Visualization with Data Clustering DIVA Seminar Winter 2006 University of Fribourg

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1 Visualization with Data Clustering DIVA Seminar Winter 2006 University of Fribourg Terreaux Patrick February 15, 2007 Abstract In this paper, several visualizations using data clustering are presented. The first part explains the various kind of clustering methods used to organize data, and we will see that two most used are hierarchical clustering and localitybased clustering. The next parts present seven types of visualization like Hierarchical Parallel Coordinates, Dendrogram, H-BLOB, Mountains and hills and others. Keywords: clustering, visualisation, hierarchical, partitioning, localy-based, tree, parallel coordinates, mountains and hills 1 Introduction The arrival of computers facilitated the acquisition and the processing of data. After several years of use and with the help of Internet, a lot of data has been collected. The analysis of these data can become very difficult due to their quantity. 2 Data clustering methods The clusterization of data is the method used to analyse large quantitiy of data. Each characteristic can be represented by a vector. The main principe is to group near object together, based on euclidian or other distance between each object. There exists three categories of clustering: partitioning, hierarchical and localy-based. The following parts explain theses three categories. The four first visualization use hierarchical clustering, and the two following use localy-based clustering. 2.1 Partioning The goal of partitioning is to subdivide a set of data objects into a certain number of clusters. The two more known are C-Means and K-Means. C-Means The principe of the c-means is to create several cluster containing objects having a similar threshold value of δ. The resulting number of clusters cannot be known in advance. Let us take for example of cereals. Today there is a very large quantity of cereals, with various characteristics, adapted for children, regime and others. The analysis of all these data must be done by using an interactive visualization to have a better understanding. This visualization is limited to draw a simple shape for each object. With a large scale of data, it is not possible today to draw all data in the same time. The solution consists to have a level of details. Similar objects are grouped together and the level of details indirectly defines the numbers of groups. To resolve that, the clusterization of data enters in action. The first step is to calculate the cluterization of data. The second is to define a space to each cluster. Figure 1: a) The construction of clusters. Object x is in 2 clusters and this is not possible. b) Final result The disadvantage with this method is that the user must define the threshold value δ. K-Means The principe of k-means is to create k clusters containing all objects. The similarity between objects into a same cluster must be maximal and minimal with others clusters. 1

2 Figure 2: a) The same scene as in figure 1. b) K = 3 The big disadvantage of partitioning methods is that the result is static and thus the level of details is unchangeable. If we want to change the threshold δ or the k value, all must be recalculated and this is not feasible for a large quantity of data. 2.2 Hierarchical The principe is to group at each step similar object together. All clusters obtain a weight corresponding to the number of objects contained into. A tree is represented at the end. Figure 4: objects is the range of value. The goal of the visualization developped at the Polytechnic Institute of Worcester[2], is to extend parallel coordinates to support large scale of data. 3.2 Interaction Each node in the hierarchical cluster tree contains the number of enclosed objects, the mean of enclosed objects and the bounds min and max. Node are now represented with a line of the mean values using a variable-width opacity bands defining the bounds, and are represented with different colors. At the lower level of details, there is as much line than objects. At the higher, there is only one line, the mean value, with its width opacity bands. Figure 3: a) Arrangement of 8 objects. b) Hierarchical representation (tree) 3.3 Visualization The big advantage of this data structure is the facility to naviguate in the tree. This is why this is the most used. 2.3 Localy-based This method groups neighboring data elements into cluster based on local conditions, like attraction/repulsion. More explanation are available on the figure 11 on page 4. 3 Hierarchical Parallel Coordinates 3.1 About Usually, the complexity of the data isn t represented in the view. The parallel coordinates allows to show each characteristic with a new axis. However, with a large quantity of data, some axis can become illegible, and the only thing that become readable Figure 5: Variation of the level of details 2

3 3.4 Personal opinion The hierarchical clustering provides a multiresolution view of the data and aid in revealing data trends at different degrees of summarization. So, when the parallel coordinates is the appropriate view for an application, the quantity of data is not any more a problem. 4 Dendrogram 4.1 About A dendrogram is a binary tree diagram used to illustrate the arrangement of the clusters produced by a clustering algorithm. Developped by the University of Maryland[3], this view allows to see the entire hierarchy. The clustering is done with objects and with characteristics. 4.2 Interaction Through a lot of functionalities like pattern recognition, the main interaction is done by choosing the level of details with a horizontal threshold, defining the threshold value. By going down the threshold, the desired number of clusters is chosen. After choosing a specific cluster, another hierarchical view is shown where the clusterization is based on characteristics. 4.4 Personal opinion This view represents the real structure of the hierarchical clustering, a tree. The interaction is very intuitive and easy to understand. 5 Hierarchical tree-map 5.1 About Developed by the Bell laboratory[6], this visualization draws all objects in a 2D space. All data is based on a hierarchical clustering. The visual method used, a space-filling recursive division of rectangular area, keep items always at the same screen position. 5.2 Interaction Let us take this example: 4.3 Visualization Figure 7: The number under nodes indicates the dissimilarity value The tree-map has no concept of tree dissimilarity. It assumes that the user wants to cut the tree at given depths. Its alternating horizontal and vertical splits is good at showing the tree depth, but has a tendency to create a very long skinny rectangles with unbalanced trees. The view is focuses attention on the tree depth, not on clusters. The solution is to define several dissimilarities values: Figure 6: a) top level, 1 cluster. b) 5 clusters and below the clusterization of characteristics. Figure 8: Tree-map(left) compared with the Hierarchical Clustering View(right). Tree-map is cut at depths 2 and 3. The clustering view is cut at dissimilarities 5.0 and 3.5 3

4 5.3 Visualization Figure 9: Various dissimilarity values. 5.4 Personal opinion This is a good adaptation of the tree-map. The focus is now on cluster and not on the depth of the tree. The hierarchical clustering allows to interact with the level of dissimilarity. 6 H-BLOB 6.1 About Meaning Hierarchical Binary Large Object, this visualization was created at ETH Zurich[1]. Based on hierarchical and localy-based clustering, this is a 3D visualization where each object is represented by a elipse. 6.2 Interaction By using a localy-based clustering, each object are always in the same screen position. By using a hierarchical clustering, we have the possibility to choose the level of details. At the lower level of details, one circle represents contains all object. At the higher, each object is represented by one circle. By grouping near object, circles increase and shapes like oil on a frying pan appear. Figure 10: a) 1 cluster. b) 5 clusters. c) 10 clusters. d) 20 clusters. 6.4 Personal opinion This is a great visualization. The color and the thickness are very good for the understanding the different cluster. I juste see one disadvantage: clusters can be hidden if there is one in the middle of another. 7 Montains and hills 7.1 About The principe of the visualization developed at the Sandia National Laboratory [4] with its software VxInsight is to represent data like mountains and valleys. Objects are stored in a database and are first disposed on a 2D plane. Each object increases the height of its region. The mountains s height depends on the number of date below. A graph is used, where each node is an object and the link defines the similarity value. Objects without similarity have a link of 0.0 and two identical have a link of 1.0. Then, objects are placed in a 2D plane using the principe of attraction/repulsion Visualization Figure 11: Data processing 4

5 7.2 Interaction The interaction is done by zooming in and out. At the lower level of details, there is only one mountain. At the biggest, each object represents a mountain. 7.3 Visualization 8 HD-Eye 8.1 About This last visualization is near than mountains and hills. This one is developed at the University of Halle in Germany[5]. 8.2 Interaction The interaction is done by choosing the threshold of the most present clusters. 8.3 Visualization Figure 12: Global view of mountains Figure 14: Global of mountains with different threshold values 8.4 Personal opinion This last visualization presents another principe of interaction with mountains. Besides, it is similar. Figure 13: Global view with mountains and objects 7.4 Personal opinion This is the first visualization in this paper that doesn t use a hierarchical clustering. After trying the software VxInsight, I throught that the interaction is very userfriendly. 9 Conclusion In this paper we have seen that the clustering method used is specific to each visualization. Some like hierarchical parallel coordinates are adapted for a large scale of data. Some others like moutains and hills are specifically created for large scale of data. 5

6 The choice of one visualization depends of what kind of data you have to analyze. With the powerfull of the next computers, some new visualizations are going to appear. References [1] T. C. Sprenger, R. Brunella, M. H. Gross. H-BLOB: A Hierarchical Visual Clustering Method Using Implicit Surfaces, Proceedings of the 11th IEEE Visualization 2000 Conference (VIS 2000). [2] Ying-Huey Fua, Matthew O. Ward, Elke A. Rundensteiner. Hierarchical parallel coordinates for exploration of large datasets, Proceedings of the conference on Visualization 99, pp , [3] Jinwook Seo, Ben Shneiderman, Interactively Exploring Hierarchical Clustering Results, Computer, vol. 35, no. 7, pp , July, [4] George S. Davidson, Brian N. Wylie, Kevin W. Boyack, Cluster Stability and the Use of Noise in Interpretation of Clustering, infovis, p. 23, [5] Alexander Hinneburg, Daniel A. Keim, Markus Wawryniuk, HD-Eye: Visual Mining of High-Dimensional Data, IEEE Computer Graphics and Applications, vol. 19, no. 5, pp , September/October, [6] G.J. Wills, An Interactive View for Hierarchical Clustering, infovis, p. 26,