Interactive Visualization Of Multi-dimensional Data On Heterogeneous .

Journal of Theoretical and Applied Information Technology30th November 2015. Vol.81. No.3 2005 - 2015 JATIT & LLS. All rights reserved.ISSN: 1992-8645www.jatit.orgobtained calculation results into a structure,containing the parameters of graphic display (Unit4), and displays the obtained results (Unit 5), whichare observed by the user. Thus, a feedback to DSSis implemented, which makes it possible for a userto find the correct solution. The effectiveness ofwork with a DSS depends on how quickly andaccurately a user perceives the displayed results andsets the control commands, and also on the speed ofa system’s response to a user’s actions. Therefore,in addition to the software implementation of thedata processing methods, the improvement ofinteractive technologies of data management anddata visualization [12], [15] is also of considerablepractical importance for improving effectiveness ofDSS. The basic ideas of interactive datavisualization are outlined in [14], [15], [16], [18],[19], but the practical methods of interactivevisualization in each subject area should take intoaccount its specifics, therefore, they require aseparate research and development of specific tools.In the process of solving a choice problem, usingthe technologies of interactive visualization shouldensure the ease of dealing with accumulatedinformation, the ability to change the hierarchicalstructure of data and to calculate the rating (theobjective function) for alternatives. In order toeliminate the need for engaging additionalspecialists, a user in the process of working with aDSS should have an opportunity to carry out thenecessary calculations and the analysis of data onone’s own.1.3 Description of the taskThe aim of this work is to propose a method ofinteractive visualization of multi-dimensional dataon heterogeneous information objects, ships between data and makes it possible tovisualize and modify hierarchical dependencies ofthe rating of information objects, for using indecision support systems.The content of the task is the following. To carryout interactive actions of data analysis, standardinput devices should be used: a mouse with twobuttons and a scroll wheel, and a keyboard.Visualization is performed on the screen of acomputermonitor.Auserdealswithmultidimensional data, represented by the values ofa specified set of variables. For example, in theproblem of buying a house the variables are:price,E-ISSN: 1817-3195p1p1p15 – yard,6 – transportation,7size,–neighborhood. Each set of values of the variables isan information object, describing various propertiesof one of the alternatives. A user's task is to chooseone of the alternatives on the basis of building arule of calculating their rating (objective function)or identifying patterns in the form of thedependence of one of the parameters from othersbased on the statistical data.To make a decision, a user formulates the goal ofdecision-making and presupposes that this goal canbe formalized in the form of some numericalfunction, which is called the objective function. Thevalue of this function determines the rating for eachalternative, which is used to choose the bestdecision. The analytic hierarchy process is used fordecision-making [11]. According to the rules of theanalytic hierarchy process, a user carries out thedecomposition of a goal, breaking it into simplerindividual objectives, the achievement of whichleads to the achievement of the main goal. At thesame time, a user forms an objective function,which depends on several variables. These variablesare, in turn, objective functions of more specificobjectives. As a rule, the functional dependency isunderstandable, if there are from 3 to 5 variables,on which the objective function depends. Thedecomposition procedure ends at a stage wherethere is a possibility to obtain quantitative estimatesof the values of the variables, corresponding toindividual objectives. The result of thedecomposition is a hierarchical objectives tree – agraph reflecting the dependence of the main goalfrom individual objectives. The analytic hierarchyprocess involves reasoning from the general to thespecific. If there is already some data ofinformation objects in a DSS, the objectives treecan be formed by aggregation of existing variables.In the discussed example of the problem ofbuying a house, to get a clearer picture of thedependence of the main goal on individualobjectives, it can be useful to group the propertiesinto categories and present the dependence on threemain factors, which in turn depend on more specificproperties, as shown in Figure 3.p11 –1p12 – maintenance cost, p3 – age, p14 –455

Journal of Theoretical and Applied Information Technology30th November 2015. Vol.81. No.3 2005 - 2015 JATIT & LLS. All rights reserved.ISSN: 1992-8645www.jatit.orgE-ISSN: 1817-31952. THE METHOD OF THE INTERACTIVEVISUALIZATION OF DATA2.1 General characteristics of the methodFigure 3. Illustration Of Forming A HierarchicalObjectives TreeInformative examples of using the methods ofsolving this type of tasks are provided in [1], [6],[12]. The dependence of the values of an objectivefunction on the specific properties of alternatives isbuilt in the form of some function, as a rule, amultilevel linear convolution, the coefficients ofwhich should be set by the user. When retrievingdata from news flows, misrepresentation ofinformation, obtaining inaccurate data or omissionsof certain data are possible. As a result, withreference to the problem in hand, a lot ofinformation on heterogeneous objects, representingthe individual properties of selected alternatives, isaccumulated.A user can also try to group the individualobjectives into other categories (for example, as in[6]: benefits, opportunities, costs, risks) and buildan objectives tree, which is different from thatshown in Figure 3.The method of interactive visualization shouldprovide an opportunity to explore a solution to theproblem in different ways. Graphic display shouldmake it possible to quickly see the entire map ofdependencies and intuitively assess the degree ofinfluence of variables of different hierarchicallevels on the objective function. When developingthe method of interactive visualization, it should betaken into account that a user is interested in issuesrelated to consistent patterns in data: how much andwhat data is available for decision-making, what isthe degree of its validity, what actions (processing)can be carried out in relation to existing data, howthe different sides of the phenomenon areinterrelated, etc.The variables, with which a user works, can bedivided into groups according to different criteria.When forming a hierarchical structure, it isconvenient to identify primary variables (orindependent variables), the values of which alreadyexist in the database or can be set by the user, anddependent (or aggregate) variables, the values ofwhich are calculated as a functional dependency onother variables. Dependent variables are, in turn,objective functions of individual objectives.Independent variables correspond to the endvertices of an objectives tree.The degree of the achievement of the main goalis represented in the form of a functionaldependency of the objective function on theparameters. To enable the perception of the basicpatterns, an objective function is built as dependenton no more than five variables, but this requirementis not a limitation of the method of visualization.The objective function of each knot of ahierarchical scheme depends linearly on variables.Actions on data analysis and decision-making,carried out by the user, are the following:to choose variables that affect the objectivefunction;to identify groups of interrelated parameters;to set a dependency between the groups ofinterrelated parameters and the structure of thisdependency;to determine quantitative values of the obtaineddependency between parameters;to assess the degree of dispersion of the values ofthe objective function, if there are randomdeviations in the source data.In order to automate the above-listed steps, it isnecessary to display the multidimensional data,arranged in a hierarchical structure, to carry outediting of the hierarchical structure, and to changethe parameters of the functional dependency of theobjective functions on variables. A good way ofdisplaying the decision-making process using theanalytic hierarchy process is proposed in [20]. Inthis work, for the purpose of the visualization andmodification of the hierarchical data, the Tree Mapchart is applied, in which quantitative data ispresented in the form of partially filled rectanglesthat fill a rectangular area. This variation of the456

Journal of Theoretical and Applied Information Technology30th November 2015. Vol.81. No.3 2005 - 2015 JATIT & LLS. All rights reserved.ISSN: 1992-8645www.jatit.orgTree Map chart is useful for displaying and editingof quantitative data, but it is not suitable forinteractive editing of the hierarchical structure ofthe objectives tree.In view of the need for the active work with datain a DSS, the visualization method requires usingthe minimum amount of graphic elements, encodingthe greatest possible number of multidimensionaldata. The visualization of data should be interactive,and should make it possible to modify the methodsand parameters of data processing and observe theresults without long waiting. To enable a user tobuild a hierarchy of an objectives tree on one’sown, and, if necessary, quickly edit it, to set theparameters used for the calculation of the objectivefunction, to determine the sensitivity of the valuesof the objective function in relation to the change ofvariables, it is advisable to use simultaneously theTree Map and the Organization Chart, consistentlydisplaying the same hierarchical data in differentways.E-ISSN: 1817-3195the name of the individual objective, which isreflected by the variable. Each edge of the graphcorresponds to the following attributes: the numberof the vertex of an upper level; the number of thevertex of a lower level; level number; the value ofthe weighting factor.At each of the hierarchy levels, aggregatedvariables denote an objective function for anindividual objective and are presented in the formof a linear convolution of the lower-level variables:Nkpk 1n() wik pik n 1,., N k 1 ,(1)i 1where the superscript denotes the level number, thesubscript denotes the number of the parameterwkwithin one level; i denotes the weighting factors,satisfying the condition:Nk wki 1,(2)i 1The display of multiple values is implemented inthe form of a Row Graph. The resulting interactivechart is built through combination and modificationof these three types of diagrams (OrganizationChart, Row Graph, and Tree Map) with the additionof interactive elements, which make it possible toedit the presentation of data.N k is the number of variables at thepkhierarchy level with a number k ; i – variablesbelonging to the hierarchy level with a number k .The proposed method of interactive visualizationincludes the following components: displaying ahierarchical structure based on the OrganizationChart; displaying one-dimensional quantitative databasedontheRowGraph;displayingmultidimensional quantitative data based on theTree Map; combination of the Tree Map and theOrganization Chart.The visualization of an objectives tree can beimplemented in different ways. One of them is topresent the hierarchy of objectives in the form ofIshikawa diagram [21], which is also called causeand-effect diagram or fishbone diagram (Figure 4).whereThe weighting factors are equal to zero for thosevariables of the lower level, on which the objectivefunction does not depend.2.2 Displaying the hierarchical structure of thevariables.The hierarchical structure of the variables isdisplayed in the form of an objectives tree, in whichthe hierarchy levels are clearly identified. The upperlevel has a zero number, and the numbers of all thelower levels are assigned in ascending order.Formally, the hierarchical structure is representedby a graph – a tree with one root vertexcorresponding to an aggregate variable denoting themain objective function. The vertices of the graphare dependent (aggregated) and independent(primary) variables. Each vertex corresponds to thefollowing main attributes: the number of the vertex;the number of the hierarchy level; the number of thevertex in the numbering of one hierarchy level; thenumber of the vertex of an upper hierarchy level;Figure 4. Ishikawa DiagramThis chart looks impressive and makes it possibleto understand the dependency of the main goal onmultiple secondary objectives. But the hierarchicallevels of individual objectives in this diagram arelocated in different areas of the graphicalrepresentation, which makes it difficult to create457

Journal of Theoretical and Applied Information Technology30th November 2015. Vol.81. No.3 2005 - 2015 JATIT & LLS. All rights reserved.ISSN: 1992-8645www.jatit.orginteractive elements and carry out interactiveactions.The other ways of displaying a hierarchicalstructure (Organization Chart, Tree Ring, IciclePlot, and Tree Map) were studied in [22]. Theresults, obtained in this work, make it possible toconclude that the Organization Chart is morepreferable for displaying a hierarchical structurewith regard to several criteria, if there is no need fordisplaying quantitative values. If it is required todisplay quantitative values, for example, the discspace taken up for displaying the hierarchical filestructure, Tree Map and Tree Ring are preferable.In [23] the advantages of the Tree Map fordisplaying the directory structure are demonstratedin comparison with the circular (Sunburst) chart.With regard to the criteria of clarity, simplicity,convenience of interactive action, the visualizationof the objectives tree in the form of theOrganization Chart is considered to be a preferredoption.The display of the objectives tree is buildaccording to the following rules. The hierarchicallevels are indicated by rectangles of equal width,spaced vertically. Inside each of such rectanglesthere are images in the form of smaller rectangles orcircles, denoting the vertices of the objectives tree,belonging to one hierarchical level. Therelationships between vertices of different levels areindicated by straight or broken lines. The originalchart, showing only the main objective function andindependent variables, consists of two levels(Figure 5). The inscriptions, indicating the names ofindividual objectives, are placed inside therespective rectangles. If the names of individualobjectives are in natural language, the preferredform of graphic elements is a rectangle (Figure 5,a).E-ISSN: 1817-3195When displaying the relationships betweenvariables of different levels, the encoding ofweighting factors, with which the variables form alinear convolution, is possible through the thicknessof lines. This method makes it possible to displaythe relevance of variables, but it is not convenientfor the interactive modification of weightingfactors.Editing of this chart is implemented throughinteractive actions, which include: selecting,aggregating, refinement, changing a hierarchicallevel, adding a hierarchical level, adding a newvariable, deleting a variable, setting a relationshipbetween the variable of adjacent levels, zooming,changing the color coding of vertices.Most interactive actions are carried out usingcommon techniques, with the use of input devices,and include changing the parameters of thefunctional dependency (Figure 2, unit 2). Selectionmakes it possible to choose several vertices of a treebelonging to one level. Aggregation involvescombining multiple vertices and forming a newaggregate variable (an individual objectivefunction). Aggregation can be used, when thedecision-making problem is solved according to thescheme “from the specific to the general” (when itis necessary to build an objective function on thebasis of existing variables, the values of which arealready known). The transformation of theobjectives tree in the process of aggregation isshown in Figure 6.Figure 6. Interactive Aggregation Of The Variables OfThe Objectives TreeFigure 5. The Ways Of The Visualization Of TheObjectives Tree On The Basis Of The Organization ChartFor the formal definition of this action, a newvertex is added to the objectives tree, which denotesan aggregate variable, belonging to the level, atwhich the aggregation of variables takes place. Allvertices, corresponding to the grouped variables,are moved to a lower level. After this, therenumbering of variables takes place. Refinement isthe operation inverse to aggregation, whichinvolves deleting an aggregate variable and moving458

Journal of Theoretical and Applied Information Technology30th November 2015. Vol.81. No.3 2005 - 2015 JATIT & LLS. All rights reserved.ISSN: 1992-8645www.jatit.orgall the variables, on which it depends, to an upperlevel.Changing the hierarchical level is implementedthrough specifying a parameter, which shouldbecome subordinate to another aggregate parameter.An interactive action involves moving the graphicalrepresentation of the first parameter to the graphicalrepresentation of the second parameter (Figure 7).correlation analysis, etc.) can also be used in theinteractive chart for displaying and implementing ofinteractive actions.This chart shows the structure of relationshipsbetween variables and makes it possible to build anobjectives tree, but the quantitative values ofvariables and weighting factors are not shownclearly enough (they can be presented in the form oftooltips or inscriptions). The display of quantitativevalues of multidimensional data is based on thecharts, similar to the Row Graph and the Tree Map.2.3 The visualizationquantitative dataFigure 7. Changing The Hierarchical Level Of TheVariableAdding a hierarchical level is intended for therefinement of existing goals, if the decision-makingproblem is solved according to the scheme “fromthe general to the specific”. After adding a newhierarchical level, primary variables are added tothis level, representing independent variables thatmay be obtained from the database, or representingmore specific objectives. Deleting a variable is usedin cases when it is necessary to modify the originalhierarchical structure. In case of deleting anaggregate variable, all the variables, on which itdepends, are also deleted. Setting a relationshipbetween variables of adjacent levels makes itpossible to set hierarchical dependencies forobjective functions.Scaling is changing the settings of display(Figure 2, unit 3), which involves changing thedegree of refinement of the display of the objectivestree by identifying the number of displayedhierarchical levels (it is reasonable to display nomore than 5 levels). Changing the color coding ofvertices is used, when in is necessary to provideselection of individual vertices of the objectivestree, which is more convenient for the user.The functional capabilities of the chart are notlimited to the interactive building of the objectivestree. The aggregation of variables can be carried outby using statistical dimension-decreasing methodsand identifying the main components [4], [5]. Inthis case, the hierarchical structure is built on thebasis of the results of the appropriate calculations.Other data-processing algorithms (clustering,E-ISSN: 1817-3195ofone-dimensionalQuantitative values of individual variables aredisplayed on the basis of the RowGraph.Information is encoded by geometrical size, color,color transparency, the chart of the sampledistribution function. To display one value of avariable, a chart in the form of a partially filledrectangle is used. Intuitively, such a chart representsthe relative amount of fluid in a cylindrical vessel (aglass), which is not full to the brim; therefore, it isalso called a Glassful.First of all, quantitative values should benormalized by means of a monotone function thatperforms mapping of the range of values of thevariable into an interval from 0 to 1. The worst(lowest) value corresponds to 0 in the relative scale,while the best (highest) value corresponds to 1.Normalization can be performed for bothquantitative and qualitative data [24].The rule of displaying the chart is the following.The elementary displayed item is a rectangle,divided into two parts (upper and lower) by ahorizontal line. The height of the rectangle is takento be equal to 1 according to the relative scale. Theheight of the lower part is equal to the displayedquantitative value in the relative scale and is filledwith opaque color; the upper part is filled with thesame color, but with transparency of about 90%, asshown in Figure 8.a.If it is necessary to display several differentvalues in one chart, the color transition is used witha change in the intensity of transparency from 0 to90% (Figure 8). The horizontal line dividing therectangle is equal to the average sample value. Fora sample, a sample distribution function is built,and the transparency of the color is changed fromthe minimum value to the maximum. The minimumand maximum values are indicated by horizontallines, and the sample distribution function isdisplayed as a chart in the same rectangle (Figure459

Journal of Theoretical and Applied Information Technology30th November 2015. Vol.81. No.3 2005 - 2015 JATIT & LLS. All rights reserved.ISSN: 1992-8645www.jatit.org8.c), which is turned through 90 degrees counterclockw

necessary calculations and the analysis of data on one's own. 1.3 Description of the task The aim of this work is to propose a method of interactive visualization of multi-dimensional data on heterogeneous information objects, which facilitates the formation of hierarchical relationships between data and makes it possible to visualize and .