Multi-Scale Local Shape Analysis and Feature Selection in Machine Learning Applications

The goal of this paper is to introduce a preliminary version of what we call multi-scale local shape analysis (MLSA), a method for extracting features of a dataset that describe the local structure, both manifold and singular, of points within the dataset. MLSA is a mixture of multi-scale local principal component analysis (MLPCA) and persistent local homology (PLH). In this paper, we will describe both of these techniques and our merger of them, and we will demonstrate the potential of MLSA on two synthetic datasets and one real one. The potential of these methods and their merger is investigated in the context of one of the typical applications for data analytics: the classification problem for multidimensional datasets. Thus the relevance of the developed techniques is assessed as the quality of the resulting classification decision rule, measured by the expected test misclassification error, its sensitivity and specificity (false positive and false negative error rates).