Multi-Perspective, Simultaneous Embedding

Hossain, Iqbal; Huroyan, Vahan; Kobourov, Stephen G.; Navarrete, Raymundo

doi:10.1109/tvcg.2020.3030373

Cited by 4 publications

(7 citation statements)

References 33 publications

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“…However, it is possible that the different dissimilarity matrices measure different relationships in the data. MPSE aims to find an embedding of a graph, such that the different perspectives P k (X) of the embedding X can visualize the different dissimilarities D k simultaneously [15].…”

Section: Multi-perspective Simultaneous Embedding (Mpse)mentioning

confidence: 99%

“…For ENS-t-SNE, we assume a set of distance matrices for the same set of objects. Similar to Multi-Perspective Simultaneous Embedding [15], where the goal was to generalize the MDS in order to achieve a multi-perspective visualization of a dataset that would preserve distances for corresponding projections, we generalize t-SNE. For this purpose we generalize the objective function of t-SNE onto the one that would take multiple distance matrices and have one projection for each on which the desired distances would locally be preserved.…”

Section: Multi-perspective Simultaneous Embedding (Mpse)mentioning

confidence: 99%

“…. , perp M ) = M m=1 C(Π m X; perp m ) (15) where Y → C(Y ; perp m ) is the t-SNE cost function with perplexity parameter perp m . Minimizing ( 15) is achieved using Algorithm (1) (varying the perplexity parameters while using the same distance matrix D).…”

Section: Visualizing the Effect Of Perplexitymentioning

confidence: 99%

“…Instead we propose to embed the dataset in 3D and use different perspectives (or view-points, or projections) to present the desired information. Hossain et al [15] first used 3D space for multi-perspective simultaneous embedding, where the goal was to capture global distances between the datapoints. In this work we focus on preserving local relationships, i.e., we aim to preserve the local neighborhoods and pay less attention to points that are far from each other.…”

Section: Introductionmentioning

confidence: 99%

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Embedding Neighborhoods Simultaneously t-SNE (ENS-t-SNE)

Huroyan¹,

Navarrete²,

Hossain³

et al. 2022

Preprint

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Fig. 1: The ENS-t-SNE embedding of a 400-point dataset with three perspectives: in each perspective there are two clusters. The dataset is created as follows: half of the points are randomly assigned to one group and the other half to the other group. The distance between points within the same group is 1 (plus small Gaussian noise) while the distance between points in different groups is 2 (plus small Gaussian noise). The left figure shows one view of the 3D ENS-t-SNE embedding; the next three figures show the corresponding three projections. The original clusters are shown in color (blue, orange), shape (square or circle) and texture (filled or not). The ENS-t-SNE algorithm recovers the clusters and creates an embedding which respects all 3 types of clusters simultaneously.

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Section: Multi-perspective Simultaneous Embedding (Mpse)mentioning

confidence: 99%

Section: Multi-perspective Simultaneous Embedding (Mpse)mentioning

confidence: 99%

Section: Visualizing the Effect Of Perplexitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Embedding Neighborhoods Simultaneously t-SNE (ENS-t-SNE)

Huroyan¹,

Navarrete²,

Hossain³

et al. 2022

Preprint

Self Cite

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“…Results here focus on theoretical aspects, establishing computational complexity, i.e., showing that the problem is hard in general [16] but that other variants admit polynomialtime solutions [12,18,22]. Recently, simultaneous embeddings were generalized to graphs drawn in 3D, with the goal that different twodimensional projections preserve user specified distances [24]. Beck et al [5] present an extensive overview on visualization techniques for dynamic graphs, which also touches upon matrix visualizations.…”

Section: Introductionmentioning

confidence: 99%

Simultaneous Matrix Orderings for Graph Collections

Beusekom

Meulemans

Speckmann

2022

IEEE Trans. Visual. Comput. Graphics

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Undirected graphs are frequently used to model phenomena that deal with interacting objects, such as social networks, brain activity and communication networks. The topology of an undirected graph G can be captured by an adjacency matrix; this matrix in turn can be visualized directly to give insight into the graph structure. Which visual patterns appear in such a matrix visualization crucially depends on the ordering of its rows and columns. Formally defining the quality of an ordering and then automatically computing a high-quality ordering are both challenging problems; however, effective heuristics exist and are used in practice. Often, graphs do not exist in isolation but as part of a collection of graphs on the same set of vertices, for example, brain scans over time or of different people. To visualize such graph collections, we need a single ordering that works well for all matrices simultaneously. The current state-of-the-art solves this problem by taking a (weighted) union over all graphs and applying existing heuristics. However, this union leads to a loss of information, specifically in those parts of the graphs which are different. We propose a collection-aware approach to avoid this loss of information and apply it to two popular heuristic methods: leaf order and barycenter. The de-facto standard computational quality metrics for matrix ordering capture only block-diagonal patterns (cliques). Instead, we propose to use Moran's I, a spatial auto-correlation metric, which captures the full range of established patterns. Moran's I refines previously proposed stress measures. Furthermore, the popular leaf order method heuristically optimizes a similar measure which further supports the use of Moran's I in this context. An ordering that maximizes Moran's I can be computed via solutions to the Traveling Salesperson Problem (TSP); orderings that approximate the optimal ordering can be computed more efficiently, using any of the approximation algorithms for metric TSP. We evaluated our methods for simultaneous orderings on real-world datasets using Moran's I as the quality metric. Our results show that our collection-aware approach matches or improves performance compared to the union approach, depending on the similarity of the graphs in the collection. Specifically, our Moran's I-based collection-aware leaf order implementation consistently outperforms other implementations. Our collection-aware implementations carry no significant additional computational costs.

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