominal) class, a MOS is constructed to detect anomalous signal components, treating the second class as an outlier of the first. The projection coefficients of the input data into these subspaces are then used to train a Machine Learning (ML) classifier. These coefficients become new features from which much clearer separation surfaces can arise for the underlying classes. Tests in the blood plasma dataset (Alzheimer's Disease Neuroimaging Initiative) show dramatic increases in accuracy. This contrast to popular ML methods such as Gradient Boosting, RUS Boost, Random Forest and Neural Networks. We show that with a non-invasive blood test, high-accuracy results can be obtained for predicting AD stages such as cognitive normal, mild cognitive impairment and dementia.