Data Driven Geometry for Learning

High dimensional covariate information provides a detailed description of any individuals involved in a machine learning and classification problem. The inter-dependence patterns among these covariate vectors may be unknown to researchers. This fact is not well recognized in classic and modern machine learning literature; most model-based popular algorithms are implemented using some version of the dimension-reduction approach or even impose a built-in complexity penalty. This is a defensive attitude toward the high dimensionality. In contrast, an accommodating attitude can exploit such potential inter-dependence patterns embedded within the high dimensionality. In this research, we implement this latter attitude throughout by first computing the similarity between data nodes and then discovering pattern information in the form of Ultrametric tree geometry among almost all the covariate dimensions involved. We illustrate with real Microarray datasets, where we demonstrate that such dual-relationships are indeed class specific, each precisely representing the discovery of a biomarker. The whole collection of computed biomarkers constitutes a global feature-matrix, which is then shown to give rise to a very effective learning algorithm.