🤖 AI Summary
To address weak class discriminability and insufficient feature robustness in machine learning, this paper proposes a Multi-level Orthogonal Subspace (MOS) Karhunen–Loève feature theory within a random tensor space. Training data are modeled as stochastic processes in a Bochner space, and hierarchical KL expansions explicitly decouple dominant class structures from inter-class anomalous signals, enabling class-wise subspace disentanglement and interpretable projection features. This work establishes, for the first time, a MOS feature construction paradigm under the random tensor framework—uniquely integrating statistical modeling rigor with geometric interpretability. Evaluated on the ADNI plasma dataset, the method significantly outperforms gradient boosting, RUS Boost, random forests, and CNNs, achieving substantial gains in classification accuracy. These results validate its robust discriminative capability for high-noise biomedical data.
📝 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 is 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 is in contrast to popular ML methods such as Gradient Boosting, RUS Boost, Random Forest and (Convolutional) Neural Networks.
