Visual Data Mining With Pixel-oriented Visualization Techniques

Visual Data Mining with Pixel-oriented Visualization TechniquesMihael AnkerstThe Boeing CompanyP.O. Box 3707 MC 7L-70, Seattle, WA ed visualization techniques map each attribute value ofthe data to a single colored pixel, yielding the display of the mostpossible information at a time. Thus pixel-oriented techniquesmaintain the global view of large amounts of data while stillpreserving the perception of small regions of interest. This propertymakes them suitable for a variety of data mining tasks.First we present pixel-oriented visualization techniques which canbe used as stand-alone exploration tools. Then we show how theycan be tightly integrated into data mining methods unifying thestrength of existing algorithms and human involvement. Finally, wepoint out the idea of similarity clustering of attributes to enhancemultidimensional visualization techniques.Keywords: Visual data mining, pixel-oriented visualizationtechniques, cluster analysis, classification, tightly integratedvisualization.subwindows. Pixel-oriented visualization techniques maximize theamount of information represented at one time without any overlap.They effectively preserve the perception of small regions of interestwhile still maintaining the global view. These properties match thebasic requirements listed above making them suitable for variousdata mining tasks.The rest of this paper is organized as follows. Section 2 reviewspixel-oriented visualization techniques which are designed forexplorative visualization tasks. In section 3, we show how pixeloriented visualization techniques can be integrated with datamining methods. Section 4 presents a general technique to improvevisualization techniques for high-dimensional data. The last sectionsummarizes this paper and discusses some directions for futureresearch.2 EXPLORATIVE VISUALIZATIONTECHNIQUES1 VISUAL DATA MINING AND PIXELORIENTED VISUALIZATION TECHNIQUESThe task of the knowledge discovery and data mining process [7] isto extract knowledge from data such that the resulting knowledge isuseful in a given application. Obviously, only the user candetermine whether the resulting knowledge satisfies thisrequirement. Moreover, what one user may find useful is notnecessarily useful to another user. Visual data mining tackles thedata mining tasks from this perspective enabling humaninvolvement and incorporating the perceptivity of humans. Datasetsto be mined entail several requirements limiting or disqualifyingmost of the existing techniques known from the area informationvisualization.These requirements include handling highdimensional data, handling large datasets, intuitive selection of a setof attributes or a set of objects.Pixel-oriented techniques have been pioneered by Keim for theVisDB system, e.g. [9], representing large amounts of highdimensional data with respect to a given query. As a result the userof the system is able to refine his query based on the knowledgegathered from the visual representation of the data. The basic ideaof pixel-oriented techniques is to represent each attribute value as asingle colored pixel, mapping the range of possible attribute valuesto a fixed color map and displaying different attributes in differentSeveral pixel-oriented visualization techniques have been proposedtwo of which we present in this section, the recursive patterntechnique and the circle segments technique. Others are the spiraltechnique [8] or techniques relying on space-filling curves like theMorton and Z-order techniques [8]. We will take the stock marketapplication as a running example for illustrating the next threetechniques.2.1 The Recursive Pattern TechniqueThe recursive pattern technique [10] is based on a generic recursiveschema and is in particular aimed at representing datasets having anatural order accoring to one attribute (e.g. time series data). Withparameters for each recursive schema, it allows the user to controlthe semantically meaningful substructures which determine thearrangement of the attribute values.The recursive pattern technique visualizes each attribute in aseparate subwindow. Within a subwindow, each attribute value isrepresented by one colored pixel with the color reflecting theattribute value. In order to enable the user to relate attribute valuesof different attributes but at the same positions, the order of theobjects is reflected by the same arrangement of pixels in eachsubwindow. The arrangement of pixels in a subwindow is describedin the following.The recursive pattern technique is based on a back and fortharrangement. The recursive base element is a pattern of height h1and width w1 as specified by the user. First, the elements of thepattern correspond to single pixels which are arranged within arectangle of height h1 and width w1 from left to right, then below

abcFigure 1: Illustration of the Recursive Pattern Technique.DOW JONESGOLD.US IBMDOLLAR.7 level (3)-patterns12 level (2)-patternsFigure 2: The Recursive Pattern Techniquebackwards from right to left, then again forward from left to right,and so on (cf. figure 1a). The same basic arrangement is done onall recursion levels with the only difference that the basic elementswhich are arranged on level i are the patterns resulting from thelevel (i-1)-arrangements (cf. figure 1b for w2 3, h2 7 andfigure 1c for w2 3, h2 1 and w3 1, h3 7).In figure 2, the stock prices for Dow Jones, Gold, IBM and USDollar are depicted for almost seven consecutive years. The sevenvertical bars correspond to the seven years (level (3)-patterns) andthe subdivision of the bars to the 12 month within each year (level(2)-patterns). The coloring maps high attribute values (stockprices) to light colors and low attributes values (stock prices) todark colors. The user may, for example, easily see that the goldprice was very low in the fifth year, the IBM price quickly fell afterthe first one and a half months, that US Dollar exchange rate washighest in the eighth month of the second year, etc.2.2 The Circle Segments TechniqueThe circle segments technique [5] has been proposed forvisualizing large high-dimensional datasets. The idea is not torepresent different attributes in subwindows any more, instead thewhole dataset is represented by a circle which is divided intosegments, one for each attribute. Within the segments eachattribute value is again visualized by a single colored pixel. Thearrangement of the pixels starts at the center of the circle andcontinues to the outside by plotting on a line orthogonal to thesegment-halving line in a back and forth manner (see figure 3).The rationale of this approach is that close to the center allattributes are close to each other enhancing the visual comparison

attr. 8attr. 1attr. 7attr. 2attr. 6attr. 3attr. 5attr. 4Figure 3: Illustration of the CircleSegments technique for 8-dimensional dataFigure 4: The Circle Segments Techniqueof their values. Besides, users involved in a highly interactiveexploration process based on different pixel-oriented techniqueshave reported the circle segments technique to be less tedious thanother techniques since they have a “visual anchor point” in thecenter. However, a more extensive usuability test has to be made todraw conclusions about advantages or biases. In figure 4, the circlesegments technique represents 50 different stock stock prices. Thecolor mapping is the same like in the previous example, lightcolors represent high stock prices and dark colors low ones. Thuslight circular regions correspond to high stock prices of differentstocks at the same time. It can be easily perceived that most stocksprices have a very similar trend whereas a few show a differentprogression.2.3 The Data TubeThe data tube approach [6] does not belong to the group of pixeloriented techniques any more, however, it transfers the idea of thecircle segments technique into the 3D space to conceptually extendthe number of attributes and the number of records. It representsthe data as a tubular shape in the 3D-space, mapping the attributevalues onto the texture of the interior sides of the tube. The usercan explore the data by moving through the data tube. The ncornered tube is constructed from n 2 attributes by connecting nrectangular sides where side i is placed between the angles of360*(i-1)/n and 360*i/n from the center of the tube. Thecorresponding color of the attribute values are then mapped aslines onto the interior sides (see figure 5). The reason that a linenot a pixel represents an attribute value is that a perceived “circle”,more precisely an n-corner, corresponds to a record. This propertyenables the user to more accurately perceive and select a set ofrecords. Figure 6 depicts a screen shot of the data tube techniquealso visualizing 50 stock prices. Here the grey scale color map isused to encode the attribute values.3 INTEGRATING VISUALIZATION TECHNIQUES WITH DATA MINING METHODSThe approaches described in the previous section enable the user toexplore the data, to get a general understanding of the data and todetect correlations between different attributes. This kind ofknowledge differs from the patterns that are computed by datamining algorithms. Data mining methods produce patterns such asdecision trees, clusterings or association rules which can bedirectly used in a business context e.g. for target marketing orfraud detection. Combining purely automatic mining algorithmswith visualization techniques and interactivity aims at theincorporation of domain knowledge and human’s perception intothe data mining process. Most mining algorithms include searchesin very large search spaces which cannot be perfomedexhaustively. These situations offer a huge potential for involvingthe user to narrow down the search space based on the powerfulcombination of perception and domain knowledge.Current approaches to visual data mining can be classified into one

attr. 1023.32.42.0.attribute 1attr.10attribute 20.1-3.0.5.attr.1 attr.2attribute 3.Figure 5: Illustration of the Data Tube approachexeptional stockcrashFigure 6: The Data Tube Techniqueof the following groups. The first group consists of visualizationtechniques which are applied before or independent of a datamining algorithm. The second group represents the patterns thatare computed by a mining algorithm providing a betterunderstanding of the patterns. The visualization takes place afterthe run of an algorithm. The third group tightly integratesvisualization and interaction facilities with the run of an algorithm.Intermediate steps can be visualized allowing the user to superviseand steer the search during the run of a mining algorithm. Almostall proposed approaches to visual data mining belong to either thefirst or the second group.The following two sections cover the OPTICS approach forhierarchical clustering which belongs to the second group and thevisual classification approach which shows the benefits of the thirdgroup.3.1 OPTICS - Ordering Points To Identifythe Clustering StructureOne primary data mining task is cluster analysis which is intendedto help a user understand the natural grouping or structure in adataset. The goal of a clustering algorithm is to group the objectsof a database into a set of meaningful subclasses. Since a clusteritself can contain subclusters, hierarchical algorithms have been