Mapeamento isométrico de atributos baseado em geometria diferencial para aprendizado de métricas não supervisionado

Abstract

The act of representing a dataset in a way that’s more compact and significant is denominated dimensionality reduction. The capacity of building adaptive distance functions to each dataset before classification is known as metric learning. Manifold learning algorithms have been shown to be powerful methods for dimensionality reduction based metric learning, as they extract from the samples non-linear attributes that are relevant for classification. This work proposes K-ISOMAP, a method that uses differential geometry concepts to build a intrinsic distance function to approximate the geodesic distances in the KNN graph using the notion of curvature. By replacing the extrinsic Euclidean distance between neighboring samples by a measure of the variation in the tangent space at each neighborhood, there are signs that the proposed method is more robust against the presence of noise in data. Experimental results with several real world datasets show that the proposed method is capable of producing better classification performance than other dimensionality reduction methods that exist in the literature.