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S Liu D Maljovec B Wang P T Bremer V Pascucci Visualizing High Dimensional Data Advances in the Past Decade. free summary of high dimensional data Car09 Further tion This category includes visual encodings based on axes. more we connect advances in high dimensional data visu e g scatterplots and parallel coordinate plots glyphs pix. alization with volume rendering and machine learning Sec els and hierarchical representations together with anima. tion 7 Finally we reflect on our categorization with respect tion and perception View transformation Section 5 corre. to actionable tasks and identify emerging future directions sponds to methods focusing on screen space and rendering. in subspace analysis model manipulation uncertainty quan including illustrative rendering for various visual structures. tification and topological data analysis Section 8 as well as screen space measures for reducing clutter or arti. facts and highlighting important features, Such a design allows us to easily classify the core con. tribution of vastly different methods that operate on en. tirely different objects but at the same time reveal their. interconnections through the linked pipeline In addition. the pipeline based categorization provides the reader with. a modular view of the recent advances allowing new sys. tems to be configured based on possibilities provided by the. reviewed methods, User interactivity is an integral part within each pro. cessing step of the pipeline as illustrated in Figure 2. Based on the amount of user interaction we can classify. Figure 1 Interactive survey website for paper navigation all high dimensional data visualization methods into three. categories computation centric interactive exploration and. model manipulation The distinction between interactive ex. 2 Survey Method and Categorization ploration and model manipulation is made to emphasize a. We conduct a thorough literature review based on relevant particular manipulation paradigm where the underlying data. works from major visualization venues namely Visweek model is modified based on interaction to reflect user inten. EuroVis PacificVis and the journal IEEE Transactions on tion A summary of the interplay between processing steps. Visualization and Computer Graphics TVCG from the pe and interactions is illustrated in Table 1 where user interac. riod between 2000 and 2014 To ensure the survey covers tions are put into a measurable context The corresponding. the state of the art we further selectively search through ref details are discussed in Section 6. erences within the initial set of papers Beyond the visual. ization field we also dedicate special attention to the ex 3 Data Transformation. ploratory data analysis techniques in the statistics commu We start by describing different types of high dimensional. nity Through such a rigorous search process we have iden datasets We then give an in depth discussion on the action. tified more than 200 papers that focus on a wide spectrum driven subcategories centered around typical analysis tech. of techniques for high dimensional data visualization To niques during data transformation namely dimension re. help organize the large quantity of papers we have produced duction clustering in particular subspace clustering and. an interactive survey website www sci utah edu regression analysis We focus especially on their usages in. shusenl highDimSurvey website based on the visualization methods In addition we pay special attention. SurVis Bec14 framework a screen shot is shown in Fig to topological data analysis which is a promising emerging. ure 1 that allows readers to interactively select and filter field. papers through various tags However due to the space limi. tation only a subset of the complete list of references avail 3 1 High Dimensional Data. able through the survey website is mentioned in the paper We provide an overview of the different aspects of high. As illustrated in Figure 2 we base our main catego dimensional datasets to define the scope of our discussion. rization on the three transformation steps of the informa and highlight distinct properties of these datasets Our dis. tion visualization pipeline CMS99 and its minor varia cussions on different data types are inspired by the book by. tion in BTK11 namely data transformation visual map Munzner Mun14. ping and view transformation Each category is enriched Data Types In our survey we limit our exposition to. with novel customized subcategories Data transformation table based data and exclude potentially high dimensional. Section 3 corresponds to the analysis centric methods such graph network data from the discussion A high dimensional. as dimension reduction regression subspace clustering fea dataset is commonly modeled as a point cloud embedded in. ture extraction topological analysis data sampling and ab a high dimensional space with the values of attributes cor. straction Visual mapping Section 4 the key for most vi responding to the coordinates of the points Based on the un. sual encoding tasks focuses on organizing the information derlying model of the data and the analysis and visualization. from the data transformation stage for visual representa. c The Eurographics Association 2015, S Liu D Maljovec B Wang P T Bremer V Pascucci Visualizing High Dimensional Data Advances in the Past Decade. Source Data, Dimension Reduction Subspace Clustering Regression Analysis Topological Data Analysis. Data Transformation, linear projection KC03 Dimension Space Exploration Optimization Morse Smale Complex.

Data non linear DR WM04 TFH11 YRWG13 Design Steering GBPW10 CL11. Transformation Control Points Projection DST04 Subset of Dimension TMF 12 BPFG11 DW13 Reeb Graph. Distance Metric LMZ 14 Non Axis Parallel Subspace Structural Summaries Contour Tree PSBM07. Precision Measures LV09 Vid11 AWD12 PBK10 GBPW10 Topological Features WSPVJ11. Transformed, Axis Based Glyphs Pixel Oriented Hierarchy Based Animation Evaluation. Visual Mapping,User Interactions, Mapping Scatterplot Matrix WAG06 Per Element Glyphs Jigsaw Map Dimension Hierarchy GGobi SLBC03 Scatterplot Guideline. Parallel Coordinate JJ09 CCM10 GWRR11 Pixel Bar Charts WPWR03 TripAdvisorND SMT13. Radial Layout LT13 CCM13 KHL01 Topology based Hierarchy NM13 PCPs Effectiveness. Visual Hybrid Construction Multi Object Glyphs Value Relation HW10 OHWS13 Rolling the Dice HVW10. YGX 09 CvW11 War08 CGSQ11 Dispaly YHW 07 Others ERHH11 EDF08 Animation HR07. View Transformation,Transformation, Illustrative Rendering Continuous Visual Representation Accurate Color Blending Image Space Metrics. Illustrative PCP MM08 Continuous Scatterplot BW08 Hue Preserving Blending Clutter Reduction. Views Illuminated 3D scatterplot SW09 Continuous Parallel Coordiante KGZ 12 AdOL04 JC08. PCP density based HW09 LT11 Weaving vs Blending Pargnostics DK10. transfer function JLJC05 Splatterplots MG13 HSKIH07 Pixnostic SSK06. Figure 2 Categorization based on transformation steps within the information visualization pipeline with customized action. driven subcategories, goals the attributes consist of input parameters and output pects of high dimensional data Visual analysis of the finan. observations and the data could be modeled as a scalar or cial time series data is explored in the work by Ziegler et. vector valued function where the function values are based al ZJGK10 The work presented by Tam et al TFA 11. on the output observations on the point cloud defined by the studies facial dynamics utilizing the analysis of time series. input parameters Topological data analysis Section 3 5 ap data in parameter space Datasets with spatial information. plies to both point cloud data and functions on point cloud such as multivariate volumes BDSW13 or multi spectral. data e g GBPW10 SMC07 while regression analysis images LAK 11 are very common in scientific visualiza. Section 3 4 typically applies to the latter e g PBK10 tion and numerous methods have been introduced within the. Attribute Types The attribute type e g nominal vs nu scientific visualization domain see BH07 KH13 for com. merical can greatly impact the visualization method In prehensive surveys on these topics We discuss the intrinsic. many fields and applications the value of the attributes is interconnections between these two areas in Section 7. nominal in nature However most commonly available high 3 2 Dimension Reduction. dimensional data visualization techniques such as scatter. Dimension reduction techniques are key components for. plots or parallel coordinate plots are designed to handle. many visualization tasks Existing work either extends the. numerical values only When utilizing these methods for. state of the art techniques or improves upon their capabili. visualizing nominal data information overlapping and vi. ties with additional visual aid, sual elements stacking usually exist One way to address.

the challenge is mapping the nominal values to numeri Linear Projection Linear projection uses linear transfor. cal values RRB 04 e g as implemented in the Xmdv mation to project the data from a high dimensional space to. Tool War94 Through such a mapping each axis is used a low dimensional one It includes many classical methods. more efficiently and the spacing becomes more meaningful such as Principal component analysis PCA Multidimen. In the Parallel Sets work BKH05 the authors introduce a sional scaling MDS Linear discriminate analysis LDA. new visual representation that adapts the notion of parallel and various factor analysis methods. coordinates but replaces the data points with a frequency PCA Jol05 is designed to find an orthogonal linear. based visual representation that is designed for nominal transformation that maximizes the variance of the result. data The Conjunctive Visual Form Wea09 allows users to ing embedding PCA can be calculated by an eigende. rapidly query nominal values with certain conjunctive rela composition of the data s covariance matrix or a singular. tionships through simple interactions The GPLOM Gener value decomposition of the data matrix The interactive PCA. alized Plot Matrix IML13 extends the Scatterplot Matrix iPCA JZF 09 introduces a system that visualizes the re. SPLOM to handle nominal data sults of PCA using multiple coordinated views The system. Spatiotemporal Data Some recent advances focus on de allows synchronized exploration and manipulations among. veloping visual encoding that capture the spatiotemporal as the original data space the eigenspace and the projected. space which aids the user in understanding both the PCA. c The Eurographics Association 2015, S Liu D Maljovec B Wang P T Bremer V Pascucci Visualizing High Dimensional Data Advances in the Past Decade. process and the dataset When visualizing labeled data class inspired by the perceptual processes of identifying distance. separation is usually desired Methods such as LDA aim to relationships in parallel coordinates using polylines. provide a linear projection that maximizes the class separa Dimension Reduction Precision Measure One of the fun. tion The recent work by Koren et al KC03 generalizes damental challenges in dimension reduction is assessing and. PCA and LDA by providing a family of flexible linear pro measuring the quality of the resulting embeddings Lee et al. jections to cope with different kinds of data introduce the ranking based metric LV09 that assesses the. Non linear Dimension Reduction There are two distinct ranking discrepancy before and after applying dimension re. groups of techniques in non linear dimension reduction un duction This technique is then generalized MLGH13 and. der either the metric or non metric setting The graph based used for visualizing dimension reduction quality A projec. techniques are designed to handle metric inputs such as tion precision measure is introduced in SvLB10 where a. Isomap TDSL00 Local Linear Embedding LLE RS00 local precision score is calculated for each point with a cer. and Laplacian Eigenmap LE BN03 where a neighbor tain neighborhood size In the distortion guided exploration. hood graph is used to capture local distance proximities and work LWBP14 several distortion measures are proposed. to build a data driven model of the space for different dimension reduction techniques where these. The other group of techniques address non metric prob measures aid in understanding the cause of highly distorted. lems commonly referred to as non metric MDS or stress areas during interactive manipulation and exploration For. based MDS by capturing non metric dissimilarities The MDS the stress can be used as a precision measure Seifert. fundamental idea behind the non metric MDS is to mini et al SSK10 further develop this idea by incorporating the. mize the mapping error directly through iterative optimiza analysis and visualization for better understanding of the lo. tions The well known Shepard Kruskal algorithm Kru64 calized stress phenomena. begins by finding a monotonic transformation that maps the 3 3 Subspace Clustering. non metric dissimilarities to the metric distances which pre. Clustering is one of the most widely used data driven. serves the rank order of dissimilarity Then the resulting. analysis methods Instead of providing an in depth discus. embedding is iteratively improved based on stress The pro. sion on all clustering techniques in this survey we fo. gressive and iterative nature of these methods has been ex. cus on subspace clustering techniques which have a great. graph network data from the discussion A high dimensional dataset is commonly modeled as a point cloud embedded in a high dimensional space with the values of attributes cor responding to the coordinates of the points Based on the un derlying model of the data and the analysis and visualization c The Eurographics Association 2015

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