Class visualization of high-dimensional data with applications

Consider the problem of visualizing high-dimensional data that has been categorized into various classes. Our goal in visualizing is to quickly absorb inter-class and intra-class relationships. Towards this end, class-preserving projections of the multidimensional data onto twodimensional planes, which can be displayed on a computer screen, are introduced. These class-preserving projections maintain the high-dimensional class structure, and are closely related to Fisher’s linear discriminants. By displaying sequences of such two-dimensional projections and by moving continuously from one projection to the next, an illusion of smooth motion through a multidimensional display can be created. We call such sequences class tours. Furthermore, we overlay class-similarity graphs on our two-dimensional projections to capture the distance relationships in the original high-dimensional space. We illustrate the above visualization tools on the classical Iris plant data, the ISOLET spoken letter data, and the PENDIGITS on-line handwriting data set. We show how our visual examination of the data can uncover latent class relationships.