Cubix Visualizing Dynamic Networks with Matrix Cubes
Contents
1. When rotating the cube to its left side face a projection as shown in Figure 8 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 8 b for example the year 2008 shows less publications than 2007 because the corresponding column contains smaller cells 3 4 Rotating Slices 5 6 To individually observe slices when in Front or Side view you can rotate individual time slices in the side view or vertex slices in the front view To rotate a slice right 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 SD Projection side by side Rotation Time Multiplex 3 5 9 hai 2 Figure 7 Views in Cubix The eye indicates the position of the user R GIA FR eos a o 8 o F amp Bb ga SN Lucas Lies Lucas Lucas Louise n Louise Louise Louise Nethen Nathan Nathan Nathan Gabriel Gabriel Gabriel Gabriel Camille Camille Camille Camille Lea Lea Lea Lea Hugo Hugo Hugo Hugo serah Sach Serch Sarah Enzo Enzo Enzo Enzo Chloe Chloe Chloe Chloe Emma Emma Emma Emma segs ggg 885888 6 4G 3 amp aS 2 ZS 8 RR RR a Front V2. p Cubix Visualizing Dynamic Networks with Matrix Cubes User Manual benjamin bach inria fr INRIA France http www aviz fr Research Cubix September 9 2013 This manual is a short introduction on How to Explore Dynamic Networks with Cubix Visit http www aviz fr Research Cubix for a general introduction and a video showing Cubix in action Contact benjamin bach inria fr in case of any problems or ambiguities Contents 1 The Matrix Cube 2 Interface and Visual Encoding 2 1 CellShape Encoding 2 2 a d ana a e a a deao aE a aaa a 22 Gell Color EneodinG 2 aries e aa a aa aaa a a a a a o n a SES 3 Views Ddr SGD VIE ON seeren ees ad ie eat hee a ne eae A oe a e EE T Die FONC WIGW Ul poserar COD ec a a E E po Sn Aea ee Boor ENON a meia ta Seaan qu ee e e ae ee 2 E wh IE RU Bree 34 Rotating SIICOS DO pa Aah ee eed E EE Eo ee Ee Got ee doe 3 5 Time Side by Side View 3 a noonoo a a a 3 6 Vertices Side by side View 4 aoaaa a a a a a 3 7 Sde Show VIEW LO suas ss E BO SS ele we ae a oe eee eee ee 4 View Changes and the Cubelet Widget 5 Filtering 5 1 Lasso Selection ssa 4 ack amp do a ow EG BEBE E ES SESE Se EKA 52 Cell SeClCHOM mms LEE Be E SE ee eet da eh ee ee oe ee a 6 Slice Coloring 7 Row and Column Reordering 8 Controls Summary Sd Keyboard CONTOS ss x 6 46 d3 4 a hed eed ee EY Be SSS 82 MOUSE CORIIOIS co he Seale Be ec o B S Se Be dae a ent atte ga al a Be 1 The Mat
3. Edge Weight light to dark None all same gray VISUAL PARAMETERS G fps 0 0 h i Cell Shape lt a _ e Edge Weight 1 small to l b mm p S i Edge Weight 2 small to l E mt amam 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 ig Cell Opacity Min Max f M Show Self Edges M Show Non Self Edges 9 maa MISC Animation Ro h Vertices Vertex Slices ia NE Vertex Slices Time Slices Figure 3 Cubix user interface with the Matrix Cube in the center the Cubelet widget at the bottom left and the control panel on the right a Change the color encoding of cells b Change the size encoding of cells c Apply new row and column ordering d Time range slider to determine the set of visible time slices e Edge weight slider to determine visiblity of cells depending on their edge weight A histogram indicates distribution of edge weight g Settings to show or hide self and or non self edges h Slider to set animation speed 2 Interface and Visual Encoding The interface of Cubix is show in Figure 3 The cube in the center shows a collaboration network which is used for demonstration purposes in this manual Persons the network s vertices are shown along the the vertical and horizontal red axes Time is shown along the blue axes Conne
4. Figure 14 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 or outside the cube while holding the ALT key deactivates the lasso selection 10 a Value encoding b Time encoding Figure 15 Two edge vectors in value and time encoding 5 2 Cell Selection Cells can be selected to better see their context When a cell in the 3D view is clicked once only the three slices time slice and two vertex slices which the cell is the intersection of remain visible Figure 16 a The front and side views show only the time and vertex slice respectively allowing to investigate the cell s context Clicking the selected cell twice leaves only the vectors which the cell is the intersection of visible Figure 16 b a Slices of selected node b Vectors of selected node Figure 16 Selecting a cell can show slices or vectors this cell is part of The selected cells becomes brown 6 Slice Coloring Slices can be colored manually to track its cells across views Simply press Shift and click on the desired slice label Another click removes the coloring Colors are assigned in randomly 7 Row and Column Reordering The order or rows and columns in the cube is determined
5. by an algorithm that optimizes patterns in the matrices Across all matrices in the cube there is only one ordering of rows and columns horizontal and vertical vertex slices possible Hence the more time slices exist and the more they differ the less 11 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 The ordering takes only the currently visible cells into account 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 8 Controls Summary 8 1 8 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 When in Time Side by side or Vertex Side by side view used to pan Arrow Down Move horizontal vertex slice selection in the cube down When in Time Side by side or Vertex Side by side view used to pan Arrow Left Move vertical vertex slice selection in the cube to the left When in Time Side by side or Vertex Side by side view used to pan Arrow Right Move vertical vertex slices selecti
6. Lea Hugo Hugo Soroh Sakai Enzo Chloe Emmo Siad Louise Gobrial Camille Luccs a Louise Louise Nathan Nathan Gobriel Gobriel Camille Camille Lea Lea Hugo Hugo Sarch Search Enzo Enzo Chloe Chive Emma Emma a Hugo Enzo Emma Figure 11 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 12 e Use the time slider Figure 3 d to change the visible set of time slices e Use the left and right arrow keys to switch between the next and previous vertex slice a b Figure 12 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 indicated alongside with the Cubelet on the screen or alternatively the Cubelet widget shown in Figure 13 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 The Cubelet indicates the current view by shading the corresponding face Vertes Slices Time Slices Time Slices Vertex Slices a b c Figure 13 Different states of the Cubelet widget indicating the current view of the matrix cube a fro
7. andle of the slider labeled F for filtered cells sets opacity of cells which are a not in the current time range or b not in slices currently selected Increasing the value of the F side allows to explore the cube while not completely removing all filtered cells e Cell Weight Figure 3 e The weight range slider allows to see only cells of a particular edge weight range A histogram above the slider indicates the distribution of edge weights across the scale When the ADAPT WEIGHT button is active the remaining cubes are scaled so that their size varies according 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 adapted weight range allows to better perceive the weight distribution within a given weight range Figure 14 e Time Figure 3 d The time range slider allows to see only cells of a particular time range e Vertices Similiar to time filtering vertex slices can be selected by clicking on the corresponding labels on the cube Non selected slices are rendered translucent according to the F value of the opacity slider The examples in Figure 15 have been created using vertex filtering selecting horizontal and vertical vertex slides and show the evolution of weight of two edges over time All filtering mechanisms are independent from each other a No weight adaption b Weight adaption
8. ctions be tween 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 see Section 4 The remaining interface components are explained briefly in Figure 3 and explained in detail in the corresponding sections of this manual 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 Cubix provides three ways to encode information in the size of cells Figure 3 b a Edge Weight 1 By default cell size indicates edge weight in a linear scale Larger cells indicate higher edge weight smaller cells indicate lower edge weight In our example edge weight refers to the number of co publications per year b Edge Weight 2 Scaling cells introduces visual spaces between cells which in turn can hinder to see cells belonging to the same edge or neighborhood vectors This second encoding stretches 1A collaboration network shows coauthorship relations between authors of papers Authors are vertices in the network and edges indicates how ao authored with whom cells to connect all cells in the same time vector Figure 4 illustrates the differences between Edge Weight 1 and Edge Weight 2 a Edge Weight 1 b Edge Weight 2 Figure 4 Difference between Edge Shape Encoding seen in Side View Edge Weight 2 connects the cells of
9. gure 7 Summarizes the different views currently implemented in Cubix a Quantity of connection between node pairs over time b Edge weight encoded in cell size Figure 6 No cell color encoding can highlight quantity of connections between nodes over time 3 1 3D View 9 The 3D view as shown in Figure 3 view can be e rotated drag mouse while left button pressed e panned drag 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 A pop up label indicates the edge s weight 3 2 Front View 1 Figure 8 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 can be made translucent right handle of the opacity slider Figure 3 e to 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 8 a Luise and Lucas collaborate frequently while Nathan and Lucas collaborated in a few years only but on many articles Using 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 3 3 Side View 2
10. iew of Matrix Cube in time encoding b Side view of Matrix Cube Figure 8 Projections on the cube be observed individually while context of the current view is preserved This view is useful when an interesting pattern in the front 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 9 shows the rotation of a time slice from the view in Figure 8 b Slices can be rotated back to its initial position by right clicking on the label again 3 5 Time Side by Side View 3 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 10 Hovering a cell highlights all connections between the same node pair over time When in this Daio mr a Schematic view of slice rotation 2009 2 ag5e Fees g ccis oN ON N ne Ss o 4 6 4 4 N Luces W Lucas Louise Louise Nathan m Nathan Gabriel Gabriel Camille Camille Leg a Lea Huge Hugo Sard Sarah Ergo z Enzo Chloe Chloe Emma Ermima 3288 segseegeuag eas AA N N AD E o G 4 Og 3 E b View the users sees Figure 9 Focus and context view of a time slice a Time x vertices projection b after rotating time slice for 2009 view use
11. nt face is shaded and selected slices highlighted b slicing along the time dimension with selected slice highlighted and c slicing along the vertex dimension Number shortcuts and interaction with the Cubelet are 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 becomes gray to indicate the front projection 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 apart Results in the image show in in Figure 13 b Q 5 Vertices Side by Side Drag on left side of cubelet as to pull it apart Results in the image show in in Figure 13 c All view switches are indicated through animated transitions Animated transitions can be short ened by holding shift and fastened with the alt key The transition speed slider Figure 3 h allows for additional control over the animation speed 5 Filtering Independently from the current view visibility of cells can be adapted by different filtering methods explained in the following The corresponding sliders are found on the right side of the screen Figure 3 e Cell Opacity Figure 3 f The right handle of the opacity range slider labeled V for visible cells sets the general cell opacity value The left h
12. on in the cube to the right When in Time Side by side or Vertex Side by side view used to pan 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 Shift click on slice label color slice
13. rix Cube 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 HDANDT YD a abcdef deL N tT a y R i Mi M y H i O Q0T0 pw mH OAV TY 2 3 19 4 V aS 1234a Adjacency Matrices Time b Matrix Cube c Vertex Slices 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 the
14. the arrow keys for panning 3 6 Vertices Side by side View 4 Figure 11 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 across vertices of the network Note that pan and zoom is enabled in both side by side representations 3 7 Slide Show View 7 8 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 O Z m Oo Z m O Z m ERG Gores E9 mprbior s mprgio BG ESGRGH SAS RG eRIRGH ese ae eERIRGH sss Lucas E Lucos Louise Louise Camille Re Lea Nathan ha Enzo Enzo Sach rial Hugo Gabriel fog iel Emma Emma Chloe Chloe Lucce Lucas Louise Louise Canille Camille Lea Lea Nathan Nathan Enzo Enzo Sad Sarah Hugo Hugo Gabriel Gabriel Emmo Emma Chloe Chloe Figure 10 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 LO O O WwW jan Ow 5 Be 38 i Be a 58 82 SS So Be SBS SSS SSSSse 589855 BSSDBS SBSSSs 85508 ANNANN NANNAN ANANA NN NIANIANA NNNNA NAN ANAAAA Lucas Luccs Louise ira Nathan Gabriel Seria Camile Camille Leo
15. the same node pair leading to visual continuity c None No shape encoding means that all cells have equal size This is useful to i get a better impression of edge density number of cells in the cube i e edges in the dynamic network and ii when showing slices side by side and cells get very small 2 2 Cell Color Encoding For coloring cells three modes exist Figure 3 a a Weight Encoding colors cells according to their weight ranging from light turquise low weight to dark blue high weight Figure 5 a Weight encoding makes heavy edges dark cells stick out Weight encoding is the default setting in Cubix b Time Encoding colors cells according to which time slice they belong to Figure 5 b The color scale ranges from blue early times via purple and indigo middle time steps to orange recent times a Value encoding light to dark b Time encoding blue to orange Figure 5 Cell encoding in Cubix c None 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 6 More on the Front view and other views in Section 3 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 On how to quickly switch between views using the Cubelet Widget see Section 4 Fi
16. y are employed Throughout this manual we use the following terminology Cell Similar to cells in adjacency matrices a cell in the Matrix Cube corresponds to a connection between two vertices at one time Time Slice A time slice corresponds to the adjacency matrix for one time step Figure 1 a A time slice shows the network s topology at one time step Vertex Slice A vertex slice results from cutting the cube orthogonally to time slices It resembles a table where a vertex s neighbors are shown in rows and time steps are columns Figure 1 c A vertex slice shows the evolution of a vertex s neighborhood over time dynamic ego network A cell in a vertex slice indicates a connection between the vertex of the slice and the vertex in a row at the time indicated by the column Vector A vector corresponds to a single line of cells inside the cube Figure 2 Time vectors blue vector in Figure 2 show the evolution of connectivity between a node pair while neigborhood vectors red vectors in Figure 2 show the neighborhood of one vertex at one time we OB Er GU Sc n Vertices a L q Neighborhood NS O E Vectors A b 40 Edge Vector d e Figure 2 Edge blue and neighborhood vectors red in the matrix cube Esges I Celis Time Steps Time slices GRAPH VISUAL MAPPING Roses 1h Cell Color Encoding Ede ge 208 O aa a un abe i sity 0 034903847 Pa e Time blue to orange
Download Pdf Manuals
Related Search