Low-dimensional projections

In this chapter, we will cover various visualization methods to help researchers understand large multidimensional datasets. We will start with traditional statistical low-dimensional projection methods that have been widely used to reveal patterns in multidimensional datasets, and then we will present a novel analysis framework to help users systematically explore ID and 2D projections of large multidimensional datasets. 

Example 7.2 The same researcher in Example 7.1 wants to visually examine the same multidimensional dataset, but now he or she is interested in a low-dimensional projection where the similarity/distance information in the original multidimensional dataset is preserved as much as possible. What is an appropriate way to visualize the dataset ... 

These automatic projection pursuit methods using a series of low-dimensional projections have made impressive gains in the problem of multidimensional data analysis, but they have limitations. One of the most important problems is the difficulty in interpreting the solutions from the automatic projection pursuit. Since the axes are the linear/nonlinear combination of the variables (or dimensions) of the original data, it is hard to determine what the projection actually means to users. Conversely, this is one of the reasons that axis-parallel projections (projection methods in category 2) are used in many multidimensional analysis tools (Guo, 2003 Ward, 1994). 

Techniques in category 3 remain important. These techniques involve a unique method to map dimensions to some visual forms. However, users often have difficulty in grasping the meaning of the low-dimensional projections made by the techniques in category 3. 

Seo, J., and Shneiderman, B. (2004). A rank-by-feature framework for unsupervised nniltidimensional data exploration using low dimensional projections. In Proceedings of IEEE Symposium on Information Visualization, M. Ward and T. Munzner (Eds.). Austin, TX lEER Computer Society Press, pp. 65-72. Seo, J., and Shneiderman, B. (2005). A rank-by-feature framework for interactive exploration of multidimensional data. Informat Visualiz, 4(2) 99-113. 

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