On the Suitability of Connectivity- Extended Local Embedding for Drawing Multivariate Graphs: An Evaluation - Appendix

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On the Suitability of Connectivity-

Extended Local Embedding for Drawing Multivariate Graphs: An Evaluation

- Appendix

Appendix A Graph Visualizations 2

Appendix B Quantitative Results 9

B.1 Graph Aesthetics: Edge Crossings . . . 10

B.2 Graph Aesthetics: Even Edge Distribution . . . 11

B.3 Graph Aesthetics: Layout Energy . . . 12

B.3.1 Global Layout Energy . . . 12

B.3.2 Local Layout Energy Variance . . . 13

B.4 Similarity Representation: General Distance Preservation . . . 14

B.4.1 General Distance Preservation: Regulation Dataset . . . 14

B.4.2 General Distance Preservation: Households Dataset . . . 15

B.4.3 General Distance Preservation: Documents Dataset . . . 16

B.4.4 General Distance Preservation: Phone Calls Dataset . . . 17

B.4.5 General Distance Preservation: Amazon Dataset . . . 18

B.4.6 General Distance Preservation: Patents Dataset . . . 19

B.5 Graph Aesthetics versus Projection Quality . . . 20

Appendix C Impact of Varying Neighborhood Sizes 24

Appendix D Interactive Exploration of Graph Connectivity and Node Similarity 27

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Appendix A

Graph Visualizations

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(a) MEU Original (b) MEU Adjacency (c) MEU Graph Path (d) MEU Combined

(e) LLE Original (f) LLE Adjacency (g) LLE Graph Path (h) LLE Combined

(i) ISOMAP Original (j) ISOMAP Adjacency (k) ISOMAP Graph Path (l) ISOMAP Combined

(m) Weighted Kamada-Kawai (n) Kamada-Kawai MDS Init. (o) MDS classic

(p) Kamada-Kawai (q) ISOM

Figure A.1: Renderings of the extitRegulation dataset 3

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Figure A.2: Renderings of the extitHouseholds dataset 4

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Figure A.3: Renderings of the extitDocuments dataset 5

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Figure A.4: Renderings of the extitPhone Calls dataset 6

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Figure A.5: Renderings of the extitAmazon dataset 7

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Figure A.6: Renderings of the extitPatents dataset 8

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Appendix B

Quantitative Results

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B.1 Graph Aesthetics: Edge Crossings

(a)Regulation (b)Households

(c)Documents (d)Phone Calls

(e)Amazon (f)Patents

Figure B.1: Edge Crossings

ISOM Kamada-Kawai

Weighted KK KK MDS Init. MDS classic

MEU Original MEU Adjacency MEU Graph Path MEU Combined

LLE Original LLE Adjacency LLE Graph Path LLE Combined

ISOMAP Original ISOMAP Adjacency ISOMAP Graph Path ISOMAP Combined

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B.2 Graph Aesthetics: Even Edge Distribution

Figure B.2: Even Edge Distribution

ISOM Kamada-Kawai

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B.3 Graph Aesthetics: Layout Energy

B.3.1 Global Layout Energy

Figure B.3: Global Layout Energy

ISOM Kamada-Kawai

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B.3.2 Local Layout Energy Variance

Figure B.4: Local Layout Energy Variance

ISOM Kamada-Kawai

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B.4 Similarity Representation: General Distance Preservation

B.4.1 General Distance Preservation: Regulation Dataset

Figure B.5:Regulation dataset: node similarity preservation. X axis: attribute space distance, Y axis: layout space distance. Red dots: adjacent vertices, gray dots: all vertex pairs. Red and gray lines are smooth interpolations.

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B.4.2 General Distance Preservation: Households Dataset

Figure B.6:Households dataset: node similarity preservation. X axis: attribute space distance, Y axis: layout space distance. Red dots: adjacent vertices, gray dots: all vertex pairs. Red and gray lines are smooth interpolations.

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B.4.3 General Distance Preservation: Documents Dataset

Figure B.7:Documents dataset: node similarity preservation. X axis: attribute space distance, Y axis: layout space distance. Red dots: adjacent vertices, gray dots: all vertex pairs. Red and gray lines are smooth interpolations.

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B.4.4 General Distance Preservation: Phone Calls Dataset

Figure B.8:Phone Calls dataset: node similarity preservation. X axis: attribute space distance, Y axis: layout space distance. Red dots: adjacent vertices, gray dots: all vertex pairs. Red and gray lines are smooth interpolations.

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B.4.5 General Distance Preservation: Amazon Dataset

Figure B.9:Amazondataset: node similarity preservation. X axis: attribute space distance, Y axis: layout space distance. Red dots:

adjacent vertices, gray dots: all vertex pairs. Red and gray lines are smooth interpolations.

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B.4.6 General Distance Preservation: Patents Dataset

Figure B.10:Patents dataset: node similarity preservation. X axis: attribute space distance, Y axis: layout space distance. Red dots:

adjacent vertices, gray dots: all vertex pairs. Red and gray lines are smooth interpolations.

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B.5 Graph Aesthetics versus Projection Quality Edge Crossing versus Projection Precision

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Figure B.11: Edge Crossing versus Projection Precision

ISOM Kamada-Kawai

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Edge Crossing versus Mean relative rank errors

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Figure B.12: Edge Crossing versus Mean relative rank errors

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Layout Energy versus Projection precision

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Figure B.13: Layout Energy versus Projection precision

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Layout Energy versus Mean relative rank errors

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Figure B.14: Layout Energy versus Mean relative rank errors

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Appendix C

Impact of Varying Neighborhood Sizes

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(a) MEU combined, 3 neighbors (b) LLE combined, 3 neighbors (c) ISOMAP combined, 3 neighbors

(d) MEU combined, 4 neighbors (e) LLE combined, 4 neighbors (f) ISOMAP combined, 4 neighbors

(g) MEU combined, 5 neighbors (h) LLE combined, 5 neighbors (i) ISOMAP combined, 5 neighbors

(j) MEU combined, 6 neighbors (k) LLE combined, 6 neighbors (l) ISOMAP combined, 6 neighbors

(m) MEU combined, 10 neighbors (n) LLE combined, 10 neighbors (o) ISOMAP combined, 10 neighbors Figure C.1: Renderings of theDocuments dataset (combined)

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(a) MEU original, 3 neighbors (b) LLE original, 3 neighbors (c) ISOMAP original, 3 neighbors

(d) MEU original, 4 neighbors (e) LLE original, 4 neighbors (f) ISOMAP original, 4 neighbors

(g) MEU original, 5 neighbors (h) LLE original, 5 neighbors (i) ISOMAP original, 5 neighbors

(j) MEU original, 6 neighbors (k) LLE original, 6 neighbors (l) ISOMAP original, 6 neighbors

(m) MEU original, 10 neighbors (n) LLE original, 10 neighbors (o) ISOMAP original, 10 neighbors Figure C.2: Renderings of theDocuments dataset (original)

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Appendix D

Interactive Exploration of Graph Connectivity and Node Similarity

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(a) Kamada-Kawai Pick 1 (b) ISOMAP Pick 1 (c) MDS Pick 1

(d) Kamada-Kawai Pick 2 (e) ISOMAP Pick 2 (f) MDS Pick 2

(g) Kamada-Kawai Pick 3 (h) ISOMAP Pick 3 (i) MDS Pick 3

(j) Kamada-Kawai Pick 4 (k) ISOMAP Pick 4 (l) MDS Pick 4

(m) Kamada-Kawai Pick 5 (n) ISOMAP Pick 5 (o) MDS Pick 5

Figure D.1: Feature Picks on theDocumentsdataset. Red vertex: picked vertex, Orange vertices: nearest neighbors to picked vertex (attribute-based euclidean distance).

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(a) Kamada-Kawai Pick 1 (b) ISOMAP Pick 1 (c) MDS Pick 1

(d) Kamada-Kawai Pick 2 (e) ISOMAP Pick 2 (f) MDS Pick 2

(g) Kamada-Kawai Pick 3 (h) ISOMAP Pick 3 (i) MDS Pick 3

(j) Kamada-Kawai Pick 4 (k) ISOMAP Pick 4 (l) MDS Pick 4

(m) Kamada-Kawai Pick 5 (n) ISOMAP Pick 5 (o) MDS Pick 5

Figure D.2: Neighbor Picks on theDocumentsdataset. Red vertex: picked vertex, Orange vertices: adjacent vertices to picked vertex, Red edges: edges connecting picked vertex and its neighbors.

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