Core zone scatterplots: A new approach to feature extraction for visual displays

Abstract

This paper presents a new scheme for mapping high dimensional data onto two-dimensional viewing spaces. The mapping procedure is carried out in two stages. In the first stage, the fuzzy c-means (FCM) algorithm is applied to the N-dimensional data to find membership functions of clusters in the data. Core subsets are then selected from the original data based upon threshold values applied to the membership functions found by FCM. In the second stage feature vectors in the selected “core” subsets are submitted to various feature extraction mappings, which yield scatterplots of the image points in 2D space. The proposed approach has two significant advantages over many previous schemes. First, changes in the core structure imposed on the original data under feature extraction can be used to gauge the relative quality of competing extraction techniques. And second, the cores provide a way to generalize almost any known method, resulting in new extraction algorithms. We also discuss various ways to color the selected data that enhance the 2D display. Our approach incorporates a means for assessing the “quality” of the 2D display via parameters which provide an evaluation of (i) the validity of clusters in the original data set and (ii) the relative ability of various extraction mappings to preserve certain well-defined structural properties of the original data. The feasibility of our approach is illustrated using two sets of data: the well known Iris data; and a set of flow cytometric data. Color displays are used to visually assess scatterplot configurations in 2-space.