4.3.1 What are 2D Parallel Coordinates?
  4.3.2 What are 3D Parallel Coordinates?
4.3.3 What is the Cell Selector Zoom?
4.3.4 What is Line Trace Highlighting?
4.3.5 What is Line Trace Animation?
  4.3.6 Main User Interface
  4.3.7 View Properties
4.3.7.1 Line Properties
4.3.7.2 Axis/View Properties
4.3.7.3 Color Mapping Options
4.3.7.4 Cell Selector Visualization
4.3.8 Cell Selection in Parallel Coordinates
4.3.9 User Controls
4.3.6.1 Pointer Modes
4.3.6.2 Mouse Functions
4.3.10 Line Trace Animation
4.3.10.1 Line Trace Animation Controls
4.3.10.2 Line Trace Animation Settings

4.3.1 What are 2D Parallel Coordinates?

Parallel coordinates are a common information visualization technique for high-dimensional data sets. In a parallel coordinate view, a data set consists of a set of samples, which in our case are the cells in a Drosophila embryo. Each sample (cell) has a set of associated quantities, which in our case are the relative expression levels for multiple genes. Expression data for each gene corresponds to a dimension in the data set, with data for each gene being represented by one of a series of  parallel vertical axes (see Figure below). Each sample (cell) defines a data line, i.e., a zigzag line connecting adjacent parallel axes. The intersection point of the data line with each vertical axis corresponds to the value of the sample for the corresponding dimension (i.e., the relative expression level for the corresponding gene in that cell). The figure shown below illustrates parallel coordinates by using them to visualize imaginary expression levels  for four genes  fushi tarazu (ftz), snail (sna)}, hunchback (hb), and kruppel (kr) in two cells. In the example, one cell expresses ftz at 95\%, sna at 5\%, hb at 24\% and kr at 26\%; and the other cell expresses ftz at 10\%,  sna at 90\%,  hb at 25\% and kr at 26\% of maximum relative value. 



4.3.2 What are 3D Parallel Coordinates?

3D parallel coordinates are a direct extension to 2D parallel coordinates. Here the coordinates axes are extruded into the third dimension. Data lines are then ordered back-to-front along the z-axis according to either AP- ,or DV cell positions, or the expression values of another gene. Each parallel coordinate axis then defines a 2D scatter-plot of geneversus dataz (the information displayed along the z axis). As in 2D parallel coordinates, corresponding points on neighboring axis are then connected via line segments. Each sample (cell) then again defines a data line  i.e., a zigzag line connecting adjacent parallel axes. Along any given data line the is dataconstant, such that data lines do not intersect each other in this third dimension. See View Properties/Line Properties for more information about how to define which data should shown along the z-Axis in 3D parallel coordinates.

In the illustration, below, a 3D parallel coordinate plot of hb, gt , and Kr is shown with data lines sorted according to the expression of hb. Data lines are colored with respect to hb (red), gt (green) and Kr (blue) using the same coloring scheme as in the physical view of the embryo. Initially a series of 2D scatter-plots of hb/hb, gt/hb, and Kr/hb is shown. The corresponding data points of neighboring scatter-plots are then connected to define a 3D parallel coordinate view.



4.3.3 What is the Cell Selector Zoom?

As shown in the Figure a) below, a Cell Selectors defines a subspace of the data across each parallel coordinate axis. The Cell Selector Zoom  is used to support exploration of the details in this subspace.  Each of the dimensions is scaled independently according to the minimum and maximum value selected by the displayed cell selector.  After scaling, the subspace within the cell selector fills the display area, and the details are revealed (see Figure b) below). This distortion technique is in general referred to as dimensional zooming. See the "Main User Interface" for more information about how to access and use the Cell Selector Zoom.

a)
b)     



4.3.4 What is Line Trace Highlighting?

Even though the line transparency and the available coloring options improve the view, it can still be hard to follow the course of a single line through the graph. Line trace highlighting overcomes this problem. The user can select data lines by selecting a point, in other words a gene expression level, on a parallel coordinate axis. All data lines passing the region defined by this point are drawn in front of all other lines using a gray scale. In addition, the selected range and the percentage of highlighted lines are displayed (see Figure a) below. Moving the cursor
along a parallel coordinate axis reveals information about the data line density and line distribution along that axes. When line trace highlighting is used then only the highlighted lines are drawn in the 3D parallel coordinate view to allow detailed analysis of the highlighted lines (see Figure b) below). To use line trace highlighting switch to the Highlight Mode (Hand Cursor) in the Pointer Mode section available in the main menu bar of parallel coordinates. For more information see the Main User Interface and Pointer Modes section.

a)
2D Parallel coordinate view with highlighted lines shown using a gray color scale/
 
b)
The same highlighted lines as in Figure a) but here shown in a 3D parallel coordinate view with lines sorted according to AP cell positions.



4.3.5 What is Line Trace Animation?

Animation of line traces can help the user to follow the course of data lines as well. Line trace animation means that a user-defined subset of data lines is drawn in an animation process beginning from the first parallel axis to the last (see figure shown below). To define a subset of data lines to be animated, the user needs to define both the number of lines to be traced and a data range on the first parallel axis. Data lines are then selected automatically, being roughly equidistant in the user-defined range. Alternatively it is also possible to trace only lines which are selected by the current cell selectors. For more information about how to use line trace animation see the "Line Trace Animation Controls" below.



4.3.6 Main User Interface

The main GUI of the parallel coordinates consists of four main parts: i) The main menu bar with basic controls; ii) a 3D parallel coordinate view; iii) a 2D parallel coordinate view; and iv) the bottom menu bar with additional controls.

 

Name

Function
1 Pointer Mode Selection Select the current pointer mode. See the "Parallel Coordinate Controls" for more details about the function of the pointer modes.
2 Select Genes Click this button to show a pop-up with the "Gene Selection Table" to select which genes should be displayed in parallel coordinates. Each row in the "Gene Selection Table" represents one gene and each column one time-step. Select the genes to be displayed by checking the accoring check-boxes and click "OK" to confirm the new selection.

3 Reset Axis Positions Reset the vertical (x) position of the axis so that all axes are equidistant to each other.
4 Cell Selector Zoom Mode Select this check box to display the cell selector zoom in the top parallel coordinate viewer (see 8) instead of the regular 3D parallel coordinate view. See "What is the Cell Selector Zoom" for general information about this mode.
 5 3D Parallel Coordinates /
Cell Selector Zoom
Depending on the status of the "Cell Selector Zoom Mode Check Box" (2) here either a
  1. 3D parallel coordinate view is shown ( 2 not checked) ; or the
  2. Cell Selector Zoom ( 2 checked ): is shown.
6 Split-bar The two viewers (6,8) are separated by a horizontal movable split-bar. The split-bar can be moved up/down using the left mouse button.  
7 2D Parallel Coordinates In this viewer the 2D parallel coordinates are shown.
8 Enable Trace Animation Enable the controls for trace line animation. If this box is checked then additional controls to perform line trace animations are shown right of the "Basic Properties" box in the parallel coordinates main menu. See the Line Trace Animation Controls for more details.
9 Create Cell Selector Open the Create Cell Selector Window. After a color and name have been defined and confirmed by clicking the "OK" button,  a new PATTERN cell selector is created.
10 View Properties Open the View Properties Window. See the View Properties for more details.


4.3.7 View Properties

The view properties window is used to define basic visual properties of parallel coordinates. The window consists of four tabs:



4.3.7.1 Line Properties


 

Name

Function
1 Line Width Define the width of all data lines
2 Line Sorting Define how data lines should be sorted in parallel coordinates. This option defines also which information is shown along the z-Axis in 3D Parallel Coordinates. Available sorting options are:
  1. AP sort: Sort data lines with respect to AP-cell positions (x-cell positions)
  2. DV sort: Sort data lines with respect to DV-cell positions (derived from the Unrolled View).
  3. Gene sort: Sort lines with respect to the expression of a selected gene (see 3 for more information about how to define the gene used for sorting of data lines)
3 Select Gene for Line Sorting Click this button to show a pop-up with the 'Gene Selection Table" to select which genes should be used for sorting of data lines in parallel coordinates.
4 Update opacity immediately Update the opacity of data lines in parallel coordinates immediately when editing either the opacity of colored or black data lines. This option is provided for convience to make it easier to quickly find appropriate opacity values.
5 Colored Line Opacity Define the opacity of active (colored) data lines. The opacity of black data lines can be defined separately in the View Properties. In all color mappings lines (cells) of low interest are shown in black. By lowering the opacity of black data lines it is possible to highlight the lines of interest while preserving the surrounding background information. Set the line opacity to 0 in order to hide all data lines (including black data lines).
6 Black Line Opacity Define the opacity of black data lines. Line of low interest are in general colored in black. To highlight the colored data lines of interest one can define the opacity of black data lines independently here (in general lower then the Active Line Opacity)



4.3.7.2 Axis/View Properties


 

Name

Function
1 Distance Between Axis Define the default distance between two neighboring parallel axis.
2 Axis Width (X) Define the width of the parallel axes.
3 Axis Length (Y) Define the default length of parallel axes.
4 Axis Depth (Z) Define the default depth of parallel axed (only relevant in 3D parallel coordinates).
5 Axis/Font Color Define the color of the parallel axes as well as of the text and labels shown in parallel coordinates/
 6 Background Color Define the background color of parallel coordinates by clicking on the color label.
7 Select Font Select the default font used for rendering of text and labels in parallel coordinates.  



4.3.7.3 Color Mapping Options

 

Name

Function
Embryo Color Mapping
1 Import Colors from
Embryo View
Use the same colors as defined in the physical view of the embryo for coloring of data lines (each representing one cell) in parallel coordinates.
Cell Selector Color Mapping These color mappings are specially designed for display of cell selectors in parallel coordinates. First colors are computed for the different displayed cell selectors and then mixed in order to derive the final color.
2 Distance to First Average Color all data lines (cells) selected by a cell selector with respect to the distance of that line (cell) to the average expression of the cell selector in the gene represented by the first parallel axis.
3 AP Color lines (cells) selected by a cell selector with respect to the AP position of cells (x-coordinate) in the embryo.
 4 DV Color lines (cells) selected by a cell selector with respect to the DV position of cells  (derived from the Unrolled View) in the embryo.



4.3.7.4 Cell Selector Visualizations


 

Name

Function
1 Show min/max lines Show two additional data lines for each displayed cell selector showing the minimum/maximum values selected by each cell selector.
2 Width of min/max Lines
Define the width of the min/max cell selector lines.
3 Show Cell Selector Values If Cell Selector Mode is the current Pointer Mode then show the value of the cell selector sliders in addition on the bottom and top of the parallel axis used by the cell selector.
4 Show average lines Show one additional data line for each displayed cell selector showing the average expression values of all cells selected by each cell selector. If this option is active then additional boxes are shown on each parallel axis showing the standard deviations from the average expression line for each displayed cell selector.
5 Width of Average Lines Define the width of the average cell selector lines.
 6 Show Cell Selectors as
colored bands
Use additional transparent color bands to visualize cell selectors in parallel coordinates.
Define Cell Selector
 Band Type
Define additional parameters used for drawing of cell selector bands.
7 Use Smooth Cell Selector Bands Draw cell selector bands as solid bands with varying transparency. The transparency of a cell selector band is determined according to the distance of a point to the average expression line of the cell selector.
8 Use Textured Cell Selector Bands Draw cell selector bands as textured line bands with varying transparency. The transparency of a cell selector band is determined according to the distance of a point to the average expression line of the cell selector.
9 Minimum Band Opacity Define the minimum opacity of a cell selector band.
10 Maximum Band Opacity Define the maximum opacity of a cell selector band.

 
a) Three cell selectors shown in parallel coordinates by coloring lines according to the basic color of the cell selector using the Embryo View Coloring scheme   b) Same view as in Figure a) but with min/max cell selector lines (line width 2), average cell selector lines (line width 4), and cell selector band (min opacity=0.2 , max opacity = 0.6) visualization options enabled.



4.3.8 Cell Selection in Parallel Coordinates

Parallel coordinates support editing of two types of cell selectors, Data- and Pattern cell selectors. Data cell selectors are usually used for cell selection in scatter-plots but can also be edited here. Pattern cell selectors now have been specially developed to support cell selection in parallel coordinates. A new pattern cell selector can be created by using the Create Cell Selector button in the bottom menu bar of the Main User Interface of parallel coordinates.

In order to edit a cell selector one needs to switch to the Cell Selector Mode (Cross Cursor) using the according button in the Pointer Modes section in the main menu of the parallel coordinates GUI. If the current cell selector can be edited in parallel coordinates then additional sliders are displayed along each parallel axis that can be used for cell selection. Select and move a cell selector slider using the left mouse button in order to change the value of a cell selector slider. Only those cells that express the genes used in the selection process in the according ranges are then selected by the cell selector.

In 3D parallel coordinates only selection along the z-Axis of the plot is currently supported in PointCloudXplore. If data lines are sorted according to AP- or DV cell positions then also selection of cells with respect to these spatial dimension is directly possible.



4.3.9 User Controls:

4.3.9.1 Pointer Modes

As in the Physical Views different modes are used in Parallel Coordinates to simply user controls. In each mode different types of user interactions can be performed. Select the according button to activate the corresponding pointer mode. The currently active mode button is highlighted in green.
Name Cursor

Description

Axis Mode Define axis properties such as position, order, and length of axis
Cell Selector Mode

Edit the current cell selector.

Highlight Mode

Select a subset of lines to be highlighted in the view by selecting a point on a parallel axis


4.3.9.2 Mouse Functions

Button(s) Axis Mode Cell Selector Mode Highlight Mode
2D 3D 2D 3D 2D 3D
MOUSE L No Action Rotate Edit Cell Selector Highlight Lines Rotate
SHIFT + MOUSE L Re-order axes No Action Rotate No Action Rotate
MOUSE R Translate Translate Translate
SHIFT + MOUSE R Change axis length Translate Translate

 

Button(s)

Mode

Description

MOUSE L double click

All

Aligns camera (function only available in 3D parallel coordinates).
MOUSE R double click All Centers the parallel coordinate view.
MOUSE WHEEL All

Zoom in and out.

MOUSE WHEEL    double click All Show entire scene
CTRL+S All

Save snapshot of the current parallel coordinate view.


4.3.10 Line Trace Animation

The controls for line trace animation are only displayed if the Enable Trace Animation check box is checked available in the bottom menu of the Main User Interface of the parallel coordinates. If line trace animation is enabled then the Trace Animation Controls are shown in the main menu of the parallel coordinates. For general information about line trace animation see What is Line Trace Animation? above.



4.3.10.1 Line Trace Animation Controls

The controls for line trace animation are designed similar to the controls of a music player. Three buttons are used to start. pause, resume, and stop an animation while a slider is used to define the current time step of the current animation. Which line traces should be animated and other line trace animation properties can be defined in the  Line Trace Animation Settings window.



 

Name

Function
1 Settings Open the Line Trace Animation Settings window to define, e.g., which lines should be animated.
2 Play Start the animation process.
3 Pause / Resume Pause or resume the animation process.
4 Stop Stop the current line trace animation.
5 Animation Time Step Define the time step of the animation by moving the time step slider.



4.3.10.2 Line Trace Animation Settings



 

Name

Function
1 Animation Time Define the duration time of the animation. This is only a very rough estimate. The actual duration time of the animation depends only on the maximum rendering speed that can be achieved by the system PointCloudXplore is running on.
2 Animation Steps Number of steps (or frames) used in the animation.
3 Trace current cell selector Trace all lines (cells) selected by the current cell selector.
4 Expression Range Trace all lines that start in the given range on the first parallel axis, i.e, trace all cells that express the gene represented by the first axis in the according range.
5 Use gray color Use a gray color scale for coloring of trace lines/points. 
 6 Use original line colors Use the same colors as defined the parallel coordinate view also for the animated traces. Here only the opacity of traced lines is chosen higher.
7 Draw lines while tracing Check this option to show the actual line traces. If this option is not enabled then only the end points of the line trace are drawn in the animation.  
8 OK Confirm the current settings for line trace animation.