Hierarchical Aggregation for Information Visualization: Overview, Techniques, and Design Guidelines <s> Aggregation <s> 1. Introduction. 2. Partitioning Around Medoids (Program PAM). 3. Clustering large Applications (Program CLARA). 4. Fuzzy Analysis. 5. Agglomerative Nesting (Program AGNES). 6. Divisive Analysis (Program DIANA). 7. Monothetic Analysis (Program MONA). Appendix 1. Implementation and Structure of the Programs. Appendix 2. Running the Programs. Appendix 3. Adapting the Programs to Your Needs. Appendix 4. The Program CLUSPLOT. References. Author Index. Subject Index. <s> BIB001 </s> Hierarchical Aggregation for Information Visualization: Overview, Techniques, and Design Guidelines <s> Aggregation <s> Clustering is the unsupervised classification of patterns (observations, data items, or feature vectors) into groups (clusters). The clustering problem has been addressed in many contexts and by researchers in many disciplines; this reflects its broad appeal and usefulness as one of the steps in exploratory data analysis. However, clustering is a difficult problem combinatorially, and differences in assumptions and contexts in different communities has made the transfer of useful generic concepts and methodologies slow to occur. This paper presents an overviewof pattern clustering methods from a statistical pattern recognition perspective, with a goal of providing useful advice and references to fundamental concepts accessible to the broad community of clustering practitioners. We present a taxonomy of clustering techniques, and identify cross-cutting themes and recent advances. We also describe some important applications of clustering algorithms such as image segmentation, object recognition, and information retrieval. <s> BIB002 </s> Hierarchical Aggregation for Information Visualization: Overview, Techniques, and Design Guidelines <s> Aggregation <s> Most analysts start with an overview of the data before gradually refining their view to be more focused and detailed. Multiscale pan-and-zoom systems are effective because they directly support this approach. However, generating abstract overviews of large data sets is difficult and most systems take advantage of only one type of abstraction: visual abstraction. Furthermore, these existing systems limit the analyst to a single zooming path on their data and thus to a single set of abstract views. This paper presents: 1) a formalism for describing multiscale visualizations of data cubes with both data and visual abstraction and 2) a method for independently zooming along one or more dimensions by traversing a zoom graph with nodes at different levels of detail. As an example of how to design multiscale visualizations using our system, we describe four design patterns using our formalism. These design patterns show the effectiveness of multiscale visualization of general relational databases. <s> BIB003 </s> Hierarchical Aggregation for Information Visualization: Overview, Techniques, and Design Guidelines <s> Aggregation <s> This paper introduces PivotGraph, a software tool that uses a new technique for visualizing and analyzing graph structures. The technique is designed specifically for graphs that are "multivariate," i.e., where each node is associated with several attributes. Unlike visualizations which emphasize global graph topology, PivotGraph uses a simple grid-based approach to focus on the relationship between node attributes and connections. The interaction technique is derived from an analogy with methods seen in spreadsheet pivot tables and in online analytical processing (OLAP). Finally, several examples are presented in which PivotGraph was applied to real-world data sets. <s> BIB004 </s> Hierarchical Aggregation for Information Visualization: Overview, Techniques, and Design Guidelines <s> Aggregation <s> We present the zoomable adjacency matrix explorer (ZAME), a visualization tool for exploring graphs at a scale of millions of nodes and edges. ZAME is based on an adjacency matrix graph representation aggregated at multiple scales. It allows analysts to explore a graph at many levels, zooming and panning with interactive performance from an overview to the most detailed views. Several components work together in the ZAME tool to make this possible. Efficient matrix ordering algorithms group related elements. Individual data cases are aggregated into higher-order meta-representations. Aggregates are arranged into a pyramid hierarchy that allows for on-demand paging to GPU shader programs to support smooth multiscale browsing. Using ZAME, we are able to explore the entire French Wikipedia - over 500,000 articles and 6,000,000 links - with interactive performance on standard consumer-level computer hardware. <s> BIB005
Given a set of data items, hierarchical aggregation is based on iteratively building a tree of aggregate items either bottom-up or top-down. Each aggregate item consists of one or more children; either the original data items (leaves) or aggregate items (nodes). The root of the tree is an aggregate item that represents the whole data set. Bottom-up aggregation BIB002 , BIB001 starts with treating each item as its own aggregate, then iteratively combines similar aggregates into a single aggregate until only one remains. Top-down aggregation, on the other hand, starts with one aggregate containing all the items and repeatedly splits aggregates until a specific level of granularity has been reached, or all items belong to only one aggregate. The common denominator between these two approaches is a similarity measure defined using a data-specific distance function. There are several specific algorithms to perform aggregation. The most common are clustering approaches, such as graph-based or k-means clustering BIB002 , BIB001 , but other examples include quadtree and octree-based methods, such as the recursive merging of four adjacent edges into a single edge as done by Elmqvist et al. BIB005 . For cases where no suitable clustering method can be found, a good fallback may be to use data cube aggregation BIB003 (similar to PivotGraph BIB004 ) to easily turn a multivariate data set into a hierarchical structure. In order to make use of this aggregate tree, visualization techniques that support hierarchical aggregation provide not only a visual representation for the actual data items, but also for the aggregate items. The aggregate tree becomes a multiscale structure for controlling the current level-ofdetail of the visualization on the screen. Depending on the visualization technique, the visual aggregate can also convey information about the underlying data items (see the next section).