Seminar 17332

2017-08-08, 14*14

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Andreas Kerrenkerren@acm.org

• Affiliation– Professor in CS at Linnaeus University, Sweden – Head of the ISOVIS Research Group – http://cs.lnu.se/isovis/

• Current research interests– Multivariate network visualization, guidance/

provenance for visual network analytics– Text visualization– Collaborative/adaptive information visualization

Eurographics Conference on Visualization (EuroVis) 2017 Short PaperB. Kozlíková, T. Schreck, and T. Wischgoll(Guest Editors)

MVN-Reduce: Dimensionality Reduction for the

Visual Analysis of Multivariate Networks

R. M. Martins1, J. F. Kruiger2,3, R. Minghim4, A. C. Telea2, and A. Kerren1

1Linnaeus University, Växjö, Sweden2University of Groningen, The Netherlands

3École Nationale de l’Aviation Civile, France4University of São Paulo, Brazil

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Figure 1: Co-authorship network (VisBrazil data set) visualized with MVN-Reduce, using Classic MDS, Sammon Mapping, and differentvalues of the parameter w (see Eq. 2). Node colors encode attribute-based groups (from Bisecting K-Means) and node sizes encode be-tweenness. The visualization shows the split of the network into two main communities of papers, which are bridged by papers with commonco-authors. At the same time, the nodes’ content-based similarities and dissimilarities also influence the layout.

Abstract

The analysis of Multivariate Networks (MVNs) can be approached from two different perspectives: a multidimensional one,consisting of the nodes and their multiple attributes, or a relational one, consisting of the network’s topology of edges. In orderto be comprehensive, a visual representation of an MVN must be able to accommodate both. In this paper, we propose a novelapproach for the visualization of MVNs that works by combining these two perspectives into a single unified model, which isused as input to a dimensionality reduction method. The resulting 2D embedding takes into consideration both attribute- andedge-based similarities, with a user-controlled trade-off. We demonstrate our approach by exploring two real-world data sets: aco-authorship network and an open-source software development project. The results point out that our method is able to bringforward features of MVNs that could not be easily perceived from the investigation of the individual perspectives only.

Categories and Subject Descriptors (according to ACM CCS): I.3.3 [Computer Graphics]: Picture/Image Generation—ViewingAlgorithms

1. Introduction

Relational data sets—also called networks or graphs—are presentin many application areas, such as social network analysis, soft-ware comprehension, biology, and medicine. Such networks are

usually depicted by node-link metaphors, an approach that high-lights relationships (edges) between actors (nodes) and groups ofactors [BETT98]. A more general view on relational data sets leadsto Multivariate Networks (MVNs)—graphs whose nodes and/or

c� 2017 The Author(s)Eurographics Proceedings c� 2017 The Eurographics Association.

J. F. Kruiger et al. / Graph Layouts by t-SNE

Table 3: Neighborhood preservation metric n for rG = 2 (higher isbetter), indicating how well the input (graph) and output (layout)node-neighborhoods match. Cell colors encode n on the same row.

Table 4: Running time in seconds of tsNET and tsNET*.

4.7. Bundled layouts

Sect. 4.2 shows that tsNET can retain neighborhoods successfully,at the expense of introducing a few long edges. We can reduce theclutter created by these with the help of edge bundling, [vdZCT16].For this, we bundle the long edges, but keep the short ones un-changed (Fig. 3). This is easily done by modifying any exist-ing general graph-bundling method to enforce a maximal edge-displacement d as a function of the edge length, where we setd = 0.25. The result is a ‘hybrid’ graph-drawing in which shortedges are straight lines (as in classical graph drawings) and longedges are bundled, thereby reducing clutter. To our knowledge, thisis the first time that selective bundling has been applied in this wayto declutter the drawing of graphs. This method helps one clearlysee which parts of the graph layout have been ‘torn off’ by tsNETto achieve a globally optimal node placement. Of course, bundlingis also applicable to tsNET* layouts. We chose the tsNET layouts(most notably 3elt) to illustrate this idea as they contained morelong edges that could benefit from bundling.

4.8. 3D layouts

As the formulation of tsNET is independent of the output-space di-mension, it is interesting to study its ability to produce 3D graph

Figure 3: tsNET unbundled (left) and bundled layouts (right) forjazz, cage8, block_2000, and 3elt. Edge colors encode edge lengths((dark) red = shortest, green = median, blue = longest).

layouts. To do this, we consider the problem of recovering geomet-ric information from topological information present in 3D meshes,similar to work presented in [GK01,Wal01]: Given a mesh (Fig. 4,left), we consider the graph G given by its vertices V and cell-edgesE. Next, we use tsNET to create a 3D layout of G (Fig. 4, right).

The tsNET reconstructions preserve the local regular structure ofthe input meshes (Fig. 4, right). This can be attributed to the factthat the underlying t-SNE technique is very well suited to preserveneighbors.

More importantly, we see that tsNET can reconstruct the high-level structure of the input shapes well, see e.g., relative sizes andpositions of the horse’s head and four limbs. However, reconstruc-tion of the exact positions of mesh parts is not possible. This isnot surprising, as Euclidean distances between nodes in the originalmesh are not reflected by their graph-theoretical distances. E.g., theback hooves of the horse are geometrically quite close, but graph-theoretically far away, and will therefore not be placed as closetogether. Also, certain shape parts, such as the horse’s limbs, canbe articulated in the original mesh without significantly modifying

c� 2017 The Author(s)Computer Graphics Forum c� 2017 The Eurographics Association and John Wiley & Sons Ltd.

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Seminar 17332

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A. Kerren & I. Jusufi / A Novel Radial Visualization Approach for Undirected Hypergraphs

representing hypergraphs. The prototypical implementationof our approach was guided by the following requirements:

• user-friendly metaphor that is intuitively understandable• input hypergraphs should be specified by GraphML files• add standard interaction, such as zooming, filtering, or re-

ordering of hypergraph elements• hyperedges should not overlap (no crossings of hyper-

edges)• hyperedges and ordinary edges (hyperedges of cardinality

two) should be treated and shown separately

In addition, we considered several tasks that should be sup-ported by the visualization and associated interaction tech-niques:

• find the hyperedge nodes of a selected hyperedge (or setof hyperedges)

• determine all hyperedges that share a specific node (or setof nodes)

• filter nodes/hyperedges by means of topological features,such as node degree

• estimate the cardinality of hyperedges• support editing of nodes and hyperedges if needed

The remainder of this short paper is organized as follows.The next section provides a brief overview of related worksand highlights their drawbacks which are partly addressed byour own approach. In Section 3, we introduce our visualiza-tion tool including the interaction features. Section 4 shortlysummarizes the results of a small and simple evaluation toget a first impression of the user acceptance. The conclusionand future work section deals with possible improvementsof the tool.

2. Related Works

This section highlights known approaches and tools for thevisual representation of hypergraphs. We can distinguish be-tween traditional approaches that are mainly used in thegraph theory literature and more recent approaches adoptedin a variety of visualization tools. Note that we only focuson graphs with undirected hyperedges.

Traditional Approaches Methods within this category arepure diagrams, i.e., they are typically not interactive, butcomplex and do not scale well. Mostly, subset representa-tions are used which is based on the hypergraph’s interpre-tation as set system [SAA09]. Here, the vertices are repre-sented as points in the plane, and a hyperedge is shown asclosed curve (contour) that only contains those nodes thatare part of the edge. The idea is conceptually similar to Vennor Euler diagrams, but without any regional constraints thathave to be taken into account. This metaphor is also usedin modern tools as described below. Another technique isthe use of node-link diagrams with Steiner trees as edges.The so-called Steiner tree problem looks for a minimal-weight tree which connects a specific set of vertices (ter-

minals) in an undirected, weighted graph [HRW92]. Possi-ble non-terminals in the trees are called Steiner points. Theproblem is NP-complete, but there exist heuristics that runin polynomial time. Another way to build a diagram repre-senting a hypergraph is its visualization as a bipartite graphGb = (U,V,E). Vertices in V correspond to the vertices ofthe hypergraph, but those in U represent the hyperedges. Asas result of this design, the edges of Gb in E indicate vertex-hyperedge incidences. Disadvantages of this approach arethe linear structure of the bipartite graph and the massiveline intersections in worst case scenarios.

Recent Approaches Many current network visualizationtools simply handle hypergraphs by extending standardgraph layouts with colored edges, i.e., each hyperedge isreplaced by a set of binary edges with the same color as-signed. According to Ware [War04], this idea only worksefficiently up to 12 colors (hyperedges); no interaction isusually provided. A simple implementation can be found inWolfram Mathematica [Wol13]. Sometimes, this edge col-oring approach is combined with a redundant node color-ing (similar to a pie chart) to strengthen the visual percep-tion. More advanced techniques use tight colored edge hullsas described in [DvKSW12, LQB12, CC12]. Finally, sometools use closed contours for the display of hyperedges asalready described above. To distinguish them, every hyper-edge region is assigned an individual color, thus each hy-peredge node lies within a colored region which may over-lap if nodes are part of different hyperedges. This leads tomixed colors inside the intersecting regions. Prominent ex-amples can be found in the Jung library [OFN13] or in simi-lar approaches such as [CPC09,HRD10,BT09,BT06]. Evenif there are very advanced layout algorithms for Venn andEuler style diagrams that produce aesthetic results, the vi-sual complexity quickly becomes very high if the data setsare getting larger. Moreover, they usually lack advanced in-teraction techniques.

Figure 1: Visual metaphor used in our approach. The redmarked hyperedge eh connects the nodes 5, 8 and 10.

c� The Eurographics Association 2013.

Andreas Kerrenkerren@acm.org

• Previous experiences in set visualization:– Several applications, e.g., in visual text analytics incl. own

visualization solutions, such as CatCombos [ACM TiiS, 2017]

– Visualization of hypergraphs or set systems [EuroVis ‘13]

Seminar 17332

2017-08-08, 14*14

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Andreas Kerrenkerren@acm.org

• I’m interested in to work on and to discuss:– Task taxonomies in set visualization

– Integration of set visualizations into other visual representations, such as scatter plots (2D embeddings) or graphs

– Existing scalability issues that are usually reached very fast

– Novel and/or more efficient visual representations in context of set visualization

– Novel and/or more efficient interaction approaches in context of set visualization

33

direction arrows should be used to move the node with a small distance. In this way it is possible to empty a region of interest and see the connections very clearly without interference of other nodes positioned nearby.

In Figure 5.24, we have moved all nodes to sides except one. So that only node is focused on in a sense and its relations with other nodes are visible. The figure provides a clear visualization for the selected node with the help of manual node repositioning, information in status bar and coloring.

Figure 5.24: Nodes are repositioned manually in the hypergraph

6. FUTURE WORK AND DISCUSSIONS Although we belive that we could achieve our initial purposes, there could be additional features in these tools to improve their functionality. These features can be listed as:

HYPERSPACE could also be improved with more visual controls like ONION. However we have decided to focus on ONION after that we have discovered that it was more powerful than HYPERSPACE for the aspects we tested.

User could have the possiblity to save visualization parameter choices as default settings.

Node / edge deletion could be added to HYPERSPACE. Node / edge addition could be added to ONION and HYPERSPACE. Multiple tabs could be used to show multiple hypergraphs at the same time. Node and edge labels could be shown on the graph instead of being shown on

the status bar.

Evaluation of the tools could also be done on a larger number of test subjects including more questions about the quality of the tools.

[ACM TiiS, 2017]

[MS Thesis, Koctas and Cakici, 2012]