Aprendizado não supervisionado de métricas utilizando geometria diferencial e o algoritmo ISOMAP no agrupamento de dados

Abstract

Unsupervised metric learning consists of constructing adaptive distance functions without knowledge of class labels and aims to improve both clustering and supervised pattern classification. Typically, this process can be performed by multiple manifold learning algorithms, through nonlinear dimensionality reduction. Recently, a new algorithm, known as K-ISOMAP, has been proposed for this purpose. It uses differential geometry-based measures to replace the Euclidean distance with measures based on local curvature in the ISOMAP method. This method uses concepts from differential geometry to construct an intrinsic distance function that measures the variations of local tangent spaces along edges in the k-NN graph, motivated by the Frenet-Serret equations and the notion of curvature. This work investigates the quality of the clustering obtained via GMM after mapping the data to lower-dimensional spaces. The results on several datasets suggest that the K-ISOMAP method can produce better clustering than those produced by the standard ISOMAP algorithm, being competitive with the state-of-the-art in metric and manifold learning.