Sequential Principal Curves Analysis

LASSICAL unsupervised learning such as Principal Components Analysis (PCA) and Independent Component Analysis (ICA) is useful to design artificial sensory systems and to understand the organization of natural sensory systems. On the artificial side, examples include representations/transforms for image coding [6]-[9] and image categorization [10], [11]. On the natural side, examples include the analysis of visual cortex [12]-[16]. PCA and ICA obtain basis of the space according to different optimization criteria. These basis functions can be interpreted as linear sensors: the projection of data onto these basis represents the response of the set of sensors. PCA defines a sensor hierarchy: for example, an image sensory system made out of principal directions with highest eigenvalues minimizes the image reconstruction error [6], [7]. In ICA, the basis is intended to provide responses as independent as possible, which is equivalent to design a sensory system that maximizes the transmitted information (infomax) [17], [18].