Cubix Visualizing Dynamic Networks with Matrix Cubes User Manual
Contents
1. Figure 7 Views in Cubix The eye indicates the position of the user handle of the opacity slider Figure 3 h 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 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 t Bel ae ee Lucas Lucas LUCCS Louise Louise Loui Nathan Nathan ie Gabriel Gabriel Camille Camille le Lea Lea Hugo Hugo Hugo Sarar Soroh Sarch mays Enzo Enzo lo Chloe Chloe 1 Emma Emma O z O O ff Q O agaa CFORS S888 RR a Front View of Matrix Cube in time encoding b Side view of Matrix Cube Figure 8 Projections on the cube 3 3 Side View 2 When rotating the cube to its left side face a projection as shown in Figure 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 fe2. ened by holding shift and fastened with the alt key The transition speed slider Figure 3 j allows for Luccs Louise Camille Lea Nathon Enzo Sach Hugo Gabriel Emma Chice Lucce Louise Canille Lea Nathan Enzo Lucas Louise Camille Leg Nathan Enzo Sarah Hugo Gobriel Emma Chice Lucas Louise Camile Lea Nathan Enzo Sarah Hugo Gabriel Emma 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 Lucas Louise Nathan Gabriel Camille Lea Hugo Soroh Enzo Chloe Emma Luccs Louise Nathan Gobriel Camille Leg Hugo Sarch Enzo Chloe Emma att 2007 S010 2007 rob falc A Louise Lucas Louise Nathan Gobriel Camille Leg Hugo Srch Enzo Chice Emma a 3268 3 S288 53 S298 5 3288 53 32 S OS Oo S205 5 S Oo Oo S o8 5 oS IO ON ON IN ON ON GN NYEN ON ON ON ON ON ON ON GN GN GN ON NN GN ON ON GS Luccs Louise Nathan Gabriel Camille Lea Hugo Soroh Enzo Chloe Emma Gobrial Camille Enzo Emmo Figure 11 Small multiples of vertex slices using value cell encoding Cells are colored using value encoding to highlight differences in weight across slices a b Figure 12 Selecting a single slice in the 3D view and rotating the cube shows the selected slice only Vertes Slices Time Slices Time Slices Verte
3. 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 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 range slider Figure 3 f to change the visible set of time slices e Use the eft and right arrow keys to switch between the next and previous vertex slice 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 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 Number shortcuts and interaction with the Cubelet are as follows 1 3D Vie
4. largest e Logarithmic scale Maps cell weight in a logarithmic way to cell size e Diverging scale In case where edge weights can be negative checking this boxes maps the absolute weight value to size For example an edge with weight 2 is as large as a cell with weight 2 This function should be used together with Edge Weight Diverging Cell Coloring 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 Figure 7 summarizes the different views currently implemented in Cubix 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 38D Projection Small Multiples Slice Rotation Time pK ae Slices N tb d P Vertex N gt X A i D a Slices 7 CN U eX ll SL To c 8
5. 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 Diverging weight Encoding colors cells according to their weight ranging from blue lowest values to red highest values This mapping Is particulary useful for data sets where edge weights can be negative c 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 d 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 83 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 2 3 Cell Size Options Edge weight can be mapped to cells size using any of the following three options e Adapt Weight The cell with the lowest edge weight that is visible Edge weight slider is mapped to the smallest size while the cell with the highest weight that is visible becomes
6. 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 e a Figure 3 f 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 Figure 14 Weight adaption scales cube only within the currently visible weight range a Value encoding b Time encoding Figure 15 Two edge vectors in value and time encoding 5 2 Lasso Selection Holding the ALI 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 5 3 Cell Selection Cells can be selected to better see their context When a cell in the 3D view is clicked once only the
7. ature 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 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 view use the arrow keys for panning 3 6 Vertices Side by side View 4 Figure
8. e 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 e 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 Neighborhood Vectors 4 b 4 0 Edge Vector d e Figure 2 Edge blue and neighborhood vectors red in the matrix cube Edges Cells GRAPH Nodes 11 Edges 206 Times 6 Cube Density 0 034903847 Time Steps Time slices Cell Color Encoding Edge Weight light to blue Edge Weight Diverging re Time blue to orange VISUAL PARAMETERS ips 0 0 Tk None all same gray Cell Shape Edge Weight 1 small to la D Edge Weight 2 small to la None equal size N etwo rk Adapt Weight i gen Logarithmic scale C Statisitics Diverging scale Topological Order Name Ordering d Inverse Filter Time Range 6 0 6 f Edge weight Cubelet E Bia 9 1 14 1 Cell Opacity 0 1 h 3D 1 J 1 VY Show Self Edges V Show Non Self Edges i Animation Speed i vertex Slice
9. ides the NAME ORDERING button which orders vertices in an alohanumerical 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 selection 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 Alt scroll wheel Change label size
10. ime Figure shows how a matrix cube is created from the adjacency matrices Time Vertices a Adjacency Matrices b Matrix Cube c Vertex Slices Time 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 Throughout this manual we use the following terminology e Cell Similar to cells in adjacency matrices a cell in the Matrix Cube corresponds to a connection between two vertices at one time 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 topology at one time step e Vertex Slice A vertex slice results from cutting the cube orthogonally to time slices It resembles a table wher
11. op Cubix Visualizing Dynamic Networks with Matrix Cubes User Manual benjamin bach inria fr INRIA France http www aviz fr Research Cubix April 30 2014 This manual is a short introduction on How to Explore Dynamic Networks with Cubix Contact benjamin bach inria fr in case of any problems or ambiguities Please note that all material in this manual is published material and should not circulate If you got a copy be happy and keep it Thank you very much Contents 1 The Matrix Cube 2 Interface and Visual Encoding 2 1 Cell Shape Encoding 2 2 Cell Color Encoding 2 3 Cell Size Options 3 1 3D View 9 3 2 Front View 1 3 3 Side View 2 3 4 Rotating Slices 5 6 3 5 Time Side by Side View 3 3 7 Slide Show View 7 8 3 6 Vertices Side by side View 4 4 View Changes and the Cubelet Widget 5 1 Attribute Filtering 5 2 Lasso Selection 5 3 Cell Selection 6 Slice Coloring 7 Row and Column Reordering 8 Controls Summary 8 1 Keyboard Controls s sas s sawise 4e54 44 8445646 6282 8 Ss 8 2 Mouse Controls 2 a 10 10 11 11 12 12 1 The Matrix 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 t
12. s Time Slices j GI GA Vertices Vertex Slices diii j i 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 Cells size settings e Row and column ordering options f Time range slider to determine the set of visible time slices g Edge weight slider to determine visiblity of cells depending on their edge weight A histogram indicates distribution of edge weight h Slider to set cell opacity i Settings to show or hide self and or non self edges j Slider to set animation speed 2 Interface and Visual Encoding The interface of Cubix is show in Figure 8 The cube in the center shows a collaboration network which is used for demonstration purposes in this manua Persons the network s vertices are shown along the the vertical and horizontal red axes Time is shown along the blue axes Connections 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
13. side of the interface 2 1 Cell Shape Encoding Cubix provides three ways to encode information in the size of cells Figure B 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 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 8 a a Weight Encoding colors cells according to their weight
14. 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 11 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 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 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 Io facilitate the look up for vertex names Cubix prov
15. w 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 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 apart Results in the image show in in Figure 13 b Lucos Louise Nathan Gabriel Camille Leg Huge Scorch Enzo Chloe manana BRO E4994 a IRRIA Lucas Louise Nathan Gebriel b Camille Led Hugo Sarch Enzo Chloe Erma c d GEOGNNMNMNNNmM EFY Cot BESBSSSSS BEXAR S Th R a A h u G O D amp T oc Camille a Schematic view of slice rotation 2009 4005 TODE AOE orn Ssn LOUEN PLS au 2005 2006 2007 2008 spor asino7 LOLON PLS H LLALA p b View the users sees ozuJ SOH OLULUG Lucas Louise Nathan Gabriel Camille Leg Huge Sarah Enzo Chloe Erma Gabriel Camille Leg Hugo sarah Enzo Chloe Prana 2010 Figure 9 Focus and context view of a time slice a Time x vertices projection b after rotating time slice for 2009 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
16. x Slices a b c Figure 13 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 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 5 1 Attribute Filtering The corresponding sliders for setting the visibility of cells accroding to their weight are found on the right side of the screen Figuref3 e Cell Opacity Figure 3 h The right handle of the opacity range slider labeled V for visible cells sets the general cell opacity value The left handle 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 g 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
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