Distance functions for local PCA methods

The NGPCA method, a combination of the robust neural gas vector quantization method and a fast neural principal component analyzer, has proved to be a valuable tool for the generalized learning of high–dimensional data. At its core, the method uses a competitive ranking to adapt its units. The competition is guided by a specialized distance function — known as the normalized Mahalanobis distance — that assumes elliptic cluster shapes. Recently, an alternative distance function, the normalized Rayleigh quotient, has been suggested. This paper compares the performance of NGPCA on different distance functions. For the comparison a data set from a realistic robot arm experiment is used.