Curvilinear Distance Analysis versus Isomap
John A. Lee, Amaury Lendasse, Michel Verleysen · 2002
Abstract. Dimension reduction techniques are widely used for the anal-ysis and visualization of complex sets of data. This paper compares two nonlinear projection methods: Isomap and Curvilinear Distance Analy-sis. Contrarily to the traditional linear PCA, these methods work like multidimensional scaling, by reproducing in the projection space the pair-wise distances measured in the data space. They di®er from the classical linear MDS by the metrics they use and by the way they build the map-ping (algebraic or neural). While Isomap relies directly on the traditional MDS, CDA is based on a nonlinear variant of MDS, called CCA (Curvi-linear Component Analysis). Although Isomap and CDA share the same metrics, the comparison highlights their respective strengths and weak-nesses. 1