Cubix Visualizing Dynamic Networks with Matrix Cubes
Contents
1. abcdef pa a b b i 6 s d q Y be e e 1 gt w 2 2 3 4 3 4 V a Adjacency Matrices b Matrix Cube c Vertex Slices Figure 1 Contruction of the Matrix Cube a Each time step of the network 1 2 3 4 is represented as an adjacency matrix b The cube resulting from stacking those matrices Red edges of the cube hold vertices and correspond to the rows and columns of the constituent adjacency matrices blue edges of the cube hold time steps c Slicing the cube along one of the vertex dimensions yields one vertex slice per vertex showing the evolution of that vertex s ego network Visualization an exploration of three dimensional models on the screen is difficult With Cubix we provide transformation and decomposition operations which yield better readable 2D representations of the information contained in the cube This manual explains what operations and visualizations Cubix supports and how they are employed Thoughout this manual we use the following terminology e Time Slice A time slice corresponds to the adjacency matrix for one time step Figure 1 a A time slice shows the network s state at one time step e Vertex Slice A vertex slice results from cutting the cube orthogonally to time slices representing one vertex A vertex slice resembles a table where a vertex s neighbors correspond to rows and time steps to columns Figure 1 c2. p Cubix Visualizing Dynamic Networks with Matrix Cubes User Manual benjamin bach inria fr INRIA France September 4 2013 This manual is a short introduction into How to Explore dynamic networks with Cubix Contents 1 Matrix Cubes 2 2 Interface and Visual Encoding 2 2T Gell Shape Encoding s s ia eos cast bee a a So ee dd a de aoea 2 2 2 GCell Color Encoding cicle SOOO YY Se a AAO Awe BESS d 3 3 Views 4 BEM OEI ade o ee cae es te Se a es Oo a dk Gh Up ds o wee AS 4 32 RONN IEW area a oe weet Seren ak Ss ae Ge Se as E oe es te eee x Se Be Os Hes amp e 5 A Ge hee ae Ga Ge a ES Oh OE SE Be S 5 o we oe decent O the ys oe BS ph et See AA a 5 3 5 Time Side by Side VieW a 6 3 6 Vertices Side by side View a a a a 6 3 SIE SNOW IOWA a o ee 6 4 View Changes and the Cubelet Widget 8 5 Filtering 8 Bel Lasso Selecione o st A a 9 52 Cell Selection suscrita ee de A ES 9 6 Row and Column Reordering 10 7 Controls Summary 11 L1 Keyboard GOntolS usos ani Abe tenes doa eae i SE oh oe ee a 11 Te MOUSE CONOS i sR AA ORS AS OEE A 11 1 Matrix Cubes Cubix is a visualization interface for the exploration of dynamic networks with changing edge weights The central visualization is the Matrix Cube a space time cube resulting from stacking adjacency matrices one for each time step in the order of time Figure 1 shows how a matrix cube is created from the adjacency matrices
3. Chloe Emma Figure 9 Small multiples of vertex slices using value cell encoding Cells are colored using value encoding to highlight differences in weight across slices all other slices Users can then switch to the front or side view and obtain a projection that shows only the selected slice Figure 10 e Using the up and down arrow keys switches to the next or previous time slice e Using the left and right arrow keys switches to the next or previous vertex slice a b Figure 10 Selecting a single slice in the 3D view and rotating the cube shows the selected slice only 4 View Changes and the Cubelet Widget For quick changes between the previously explained views Cubix privides number shortcuts 1 5 or alternatively the Cubelet widget shown in Figure 11 a The cubelet is a stylized representation of a Matrix Cube with sensitive surfaces Surfaces can be clicked in order to switch to the associated view Additionally the Cubelet reflects the current view Number shortcuts and Cubelet interaction is as follows 1 3D View Click on top face of the cubelet The entire cubelet becomes gray to indicate that all faces are visible 2 Front View Click on right side of cubelet The front face gets becomes to indicate the front projection 3 Side View Click on left side of cubelet The side face gets gray to indicate the side projection 4 Time Side by Side Drag mouse on right side of cubelet as to pull it a
4. A vertex slice shows a vertex s neighborhood over time dynamic ego network e Cell A cell corresponds to a connection between two vertices at one particular time e Vector A vector corresponds to a single line of cells inside the cube rows and columns in a single matrix correspond to vectors In the matrix cube vectors can also show the evolution of connectivity during time 2 Interface and Visual Encoding The interface of Cubix is show in Figure 2 The cube in the center shows a collaboration network Persons the network s vertices are shown along the the vertical and horizontal red axes Time is shown along the blue axes Connections between vertices are encoded as three dimensinal cells inside the cube Network statistics are shown on the top left and the Cubelet Widget allows to switch between views on the cube Section 4 Cells in Cubix can vary in two ways shape and color Both can be set by the radio buttons on the right side of the interface 2 1 Cell Shape Encoding a Edge Weight By default cell size indicates edge weight in a logarithmic way Larger cells mean higher edge weight smaller cells lower edge weight In this manual edge weight indicates the number Edges Cells Time Steps Time slices VISUAL MAPPING Cell Color Encoding Time blue to orange a Edge Weight light to dark None all same gray Cell Shape Edge Weight 1 small to b Edge Weight 2 small to GRA P
5. H Nodes 11 Ede ye 208 Tin abe oA sity 0 034903847 VISUAL PARAMETERS fps 0 0 None equal size N k Adapt Weight etwor Logarithmic scale Statisitics ORDERING C Topological Order Name Ordering CELL VISIBILITY Time Range 0 6 d Edge weight Cubelet e 1 18 Cell Opacity Min Max f Y Show Self Edges M Show Non Self Edges 9 ame MISC 22m Animation antag h Vertices Vertex Slices ia L 2 Vertex Slices Time Slices Figure 2 Cubix user interface a Cell color settings b Cell shape settings c Row and column ordering d Time range slider to set visible time slices e Edge weight slider to define visiblity of cells depending on edge weight A histogram indicates distribution of edge weight g Settings to show or hide self and or non self edges h Slider to define animation speed of co publications per year b Edge Weight 2 When cells are the visual space between two cells increases which can make it hard to relate cells between the same two nodes over time This second encoding shows a cells with equal length making all edges between the same two nodes one single visual vector over time Figure 3 c None No shape encoding means that all cells have equal size a Edge Weight 1 b Edge Weight 2 Figure 3 Difference between Edge Shape Encoding seen in Side View Edge Weight 2 connects the cells of the same node pair leading to visual continuity 2 2 Cell Color Encod
6. apted weight range allows to better perceive the weight distribution within a given weight range Figure 12 e Time The weight range slider allows to see only cells of a particular time range e Nodes Similiar to time filtering node slices can be selected by clicking on the corresponding labels on the cube Non selected slices are rendered translucent The examples in Figure 13 have been created by node filtering and show the evolution of weight of two edges over time Changes in opacity and time or node selection are independent from each other and remain con sistent across view changes e o a No weight adaption b Weight adaption Figure 12 Weight adaption scales cube only within the currently visible weight range 5 1 Lasso Selection Holding the ALT key while dragging the mouse activates a lasso selection tool which allows to circle cells After releasing the mouse only the selected cells remain visible throughout all views Clicking somewhere inside the cube while holding the ALT key deactivates the lasso selection 5 2 Cell Selection Cells can be selected to highlight their context When the cell is clicked once only the three slices which the cell is the intersection of remain visible Figure 14 a The front and side views show only the time and vertex slice respectively allowing to investigate the cell s context a Value encoding b Time encoding Figure 13 Two edge vectors in value and time encodi
7. e horizontal vertex slice selection in the cube down Arrow Left Move vertical vertex slice selection in the cube to the left Arrow Right Move vertical vertex slices selection in the cube to the right Mouse Controls Drag mouse left button Rotate cube Drag mouse right button Pan Drag mouse left button Alt Create lasso selection Click left mouse button Alt Remove lasso selection
8. ing For coloring cells three modes exist set by the radio buttons on the right side in the interface a Time Encoding colors cells according to which time slice they belong to Figure 4 a The color scale ranges from blue early times via purple and indigo middle time steps to orange recent times b Weight Encoding colors cells according to their weight ranging from light turquise low weight to dark blue high weight Figure 5 b Weight encoding makes heavy edges stick out 3ermany France Israel Sudan Mdaw Japan China a Time encoding blue to orange b Value encoding light to dark Figure 4 Cell encoding in Cubix c No Encoding shows all cells in the same dark gray When applying opacity to cells and seeing the cube from the Front node pairs with many connections over time stick out by appearing darker Figure 5 More on the Front view and other views in Section 3 gp A 9 2 o y E a S z a M 33585 3 6 Sases 85 fF S amp S ez gt fa Z J I j aj gt 3 zZ JI I ow U uy Lucas Lu LUXE U Louise l lathor Nathan Nathan brie riel Gabriel mille mille amill eg Le Aug Hug Hua rd Aran rd al Enz Enz i Enze hibe loe hice Er Er Erry Emma i m Z Q T rym Om 5 E 23 A amp Q A g3 5 2 8 85 amp A 2 2 7 gt 7 gR 7 Ro A E S 4 3 y Q Do y 5 D gt O a Quantity of connection between node pairs over time b Edge weight encoded in cell size Fig
9. n Nathan Nathan Nathan Gabriel Gebriel Gabriel Gabriel Camille Camille Camille Camille Lea Lea Lea Lea Hugo Hugo Huge Hugo Sarah Sarch Sarch Sarah Enzo Enzo Enzo Enzo Chloe Chloe Chloe Chloe Emma Emma Emma Emma 5s 2 ERI BE Rg ze 2858383 8 0 4 3 g a a g g E Sa ee RH amp a Front View of Matrix Cube b Side view of Matrix Cube Figure 6 Projections on the cube 3 3 Side View When rotating the cube to its left side face a projection as shown in Figure 6 b is obtained Rows still show vertices but columns represent time one column per time step Time runs from left to right Cells in this view summarize all connections of a vertex over time steps The side view makes it easy to spot the overall evolution of each vertex s degree and to identify time steps years in our example that feature denser or sparser networks In Figure 6 b for example the year 2008 shows less publications than 2007 because the corresponding column contains smaller cells 3 4 Rotating Slices To individually observe an individual slice when in Front or Side view you can rotate individual time slices in the side view or vertex slices in the front view projection To rotate a slice click on the corresponding label Rotating a slice can be compared to rotating a single book on a book shelf after rotation the slice can be observed individually while context of the current view is preserved This view is useful when an interesting pattern in the fron
10. ng Clicking the selected cell twice remains only the vectors which the cell is the intersection of visible Figure 14 b a Slices of selected node b Vectors of selected node Figure 14 Selecting a cell can show slices or vectors this cell is part of The selected cells becomes brown 6 Row and Column Reordering The order or rows and columns in the cube is determined by an algorithm that optimizes patterns in the matrices Across all matrices in the cube there is only one ordering of rows and columns possible Hence the more time slices exist and the more they differ the less efficient an optimization can be To optimize reordering for one time slice or a subset of time slices you can select individual time slices e g with the time slider or filter cells with the edge weight slider and re run the reordering RE ORDER button All time slices in the cube will consequently obtain the same ordering obtained from the visible cells To facilitate the look up for vertex names Cubix provides the NAME ORDERING button which orders vertices in an alphanumerical way Ordering remains consistent across view changes 10 7 Controls Summary 7 1 7 2 Keyboard Controls Key 1 3D Cube View Key 2 Front View Key 3 Side View Key 4 Time Side by Side Key 5 Vertices Side by Side Shift Slow View transitions Alt Fast view transitions Arrow Up Move horizontal vertex slice selection in the cube up Arrow Down Mov
11. part Results in the image show in in Figure 11 b 5 Vertices Side by Side Drag on left side of cubelet as to pull it apart Results in the image show in in Figure 11 c All view switches are indicated though animated transitions Animated transitions can be shortened by holding shift and fastened with the alt key 5 Filtering Independently from the current view visibility of cells can be adapted by different filtering methods explained in the following The corresponding sliders can be found on the bottom of the screen Figure 22 e Opacity The right side of the opacity range slider sets general cell opacity The left side sets opacity of cells which are a not in the current time range or b not in slices currently selected Vertes Slices Time Slices Time Slices Vertex Slices a b c Figure 11 Different states of the Cubelet widget indicating the current view of the matrix cube a front face is shaded and selected slices highlighted b slicing along the time dimension with selected slice highlighted and c slicing along the vertex dimension e Weight The weight range slider allows to see only cells of a particular edge weight range When the ADAPT WEIGHT button is active the remaining cubes are scaled so that their size varies accord ing to the currently visible wight range This means that cells at the lower range of visible weight are very small while cells on the higher end have maximal size Such an ad
12. s vertices of the network Note that pan and zoom is enabled in both side by side representations 3 7 Slide Show View Yet another way to explore individual slices is to present them one at a time such as in a flip book or a slide show From the 3D view users can select any single vertex or time slice consequently hiding y n 97 97 P9 D YOU A IDO MLL cl ul y E YDS uJ YO SD 7 YD DS ony In yu ony ony JAI 4QD De cin P Z soon Z 35INO7 pue JF UDUIDN apa DaT UDUJON OLJU y f UDUIDN D a i E 2 C m Luccs Louise Camille Led Nathan Enzo San HUGO Gabriel Emma Chloe Luccs Louise Comille Leg Nathan Erzo Sah Hugo Gabriel Emma Chise pu 30 Lucas Louise Camille Leo Nathan Enzo rah HUGO Gabriel Emma Chloe Lucas Louise Camille Leg Nathan Enzo Sarah Hugo Gabriel Emma C hice Figure 8 All time slices juxtaposed using value encoding and equal cell size Darker cells indicate more edge weight However switching between cell encodings must be done manually by the user Lucas Louise Nathan Gabriel Camille Lea Hugo Sarah Enzo Chloe Emma Lucas Lucas Louise Louise Nathan Nathan Gobriel Gobriel Camille Camille Lea Lea Huge Hugo Sach Sarah Enzo Enzo Chloe Chloe Emma Emma Enzo Chloe Hugo Sarah Leo Luccs Louise Nathan Gor iel Camille Lea Hugo Sarah Enzo
13. t or side view has been found and one particular slice requires particular investigation Note that you can rotate as many slices as you want Figure 7 shows the rotation of a time slice from the view in Figure 6 b Slices can be rotated back to its initial position by clicking on any cell within that slice 2009 O co m 09 lt e re o F 2858 sereaeggeeis SAA A ao 8 aeeo 4s aa ae Lucas E Lucas Louise Louise Nathan Nathan Gabriel Gabriel Camille a Camille Lea a Lea Huge a Hugo Soran Sarah Enzo oe EE Chloe Chloe Ernbra Emma 3288 segseegehaeas A AAA a e a G LO 5 a A Figure 7 Focus and context view of a time slice a Time x vertices projection b after rotating time slice for 2009 3 5 Time Side by Side View A common technique to show spatio temporal data is to use small pictures side by side one for every time step Since time in the matrix cube is discrete decomposition is straightforward In cubix time slices matrices can be juxtaposed allowing for pairwise comparison and individual analysis Figure 8 Hovering a cell highlights all connections between the same node pair over time 3 6 Vertices Side by side View Figure 9 shows all vertex slices laid out side by side In this example cell color was already mapped to cell size to allow for better cross slice comparison Each vertex slice shows the dynamic ego network for each vertex enabling the comparison of individual connection patterns acros
14. ure 5 No cell color encoding can highlight quantity of connections between nodes over time 3 Views Various views can be derived from the matrix cube by applying a combination of natural operations to it rotation projection slicing filtering layout and flip through 3 1 3D View The 3D view as shown in Figure 2 view can be e rotated move mouse while left button pressed e panned move mouse while right button pressed e zoomed scroll mouse wheel and When hovering cells the corresponding labels for vertices and times get highlighted to make their identification easier Another label indicates the edge weight 3 2 Front View Figure 6 a shows the cube rotated and projected so that it shows the adjacency matrix with all time slices superimposed using alpha blending Cells inside the cube become translucent and provide a summary of the connections between any two vertices Large cells indicate high edge weight Dark cells due to super imposition indicate frequent connections Topological clusters emerge from reordering rows and columns Illustrated in Figure 6 a Luise and Lucas collaborate frequently while Nathan and Lucas collaborated in a few years only but on many articles Using to time encoding clusters and connections can be roughly situated in time e g Lucas individual publications Lucas x Lucas are much older than his collaborations Lucas TT Lucas Lucas Lucas Louise E Louise Louise Louise Natha
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