Visualizing class structure of multidimensional data

We consider the problem of visualising multidimensional data that has been categorised into classes. Our goal in visualising is to quickly absorb inter- and intra-class relationships. Towards this end, we introduce class-preserving projections of the multidimensional data onto two-dimensional planes which can then be displayed on a computer screen. 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, we can create illusions of smooth motion through a multidimensional display. Such sequences are termed class tours. We illustrate the proposed ideas by various computer simulations on the classical Iris plant dataset and a text corpus of book reviews.