Computed Data-Geometry Based Supervised and Semi-supervised Learning in High Dimensional Data

In most high dimensional settings, constructing supervised or semi-supervised learning rules has been facing various critically difficult issues, such as no visualizing tools for empirical guidance, no valid distance measures, and no suitable variable selection methods for proper discrimination among data nodes. We attempt to alleviate all of these difficulties by computing data-geometry via a recently developed computational algorithm called Data Cloud geometry (DCG). The computed geometry is represented by a hierarchy of clusters providing a base for developing a divide-and-conquer version of a learning approach. We demonstrate the advantages of taking posteriori geometric information into learning rules construction by evaluating its performance with many illustrated examples and several real data sets compared to the performance resulting from the majority of commonly used techniques.