Class visualization of high-dimensional data with applications

• Published in: Computational statistics & data analysis Vol. 41; no. 1; pp. 59 - 90
• Main Authors: Dhillon, Inderjit S., Modha, Dharmendra S., Spangler, W.Scott
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 28.11.2002; Elsevier
• Series: Computational Statistics & Data Analysis
• Subjects: Class tours; Class-preserving projections; Classification; Linear projections; Multidimensional visualization; Similarity graphs; Class tours; Multidimensional visualization; Similarity graphs; Linear projections; Class-preserving projections; Classification
• ISSN: 0167-9473; 1872-7352
• DOI: 10.1016/S0167-9473(02)00144-5

The problem of visualizing high-dimensional data that has been categorized into various classes is considered. The goal in visualizing is to quickly absorb inter-class and intra-class relationships. Towards this end, class-preserving projections of the multidimensional data onto two-dimensional 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. Such sequences are called class tours. Furthermore, class-similarity graphs are overlaid on the two-dimensional projections to capture the distance relationships in the original high-dimensional space. The above visualization tools are illustrated on the classical Iris plant data, the ISOLET spoken letter data, and the PENDIGITS on-line handwriting data set. It is shown how the visual examination of the data can uncover latent class relationships.