Extraction of Approximate Independent Components from Large Natural Scenes

Abstract

Linear multilayer ICA (LMICA) is an approximate algorithm for independent component analysis (ICA). In LMICA, approximate independent components are efficiently estimated by optimizing only highly-dependent pairs of signals. Recently, a new method named “recursive multidimensional scaling (recursive MDS)” has been proposed for the selection of pairs of highly-dependent signals. In recursive MDS, signals are sorted by one-dimensional MDS at first. Then, the sorted signals are divided into two sections and each of them is sorted by MDS recursively. Because recursive MDS is based on adaptive PCA, it does not need the stepsize control and its global optimality is guaranteed. In this paper, the LMICA algorithm with recursive MDS is applied to large natural scenes. Then, the extracted independent components of large scenes are compared with those of small scenes in the four statistics: the positions, the orientations, the lengths, and the length to width ratios of the generated edge detectors. While there are no distinct differences in the positions and the orientations, the lengths and the length to width ratios of the components from large scenes are greater than those from small ones. In other words, longer and sharper edges are extracted from large natural scenes.