Rank-based quality assessment of nonlinear dimensionality reduction

Abstract. Nonlinear dimensionality reduction aims at providing lowdimensional representions of high-dimensional data sets. Many new methods have been proposed in the recent years, but the question of their assessment and comparison remains open. This paper reviews some of the existing quality measures that are based on distance ranking and K-ary neighborhoods. Many quality criteria actually rely on the analysis of one or several sub-blocks of a co-ranking matrix. The analogy between the co-ranking matrix and a Shepard diagram is highlighted. Finally, a unifying framework is sketched, new measures are proposed and illustrated in a short experiment.

• Type: Conference
• Year: 2008
• Where: ESANN
• Authors: John Aldo Lee, Michel Verleysen
• Keywords: Co-ranking Matrix, ESANN 2008, Many Quality Criteria, Neural Networks, Nonlinear Dimensionality Reduction