Convex coordinates from lattice independent sets for visual pattern recognition

One of the key processes in nowadays intelligent systems is feature extraction. It pervades applications from computer vision to bioinformatics and data mining. The purpose of this chapter is to introduce a new feature extraction process based on the detection of extremal points on the cloud of points that represent the high dimensional data sample. These extremal points are assumed to define an approximation to the convex hull covering the data sample points. The features extracted are the coordinates of the data points relative to the extremal points, the convex coordinates. We have experimented this approach in several applications that will be summarized in the chapter.