While clustering is one of the most popular methods for data mining, analysts lack adequate tools for quick, iterative clustering analysis, which is essential for hypothesis generation and data reasoning. We introduce Clustrophile, an interactive tool for iteratively computing discrete and continuous data clusters, rapidly exploring different choices of clustering parameters, and reasoning about clustering instances in relation to data dimensions. Clustrophile combines three basic visualizations -- a table of raw datasets, a scatter plot of planar projections, and a matrix diagram (heatmap) of discrete clusterings -- through interaction and intermediate visual encoding. Clustrophile also contributes two spatial interaction techniques, @math and @math , and a visualization method, @math , for reasoning about two-dimensional projections obtained through dimensionality reductions.
Prior work has also introduced techniques for comparing clustering results of different datasets or different algorithms @cite_33 @cite_12 @cite_14 @cite_44 . DICON @cite_33 encodes statistical properties of clustering instances as icons and embeds them in the plane based on similarity using multidimensional scaling. Pilhofer al @cite_14 propose a method for reordering categorical variables to align with each other and thus augment the visual comparison of clusterings. The recent tool XCluSim @cite_12 supports comparison of several clustering results of gene expression datasets using an approach similar to that of the Hierarchical Clustering Explorer.
@cite_44 @cite_14 @cite_33 @cite_12
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We present a new method for clustering based on compression. The method does not use subject-specific features or background knowledge, and works as follows: First, we determine a parameter-free, universal, similarity distance, the normalized compression distance or NCD, computed from the lengths of compressed data files (singly and in pairwise concatenation). Second, we apply a hierarchical clustering method. The NCD is not restricted to a specific application area, and works across application area boundaries. A theoretical precursor, the normalized information distance, co-developed by one of the authors, is provably optimal. However, the optimality comes at the price of using the noncomputable notion of Kolmogorov complexity. We propose axioms to capture the real-world setting, and show that the NCD approximates optimality. To extract a hierarchy of clusters from the distance matrix, we determine a dendrogram (ternary tree) by a new quartet method and a fast heuristic to implement it. The method is implemented and available as public software, and is robust under choice of different compressors. To substantiate our claims of universality and robustness, we report evidence of successful application in areas as diverse as genomics, virology, languages, literature, music, handwritten digits, astronomy, and combinations of objects from completely different domains, using statistical, dictionary, and block sorting compressors. In genomics, we presented new evidence for major questions in Mammalian evolution, based on whole-mitochondrial genomic analysis: the Eutherian orders and the Marsupionta hypothesis against the Theria hypothesis. When analyzing multidimensional, quantitative data, the comparison of two or more groups of dimensions is a common task. Typical sources of such data are experiments in biology, physics or engineering, which are conducted in different configurations and use replicates to ensure statistically significant results. One common way to analyze this data is to filter it using statistical methods and then run clustering algorithms to group similar values. The clustering results can be visualized using heat maps, which show differences between groups as changes in color. However, in cases where groups of dimensions have an a priori meaning, it is not desirable to cluster all dimensions combined, since a clustering algorithm can fragment continuous blocks of records. Furthermore, identifying relevant elements in heat maps becomes more difficult as the number of dimensions increases. To aid in such situations, we have developed Matchmaker, a visualization technique that allows researchers to arbitrarily arrange and compare multiple groups of dimensions at the same time. We create separate groups of dimensions which can be clustered individually, and place them in an arrangement of heat maps reminiscent of parallel coordinates. To identify relations, we render bundled curves and ribbons between related records in different groups. We then allow interactive drill-downs using enlarged detail views of the data, which enable in-depth comparisons of clusters between groups. To reduce visual clutter, we minimize crossings between the views. This paper concludes with two case studies. The first demonstrates the value of our technique for the comparison of clustering algorithms. In the second, biologists use our system to investigate why certain strains of mice develop liver disease while others remain healthy, informally showing the efficacy of our system when analyzing multidimensional data containing distinct groups of dimensions. [Read before The Royal Statistical Society at a meeting organized by the Research Section on Wednesday, May 5th, 2004, Professor J. T. Kent in the Chair ] Summary. A new procedure is proposed for clustering attribute value data. When used in conjunction with conventional distance-based clustering algorithms this procedure encourages those algorithms to detect automatically subgroups of objects that preferentially cluster on subsets of the attribute variables rather than on all of them simultaneously. The relevant attribute subsets for each individual cluster can be different and partially (or completely) overlap with those of other clusters. Enhancements for increasing sensitivity for detecting especially low cardinality groups clustering on a small subset of variables are discussed. Applications in different domains, including gene expression arrays, are presented. Classifying a set of objects into clusters can be done in numerous ways, producing different results. They can be visually compared using contingency tables [27], mosaicplots [13], fluctuation diagrams [15], tableplots [20] , (modified) parallel coordinates plots [28], Parallel Sets plots [18] or circos diagrams [19]. Unfortunately the interpretability of all these graphical displays decreases rapidly with the numbers of categories and clusterings. In his famous book A Semiology of Graphics [5] Bertin writes “the discovery of an ordered concept appears as the ultimate point in logical simplification since it permits reducing to a single instant the assimilation of series which previously required many instants of study”. Or in more everyday language, if you use good orderings you can see results immediately that with other orderings might take a lot of effort. This is also related to the idea of effect ordering [12], that data should be organised to reflect the effect you want to observe. This paper presents an efficient algorithm based on Bertin's idea and concepts related to Kendall's t [17], which finds informative joint orders for two or more nominal classification variables. We also show how these orderings improve the various displays and how groups of corresponding categories can be detected using a top-down partitioning algorithm. Different clusterings based on data on the environmental performance of cars sold in Germany are used for illustration. All presented methods are available in the R package extracat which is used to compute the optimized orderings for the example dataset.