A New Kernel Density Estimation-Based Entropic Isometric Feature Mapping for Unsupervised Metric Learning

Metric learning consists of designing adaptive distance functions that are well-suited to a specific dataset. Such tailored distance functions aim to deliver superior results compared to standard distance measures while performing machine learning tasks. In particular, the widely adopted Euclidean distance may be severely influenced due to noisy data and outliers, leading to suboptimal performance. In the present work, it is introduced a nonparametric isometric feature mapping (ISOMAP) method. The new algorithm is based on the kernel density estimation, exploring the relative entropy between probability density functions calculated in patches of the neighbourhood graph. The entropic neighbourhood network is built, where edges are weighted by a function of the relative entropies of the neighbouring patches instead of the Euclidean distance. A variety of datasets is considered in the analysis. The results indicate a superior performance compared to cutting edge manifold learning algorithms, such as the ISOMAP, unified manifold approximation and projection, and t-distributed stochastic neighbour embedding (t-SNE).