Class proximity measures – Dissimilarity-based classification and display of high-dimensional data

For two-class problems, we introduce and construct mappings of high-dimensional instances into dissimilarity (distance)-based Class-Proximity Planes. The Class Proximity Projections are extensions of our earlier relative distance plane mapping, and thus provide a more general and unified approach to the simultaneous classification and visualization of many-feature datasets. The mappings display all L-dimensional instances in two-dimensional coordinate systems, whose two axes represent the two distances of the instances to various pre-defined proximity measures of the two classes. The Class Proximity mappings provide a variety of different perspectives of the dataset to be classified and visualized. We report and compare the classification and visualization results obtained with various Class Proximity Projections and their combinations on four datasets from the UCI data base, as well as on a particular high-dimensional biomedical dataset.

Class proximity projection from a 26 dimensional feature space, using Centroids for the class proximity measure and Mahalanobis distances for the distance measure. For each instance, the axes show the logarithms of its two distances to the centroids. This biomedical dataset comprises 421 control cases (96.6% classification accuracy) and 119 colorectal cancer cases (96.4% classification accuracy).Figure optionsDownload as PowerPoint slideHighlights
► Projection of high-dimensional data onto a Class Proximity (CP) Plane.
► Concepts of class proximity measure, distance/dissimilarity measure, two computed distances for an instance or prototype in CP plane.
► Visualization/display and classification in the CP plane.
► Extensions of the CP projection: (a) iterated CP mapping and (b) concatenation of several CP-derived datasets.
► Demonstration on four datasets from the UCI Repository and to a high-dimensional biomedical dataset.