Calculation of manifold’s tangent space at a given point from noisy data

Abstract

Recently, several studies have been conducted in a field of machine learning to construct manifolds from data in a complex multidimensional space. Therefore manifold learning becomes remarkably attractable among researchers. One of the main tools to identify manifold’s structure is tangent space. In this work, first, we simulate a method for finding tangent space of manifold at some point from noisy data by Principal Component Analysis. In fact, Principal Component Analysis(PCA) provides dimension reduction by its ‘principal components’. Then we introduce concurrent method to PCA that is called Maximum Mean Discrepancy distance. It is based on measuring the distance between smooth distributions.