The problem of projecting multidimensional data into lower dimensions has been pursued by many researchers due to its potential application to data analysis of various kinds. This paper presents a novel multidimensional projection technique based on least square approximations. The approximations compute the coordinates of a set of projected points based on the coordinates of a reduced number of control points with defined geometry. We name the technique Least Square Projections (LSP). From an initial projection of the control points, LSP defines the positioning of their neighboring points through a numerical solution that aims at preserving a similarity relationship between the points given by a metric in mD. In order to perform the projection, a small number of distance calculations is necessary and no repositioning of the points is required to obtain a final solution with satisfactory precision. The results show the capability of the technique to form groups of points by degree of similarity in 2D. We illustrate that capability through its application to mapping collections of textual documents from varied sources, a strategic yet difficult application. LSP is faster and more accurate than other existing high quality methods, particularly where it was mostly tested, that is, for mapping text sets.

We survey work on the different uses of graphical mapping and interaction techniques for visual data mining of large data sets represented as table data. Basic terminology related to data mining, data sets, and visualization is introduced. Previous work on information visualization is reviewed in light of different categorizations of techniques and systems. The role of interaction techniques is discussed, in addition to work addressing the question of selecting and evaluating visualization techniques. We review some representative work on the use of information visualization techniques in the context of mining data. This includes both visual data exploration and visually expressing the outcome of specific mining algorithms. We also review recent innovative approaches that attempt to integrate visualization into the DM/KDD process, using it to enhance user interaction and comprehension.

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The one-to-one strategy of mapping each single data item into a graphical marker adopted in many visualization techniques has limited usefulness when the number of records and/or the dimensionality of the data set are very high. In this situation, the strong overlapping of graphical markers severely hampers the user's ability to identify patterns in the data from its visual representation. We tackle this problem here with a strategy that computes frequency or density information from the data set, and uses such information in Parallel Coordinates visualizations to filter out the information to be presented to the user, thus reducing visual clutter and allowing the analyst to observe relevant patterns in the data. The algorithms to construct such visualizations, and the interaction mechanisms supported, inspired by traditional image processing techniques such as grayscale manipulation and thresholding are also presented. We also illustrate how such algorithms can assist users to effectively identify clusters in very noisy large data sets.

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