Stochastic tensor space feature theory with applications to robust machine learning

In this paper we develop a Multilevel Orthogonal Subspace (MOS) Karhunen--Lo`eve 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-Lo`eve 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. We test our approach on blood plasma and cerebrospinal fluid datasets (Alzheimer's Disease Neuroimaging Initiative). The tests show significant increases in accuracy by applying them to Support Vector Machines and (Deep) Neural Networks. Furthermore, from non-invasive blood test, high-accuracy results can be obtained for predicting AD stages such as cognitive normal, mild cognitive impairment and dementia. The non-invasive nature of this test is significant since it can potentially avoid other painful tests.