From visual data exploration to visual data mining: a survey <s> Visualization of Mining Models <s> We describe a method for the visualization of information units on spherical domains which is employed in the banking industry for risk analysis, stock prediction and other tasks. The system is based on a quantification of the similarity of related objects that governs the parameters of a mass-spring system. Unlike existing approaches we initialize all information units onto the inner surface of two concentric spheres and attach them with springs to the outer sphere. Since the spring stiffnesses correspond to the computed similarity measures, the system converges into an energy minimum which reveals multidimensional relations and adjacencies in terms of spatial neighborhoods. Depending on the application scenario our approach supports different topological arrangements of related objects. In order to cope with large data sets we propose a blobby clustering mechanism that enables encapsulation of similar objects by implicit shapes. In addition, we implemented various interaction techniques allowing semantic analysis of the underlying data sets. Our prototype system IVORY is written in Java, and its versatility is illustrated by an example from financial service providers. <s> BIB001 </s> From visual data exploration to visual data mining: a survey <s> Visualization of Mining Models <s> MineSet™, Silicon Graphics' interactive system for data mining, integrates three powerful technologies: database access, analytical data mining, and data visualization. It supports the knowledge discovery process from data access and preparation through iterative analysis and visualization to deployment. Mine-Set is based on a client-server architecture that scales to large databases. The database access component provides a rich set of operators that can be used to preprocess and transform the stored data into forms appropriate for visualization and analytical mining. The 3D visualization capabilities allow direct data visualization for exploratory analysis, including tools for displaying high-dimensional data containing geographical and hierarchical information. The analytical mining algorithms help identify potentially interesting models of the data, which can be viewed using visualization tools specialized for the learned models. Third party vendors can interface to the MineSet tools for model deployment and for integration with other packages. <s> BIB002 </s> From visual data exploration to visual data mining: a survey <s> Visualization of Mining Models <s> An important issue in data mining is the recognition of complex dependencies between attributes. Past techniques for identifying attribute dependence include correlation coefficients, scatterplots, and equiwidth histograms. These techniques are sensitive to outliers, and often are not sufficiently informative to identify the kind of attribute dependence present. ::: ::: We propose a new approach, which we call independence diagrams. We divide each attribute into ranges; for each pair of attributes, the combination of these ranges defines a two-dimensional grid. For each cell of this grid, we store the number of data items in it. We display the grid, scaling each attribute axis so that the displayed width of a range is proportional to the total number of data items within that range. The brightness of a cell is proportional to the density of data items in it. ::: ::: As a result, both attributes are independently normalized by frequency, ensuring insensitivity to outliers and skew, and allowing specific focus on attribute dependencies. Furthermore, independence diagrams provide quantitative measures of the interaction between two attributes, and allow formal reasoning about issues such as statistical significance. <s> BIB003 </s> From visual data exploration to visual data mining: a survey <s> Visualization of Mining Models <s> We present a new hierarchical clustering and visualization algorithm called H-BLOB, which groups and visualizes cluster hierarchies at multiple levels-of-detail. Our method is fundamentally different to conventional clustering algorithms, such as C-means, K-means, or linkage methods that are primarily designed to partition a collection of objects into subsets sharing similar attributes. These approaches usually lack an efficient level-of-detail strategy that breaks down the visual complexity of very large datasets for visualization. In contrast, our method combines grouping and visualization in a two stage process constructing a hierarchical setting. In the first stage a cluster tree is computed making use of an edge contraction operator. Exploiting the inherent hierarchical structure of this tree, a second stage visualizes the clusters by computing a hierarchy of implicit surfaces. We believe that H-BLOB is especially suited for the visualization of very large datasets and for visual decision making in information visualization. The versatility of the algorithm is demonstrated using examples from visual data mining. <s> BIB004
Another typical use of visualization in mining resides in visually conveying the results of a mining task, such as clustering or classification, to enhance user interpretation. One such example is given by the BLOB and H-BLOB clustering algorithms BIB001 , BIB004 , which use implicit surfaces for visualizing data clusters. The authors point out that the majority of algorithms and systems treating cluster visualization are limited to drawing a simple shape for each data object, with the actual clustering being done by the user's perceptual system. Their previous work on BLOB BIB001 was an attempt to explicitly represent clusters by exhibiting them in an enclosing surface, but this and other previous work was restricted to visualizing results of partitioning FERREIRA DE OLIVEIRA AND LEVKOWITZ: FROM VISUAL DATA EXPLORATION TO VISUAL DATA MINING: A SURVEY 387 Fig. 8 . Display of data from a site in the WebCANVAS system. Each window corresponds to a cluster and each row in a window depicts the path of a single user through the site whose pages have been categorized by subject. Each path is color coded by category (color coding shown on the right). From  . cluster algorithms, rather than hierarchical ones. H-BLOB discovers and visualizes hierarchical clustering structures (cluster trees) in a two-staged approach. In the first one, called the analytical clustering step, an agglomerative hierarchical algorithm computes a cluster-tree by partitioning data objects into a nested sequence of subsets. The second stage involves the computation of a single enclosing shape for each cluster in combination with the visualization process. The enclosing shape for the cluster is a BLOB implicit surface that approximates the outline of their included data objects as closely as possible. A separate surrounding surface is computed for each cluster at each hierarchy level. Fig. 10 (from BIB004 ) illustrates the approach on a set of 100 single objects retrieved from an Intranet document query. The Self-Organizing Map (SOM) is a neural network algorithm based on unsupervised learning that has been applied in DM and multidimensional exploratory data analysis in several domains  . The SOM is a vector quantization and projection method that implements an ordered dimensionality reducing mapping which follows the probability density function of the training data. A major characteristic of the SOM is that it can be integrated with different visualization techniques. Vesanto  ,  provides an overview of techniques for visualization of SOMs and also elaborates on how the different visualizations can be linked to enhance interpretation capabilities. Mineset BIB002 is a popular commercial DM/KDD tool that includes several visualization resources, both for exploratory data analysis and visualization of mining results. Analytical mining algorithms are coupled with visualization tools to support the user's understanding. It includes, for example, an evidence visualizer to display and manipulate Simple Bayes Models  and a Tree Visualizer to display decision trees generated by a decision tree classifier. Kohavi Han and Cercone  also argue in favor of using visual representations along the KDD process to enhance user participation in the discovery process. They describe CViz, an interactive system for visualizing the process of classification rule induction. The original data is visualized using parallel coordinates and the user can see the results of data reduction and attribute discretization on the parallel coordinate representation. The discovered classification rules are also displayed on the parallel coordinates plots as rule polygons, colored strips as depicted in Fig. 11 , where a polygon covers the area that connects the (discretized) attribute values that define particular rules. Rule accuracy and quality may be coded by coloring the rule polygon and user interaction is supported to allow focusing on subsets of interesting rules. Association rules are a prime example of patterns discovered with DM and understanding them is not always simple because resulting sets are often large and the rules are not self-explanatory. The goal of Hofmann et al.  is to help the user to understand the underlying structure of association rules by visualizing the contingency tables that originate them. Contingency tables consist basically of a Mosaic plots were introduced  as a graphical counterpart of multivariate contingency tables. In the plots, each table cell is depicted as a tile (or bin). By default, the tile's size is directly proportional to the number of data items in a cell. The construction algorithm determines the arrangement and splitting of tiles based on the data and Fig. 9 . An independence diagram for visualizing dependencies between two attributes (legend on the right). The brightness of a cell in the twodimensional grid is proportional to the density of the corresponding data points. From BIB003 . Fig. 10 . A hierarchical clustering of document objects with 20 clusters, displayed at different levels of the hierarchical cluster tree. At the top level, one observes the whole set as a single cluster, the following images show lower levels of the hierarchical tree, with the lowest one, with 20 clusters shown at the the bottom right. From BIB004 . user supplied information. An example Mosaic Plot is depicted in Fig. 12 . One way to visualize an association rule X ! Y is to combine all attributes involved in the lefthand side selection X as explanatory variables and to draw them within one Mosaic plot and visualize the response Y by highlighting the corresponding categories in a bar chart. The approach is illustrated in Fig. 13 , which shows a Mosaic Plot of all possible association rules involving three attributes, A x1 , A x2 , and A y . The first attribute has two possible values and the second one has four. The second bin in the top row (A x1 ¼ x 11^Ax2 ¼ x 22 ) exemplifies a rule with very high confidence (the highlighting almost fills the bin entirely), but with relatively small support (the bin itself and, therefore, the amount of highlighting, is not very large). The first bin in the bottom row (A x1 ¼ x 12^Ax2 ¼ x 21 ) represents the rule with the highest support (this bin contains the largest amount of highlighting), but low confidence (small highlighting area). By providing the context of rules in Mosaic plots, the user can better assess their quality and, moreover, understand the relationship among association rules.