Generation of Semantic Layouts for Interactive Multidimensional Data Visualization

Erick Gomez-Nieto∗† and Luis Gustavo Nonato† ∗Research and Innovation Center in Computer Science Universidad Católica San Pablo, Arequipa, Peru †Instituto de Ciências Matemáticas e de Computação Universidade de São Paulo São Carlos-SP, Brazil

Abstract—Visualization methods make use of interactive are easily readable, but they pay the price of scalability. graphical representations embedded on a display area in order Hierarchical methods such as Treemaps mitigate the issue to enable data exploration and analysis. These typically rely of scalability while making an efficient use of display area. on geometric primitives for representing data or building more sophisticated representations to assist the visual analysis process. However, readability and semantic organization of data are One of the most challenging tasks in this context is to determinate aspects not so easily handled by those methods. Overlap-free an optimal layout of these primitives which turns out to be semantic preserving techniques generate somewhat structured effective and informative. Existing algorithms for building layouts layouts and keep instances with similar content close to each from geometric primitives are typically designed to cope with other. Nevertheless, they are not designed to make an efficient requirements such as orthogonal alignment, overlap removal, optimal area usage, hierarchical organization, dynamic update use of display area and also suffer from scalability. among others. However, most techniques are able to tackle just Handling many requirements is not straightforward because a few of those requirements simultaneously, impairing their distinct requirements can compete with each other during use and flexibility. In this dissertation, we propose a set of layout construction. For instance, to facilitate readability, approaches for building layouts from geometric primitives that layouts should be built with as large as possible geometric concurrently addresses a wider range of requirements. Relying on multidimensional projection and optimization formulations, entities. However, large objects easily fill up the display area, our methods arrange geometric objects in the visual space so as thus limiting the number of instances that can be visualized. to generate well-structured layouts that preserve the semantic Therefore, finding an optimal balance among multiple concur- relation among objects while still making an efficient use of rent requirements is a challenging task, which has not been display area. A comprehensive set of quantitative comparisons completely tackled by existing methods. against existing methods for layout generation and applications on text, image, and video data set visualization prove the In this dissertation we addressed this challenging problem effectiveness of our approaches1 2. by proposing new techniques for building layouts. We denom- inate to Semantic Layout Arrangement as the task of allocating I.INTRODUCTION efficiently a set of geometric instances, which summarizes Arranging geometric primitives to generate meaningful lay- a multidimensional dataset, into a fixed-size display area, outs is a major task in visualization, which inherently appears subject to preserve, as much as possible and at all times, in important applications such as word cloud constructionand the semantic relationships among instances. The arrangement visual boards.The difficulty in building layouts made up of should simultaneously play with several requirements, such dozens of geometric objects rests in the set of requirements as area usage optimization, overlap removal, object scaling, to be handled simultaneously, e.g., readability, overlaps, object orthogonal alignment and dynamic updating. size, semantic proximity and area usage. Moreover, the number In the proposed methods, semantic relationships are estab- of data instances represented as geometric entities is typically lished by a similarity measure. We use dimensionality reduc- much larger than the visualization area, demanding the use of tion techniques for embedding data from multidimensional clustering, hierarchies, and navigation resources to assist the to visual space in order to, subsequently, build a map of visualization. geometric entities. Then, we applied the proposed optimization Although significant advances have been made towards operators to rearrange entities according to the requirements building meaningful layouts from geometric primitives, exist- we deem the most relevant, thereby generating meaningful ing techniques are formulated to deal with a limited number visualizations. of requirements simultaneously, restricting their use to specific This document presents a compilation of different tech- applications. For instance, techniques such as visual boards niques for interactive and semantic layouts generation for data and small multiples provide well structured layouts which visualization. Each proposed method brings new contributions for the field with the purpose of addressing and solving 1Ph.D. thesis at ICMC-Universidade de São Paulo. specific problems involved in generating geometric semantic 2Email: [email protected], [email protected] layouts for interactive data visualization. Essentially, three A. The energy functional The energy functional E involves two components, one that considers the overlap of snippets, denoted by EO, and a second component related to the neighborhood relations Fig. 1: Pipeline to produce the neighborhood-preserving snip- resulting from the multidimensional projection step, denoted pet visualization. Snippet textual content is represented as by EN . In mathematical terms, the energy E is written as: multidimensional data points (left). The multidimensional data E = (1 − α)E + αE (1) is mapped to the visual space and snippets are embedded into O N rectangles (middle). Optimization is applied to avoid overlap where the parameter α ∈ [0, 1] balances the relative contribu- while preserving neighborhoods. tions of both EO and EN in the total energy. Energy E, as well as EO and EN , are functions of the coordinates of the bottom-left corners of the rectangles embed- proposed methods (ProjSnippet [1], MIOLA [2] and Dealing ding the snippets, which initially correspond to the projected with Multiple Requirements [3]) rely on novel optimization coordinates of the multidimensional snippet vectors. We omit formulations for simultaneously dealing with requirements that the independent variables from the equations to simplify the were identified as the most relevant during our study. The last notation. method (Semantically Aware Dynamic Layouts [4]) presented The example illustrates a visualization displaying the results in this summary focuses on an application that demands of a query on the terms “jaguar features” submitted to Google’s semantic preserving layout updates during analyst’s interactive search engine. The view in Figure 2a shows the 10 best ranked data exploration. snippets shown in the first page. Figure 2b displays a ProjSnip- To our knowledge, the proposed approaches figure among pet view with the 64 best ranked snippets. Inspection discloses the most straightforward, efficient and intuitive alternatives to that the snippets on the left (cyan, red, blue, yellow) all refer explore large amounts of multidimensional data while enabling to different models of Jaguar cars, whereas the green ones on a fluent interaction with data analysts. the right refer to a surprising variety of topics, that include multiple references to the wild animal (3 snippets) and also to II.PROJSNIPPET supercomputer models named Jaguar (2 instances). There are also unique references to an earlier MacOs operating system The proposed technique comprises three steps as shown named Jaguar, to a video game, a swimming pool brand, a hair in the pipeline in Figure 1: pre-processing of search results, product brand, an aircraft model and a few other varied stuff. multidimensional projection, and optimization. In the first step Looking at the left region, one identifies that most snippets in each entry returned from a textual query is processed and its the blue cluster contain general references to the car brand, term frequency vector extracted whereas the each of the three other clusters refer mostly to a Each term frequency vector may be handled as a point in specific Jaguar model, namely most yellow snippets refer to a multidimensional space that can be mapped to the visual the XK model, cyan snippets refer to XJ and red to XF models. space with a multidimensional projection technique. Albeit our There are some noticeable exceptions, e.g., a yellow snippet current implementation adopts the Least Squares Projection refers to the XF model and a blue one refers to the XJ model. (LSP) [5] – due to its good accuracy in terms of distance Still, overall the final layout depicts a representative overview preservation and low computational cost – any projection of the search hits, as far grouping/separating similar/dissimilar technique with similar properties might be employed. The results is concerned. Notice that it is pretty difficult to handle projection preserves much of the neighborhood structure of such a variety topics and subtopics in Google’s list-based view, the original data, ensuring that similar instances are placed which indeed brings only results on cars, animals and the game close to each other in the visual space. in the first page. The following step is to embed the content of each snippet within a rectangle whose bottom left corner is placed in the III.MIXED INTEGER OPTIMIZATION FOR LAYOUT snippet’s (or its multidimensional data point) projected posi- ARRANGEMENT (MIOLA) tion. A rectangle’s height and width are settled to reflect the In this section we describe a technique to tackle the problem rank of its corresponding snippet in the retrieved document list, of arranging rectangular boxes in the visual space so as so that better ranked snippets are assigned larger rectangles. to place objects representing similar content close to each A major drawback at this stage of the pipeline is that rect- other while avoiding overlaps. We formulate the problem as angles enclosing the snippets overlap considerably, impairing a Mixed Integer Quadratic Programming Problem (MIQP), identification of individual entries and the perception of the which enables well structured layouts. In contrast to other document neighborhood structure. The final step (rightmost optimal methods that take into account the similarity between box in Figure 1) optimizes the placement of the snippets in or- instances, our approach does not rely on intersection tests, der to avoid overlapping while preserving data neighborhoods making the algorithm simpler to implement. Moreover, our as computed by the projection. The optimization is driven by technique is quite flexible, being able to generate different an energy functional as follows. layouts by just handling optimization constraints. w + w h + h [21]1999 Jaguar XJ8 VDP Stk#U1118 features and test drive 2 - YouTube [18]Standard Features - 2011 Jaguar XJ XJL Supercharged - Yahoo ... i j i j Mar 30, 2011 ... 1999 Jaguar XJ8 VDP Stk#U1118 features and test drive 2. Yahoo! Autos - standard features for the 2011 Jaguar XJ ... http://www.youtube.com/watch%3Fv%3D5DE0yqQIAHM http://autos.yahoo.com/jaguar/xj/2011/xjl-supercharged/features.html

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[63]Jaguar XF V8 | Car Info XF V8 Variant, Price, Specs, Features Know all about Jaguar XF V8 Car model. Detailed and in-depth info on the V8 variant (5000 cc Engine) of the ... (a) First page of http://www.prokerala.com/automobile/jaguar/xf/xf-v8.html w w i + lbx ≤ x ≤ ubx − i (x lower/upper bounds) Google (b) ProjSnippet displaying 64 snippets 2 i 2 Fig. 2: Google and ProjSnippet views of the results of a query (3) h h with terms “jaguar features”. i + lby ≤ y ≤ uby − i (y lower/upper bounds) 2 i 2 where lbx, lby, ubx, uby are lower and upper visualization window bounds (constants) in x and y directions. If needed, visualization window bounds can also assume independent values for each box. Equations (2) and (3) provide the conditions to be held so as to guarantee that boxes do not overlap and are inside a visualization window. However, those equations do not take into account neighborhood structures, thus neighbor boxes can be placed far apart from each other after the overlap removal process. One useful way to keep up the neighborhood (a) Input layout. (b) Optimized layout. relationships is to preserve the relative order of the centroids Fig. 3: Inequalities (3) ensure that no boxes will not displayed of boxes, that is, offscreen while inequalities (4) preserve the order of the coor- xp1 ≤ xp2 ≤ ... ≤ xpn (x orthogonal order) dinates w.r.t. initial layout. (a) Input layout and (b) result after (4) yq1 ≤ yq2 ≤ ... ≤ yqn (y orthogonal order) layout arrangement (orthogonal ordering: xpi ≤ xpi+1 , p1 = 2, p2 = 3, p3 = 1, p4 = 4; similarity for y case). where p, q : {1, 2, ..., n} → {1, 2, ..., n} are permutations of indices obtained by sorting the coordinates x and y of the centroids of boxes in the visual space (see Fig. 3). Let B = {B1,B2, ..., Bn} be a set of n rectangular Therefore, by moving the centroid of the boxes while boxes arranged in the visual space such that the neighbor- ensuring Equations (2), (3), and (4) can generate an overlap hood structure of the boxes reflects a property of interest. free layout that preserves the initial neighborhood structures. For instance, if a data set is mapped to the visual space using a multidimensional projection technique and a box is B. The MIQP formulation centered on each projected data, the resulting arrangement The problem of positioning the boxes B in the visual makes neighbor boxes correspond to similar data. Boxes in i space so as to ensure that Equations (2), (3), and (4) hold this arrangement, however, should overlap considerably, im- can be formulated as a Mixed Integer Quadratic Programming pairing the visualization of individual boxes. In order to make Problem as follows: each box visible, one has to displace the boxes in the two- dimensional space so as to remove overlaps, but preserving the n n 1 T X X 2 initial neighborhood structures to keep similar objects close to min f(z) = z Qz = Dist (Bi,Bj) z 2 each other. As described next, we formulate the problem above i=1 j=i+1 as a mixed integer quadratic programming optimization.  Az ≤ b subject to lb ≤ z ≤ ub (5) A. Problem statement   x > n x = (x1, x2, ..., xn) ∈ R Let B = {B1,B2, ..., Bn} be a set of n rectangular boxes z =  y  , > n y = (y1, y2, ..., yn) ∈ R initially positioned in a two-dimensional space. Each box Bi is r B = (x , y , w , h ) ∈ > specified by a four dimensional vector i i i i i r=(r12, . . . , r1n, r23, . . . , r2n, . . . , rn−1n) , rij ∈{0, 1} 4 R , where (xi, yi), wi > 0, hi > 0 are the centroid, width and height of Bi, respectively (see Fig. 3(a)). Two boxes Bi where z is the sought solution, Dist(Bi,Bj) denotes the and Bj do not overlap if and only if one of the following euclidian distance between (xi, yi) and (xj, yj), and vectors lb inequalities holds: (lower bounds) and ub (upper bounds) are the visualization window bounds as defined in the inequalities (3). Q is the positive semi-definite matrix composed by blocks L given by:

  L 0   0 Q =  0 L  ,L = nId − ones(n, n), 0 0 where Id is the identity matrix and ones(n, n) is the n × n matrix with all entries equal one. Matrix A and vector b are defined so as to incorporate the constraints (2) and (4). Precisely, the ordering given by (4) allows us to write: (a) Input layout. (b) Optimized layout. Fig. 4: Result of our method to rearrange boxes with overlaps.

xp1 ≤xp2 ≤...≤xpn ⇒ xpi − xpi+1 ≤ 0, i = 1...n − 1, (6) with a similar expression holding for y. Additionally, the IV. DEALINGWITHMULTIPLEREQUIREMENTSFOR sorting also allows us to get rid of the absolute value function GEOMETRICLAYOUTSARRANGEMENT in (2), that is, In this section we describe a methodology for building layouts from geometric primitives which is able to deal xpi ≤ xpj ⇒ |xpj − xpi | = xpj − xpi . Thus, with a wide range of requirements simultaneously. Relying on multidimensional projection, density-based adaptive grids, (wp + wp ) x − x ≤ − i j , i < j, (7) and mixed integer optimization, our approach is semantically pi pj 2 aware, makes an efficient use of display area, and generates with a similar expression holding for y. The variables rij well structured grid-like layouts. Moreover, the formulation allows for incorporating the OR condition defined in (2) into intrinsically impose a hierarchy on the data, enabling alterna- the optimization problem as follows: tives for the scalability issue. The proposed optimization scheme arranges geometric en- xpi −xpj ≤ wij +Mrij ⇔ yqi −yqj ≤hij +M(1−rij), tities (boxes) with varying sizes so as to avoid overlaps while (8) preserving the neighborhood structure of the underlying data i < j, rij ∈ {0, 1}, (semantics). The area of each geometric primitive is also included in the optimization process to ensure that the display (wpi +wpj ) (hqi +hqj ) where wij = − 2 , hij = − 2 and M is a area will be efficiently occupied. In fact, supported by the very large constant. The rationale behind the construction in adaptive grid, our formulation is able to scale elements with

Equation (8) is that if rij = 0, the constraint xpi −xpj ≤ wij different sizes using only one variable, thus rendering the becomes mandatory while yqi − yqj ≤ hij + M is naturally optimization procedure as simple as possible. satisfied as M is a large number (if rij = 1, we have the The proposed methodology is composed by three main opposite situation, instead). Therefore, optimizing the centroid steps: multidimensional projection, density-based adaptive positions and the decision variables rij simultaneously allows grid generation, and layout optimization. us to find the optimal position for the boxes while respecting In the first step, high-dimensional data is mapped to the all the constraints as stated in Equations (2), (3), and (4). visual space so as to preserve distance among data instances. In Equations (6) and (8) are incorporated into matrix A using our implementation we use the Least Square Projection (LSP) the auxiliar matrices Cx,Cy,Dx,Dy as follows: method, which preserves distances nicely during the mapping process, thus enforcing that neighbor points in the visual space     Cx 0 0 correspond to similar/close instances in the original space. The    0 Cy 0  c use of a distance preserving mapping to place instances in the A =     b = (9)  Dx 0 −MId  d visual space provides the neighborhood structure that must be 0 Dy MId “mimicked” by the final layout. An adaptive grid is then generated from projected points. where [Cx|Cy|c] and [Dx|Dy|d] are built from constraints In contrast to typical adaptive grid generation schemes, our (6) and (8), respectively. Notice that vector c is null as approach refines the grid in less dense (but not empty) regions stated in (6). However, this constraint can be relaxed so as to of the visual space, thus placing larger grid cells in denser introduce more flexibility into the layout. Figure 4 illustrates regions. The rationale is to allow users easily identify dense the resulting layout from solving the standard MIQP (5). regions by visually recognizing large geometric objects in the Notice that the orthogonal order is accurately preserved while layout. The number of refinement levels is a user defined the boxes are thoroughly spread in the visualization window. parameter. The adaptive grid produces a size varying tiling of the visual space. Moreover, grid cells inherit the semantic relation δ αδ of the project instances, that is, neighbor grid cells tend to δ encompass similar instances. Although well structured, the cell αδ δ arrangement resulting from the refinement is typically spread, δ δ α δ making an inefficient use of display area. Therefore, in the third step of the proposed pipeline, cells are rearranged in the δ αδ visual space to optimize the area usage. The optimization is formulated to account for object scale, overlapping, and grid- (a) (b) like arrangement while preserving neighborhood relationships and the aspect ratio among cells. Fig. 5: (a) The input layout with δ0 being the length of Let G˜ = {g1, g2, ..., gN } be the set of non-empty cells in the coarser cell. The size of the remaining cells are defined G, that is, G˜ comprises the cells of G with projected points according to the initial parameter δ0 and their scale parameters in their interior. Each cell gi is a square box described by the αi. (b) The result of the optimization when δ > δ0. 3 vector gi = (xi, yi, wi) ∈ R , where (xi, yi) accounts for the center of the box and wi > 0 is the edge length of gi. The cells gi should be rearranged and resized inside a W × H display area so as to make an efficient use of display area while preserving grid alignment and neighborhood structures. k Additionally, wi = αiδ, where αi = 1/2 , k corresponding to the level of refinement of gi. Hence, δ is a parameter to

be optimized from which the size of each cell is derived, as Figure 5 shows. Rearrange cells gi so as to generate layouts that optimize

use of area while presenting a grid-like structure is an NP- hard problem present in different contexts. In order to get an approximate solution, we formulate the problem as a computationally tractable quadratic optimization problem. The optimization is formulated as in Equation (10) below:

minimize E(z) = Ecomp(z) + Erezise(z), subject to Az ≤ b, z = [x y r δ]> ,

> N x = (x1, x2, ..., xN ) ∈ R > N y = (y1, y2, ..., yN ) ∈ R > r = (r12, ..., r1N , r23, ..., r2N , ..., rN−1N ) , rij ∈ {0, 1} δ0 ≤ δ ≤ min (W, H), (10) where z is the sought solution; y and x correspond to the coordinates of the centroids of the cells; δ is the scaling factor; A and b hold the constraints imposed on the optimization problem. The unknowns rij are control variables used to properly avoid overlaps. The energy components Ecomp(z) Fig. 6: Layouts produced by our approach, ProjSnippet, MI- and Eresize(z) control the proximity between cells and the OLA, RWordle-C, VPSC and PRISM in 5 datasets. area increase, respectively. The former term accounts for overlaps and neighborhood preservation and the second term is designed to scale the box to fill up as much area as possible. from Youtube querying six distinct topics, namely, linux, civil Figure 6 depicts qualitative results comparing our approach war, fifa world cup, hawk, guitar and information visualization. with overlap removal and visual board techniques, respec- Textual information associated to each video is processed to tively. Notice that the proposed method gives rise to well generate a feature vector that represents the video in a high- structured layouts where neighborhoods (indicated by color dimensional space. The proposed methodology with three level map) are nicely preserved. Moreover, our approach makes grid refinement is employed to build a layout where larger a better use of display area, thus improving readability and cells are textured as word clouds while the cells in the lowest content analysis. refinement level (smaller cells) are textured with a snippet One of our applications regards video visualization, as build from a screenshot of a randomly chosen video contained illustrated in Figure 7. We build a collection of 300 videos in the cell as well as textual information containing title, description and URL of the video. Word clouds are generated using keywords extracted from the text associated to the video. l r e s y v d i t h e r o e h t o a i s n g u m t p h s o a s m e i n j

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Layouts generated during and after user intervention are depicted in Figures 8(b) and 8(c). More results V. SEMANTICALLY AWARE DYNAMIC LAYOUTS can be found in http://youtu.be/cqua1VerGlo In this section we describe a novel semantic aware layout construction technique that allows users to freely tailor 2D VI.PUBLICATIONS,AWARDS AND HONORS arrangements according to their interest. The proposed for- Publications (and Qualis) mulation relies on interactive mechanisms enabled by multi- [1] (A1), [2] (B1), [3] (A1), [4] (B1), [6] (B1), [7] (A2). dimensional projection methods to enforce semantic relation in the layout. Moreover, the proposed approach is based on Awards and Honors a simple energy function that can efficiently be minimized • Best paper in Graphics and Visualization at SIBGRAPI 2013 using well-known optimization libraries, thus avoiding in- • Invited IEEE TVCG paper presented at IEEE Vis 2014 tricate computational implementations while ensuring real- • Accepted proposal to Doctoral Colloquium at IEEE Vis 2015 • Invited IEEE TVCG paper presented at IEEE Vis 2016 time layout updates. Similar to state-of-the-art techniques, our methodology is able to arrange geometric primitives in REFERENCES arbitrary visual domains, what renders it quite flexible and [1] E. Gomez-Nieto, F. S. Roman, P. Pagliosa, W. Casaca, E. S. Helou, versatile. M. C. F. de Oliveira, and L. G. Nonato, “Similarity preserving snippet- The provided results show the effectiveness of our approach based visualization of web search results,” IEEE Transactions on Visual- ization and Computer Graphics, vol. 20, no. 3, pp. 457–470, 2014. in building and organizing user tailored layouts. Semantic [2] E. Gomez-Nieto, W. Casaca, L. G. Nonato, and G. Taubin, “Mixed relation between entities derives from similarity metrics, there- integer optimization for layout arrangement,” in Proceedings of the fore, the proposed methodology can be employed in different 26th Conference on Graphics, Patterns and Images, ser. SIBGRAPI’13. Washington, DC, USA: IEEE Computer Society, 2013, pp. 115–122. scenarios and applications. [3] E. Gomez-Nieto, W. Casaca, D. Motta, I. Hartmann, G. Taubin, and L. G. 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Levkowitz, “Least square resources that allow users freely modify the layout according projection: A fast high-precision multidimensional projection technique to their interest while still being able to build arrangements in and its application to document mapping,” IEEE Transactions on Visual- arbitrary visual domains. Moreover, the proposed formulation ization and Computer Graphics, vol. 14, no. 3, pp. 564 –575, 2008. [6] E. Gomez-Nieto, W. Casaca, I. Hartmann, and L. G. Nonato, “Under- combines the flexibility provided by control points used in standing large legal datasets through visual analytics,” in Proceedings..., multidimensional projection with an energy function tuned to J. L. D. Comba and L. G. Nonao, Eds., Workshop on Visual Analytics, enable interactive layout update as well as to enforce semantic Information Visualization and Scientific Visualization, 6. (WVIS). So- ciedade Brasileira de Computação, 2015. relation among neighbor entities. [7] G. G. Zanabria, L. G. 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