Brushing
Interactive Analysis through 3D Graphs
The Graph Data Editor is a special version of a spreadsheet that enables you to review directly the data that are plotted in the graph. This tool is useful for a variety of analytic applications, such as brushing or other forms of identifying specific data points. It also offers (sometimes) the only way to access data from those graphs that do not plot raw values, but values that have been derived, transformed, or result from specific analytic calculations, as well as values of the fitted functions. It can also be used to add additional plots of a compatible type to an existing graph.
This editor is available from the graph View menu, the graph Format menu, and the general graph shortcut menu (accessible by right-clicking on the background of any graph).
The following terms are used to denote specific aspects of brushing operations.
Data points that have been selected via brushing can be identified and managed in the Graph Data Editor (accessible by selecting Graph Data Editor from the Format menu) by accessing the Data Selected by Brushing submenu via the Layouts menu or the Graph Data Editor shortcut menu.
All points in the current plot of the Graph Data Editor that have been selected by brushing in the graph can be selectively copied to the Clipboard, copied to a new plot within the Graph Data Editor, moved to a new plot (i.e., deleted from their location in the original plot and pasted elsewhere), deleted, or deselected.
In addition, the attributes of points can be changed by clicking on them in the Graph Data Editor (or selecting them in a block) and using the options from the Layouts menu or the Graph Data Editor toolbar. Points can be marked, labeled, excluded, etc.
There are countless applications of brushing to explore relationships between variables and/or the contribution of specific data points or subsets to those relationships.
A "typical" illustration of the use of brushing in exploratory data analysis is the examination of the contribution of data points representing different ranges or different levels of one variable to correlations between other variables, which can be inspected visually using a scatterplot matrix. For example, by including a categorical, three-level variable such as income level (Income) in a scatterplot matrix (see above), then by using the Box, Lasso, or Slice X brush, points can be selected from one income level, and the location of these points in scatterplots of all other variables (e.g., Assets, Debt) becomes immediately apparent.
All brushed points (whether marked, labeled, excluded, or hid) are easily identified in the Graph Data Editor. When data have been marked, there is a red exclamation point icon displayed next to the case name in the Graph Data Editor. Labeled cases have a yellow label icon displayed next to the name, and cases that are temporarily turned off have a red x icon displayed next to the case name. Cases in the Graph Data Editor that fall under more than one of the categories described above will have multiple icons displayed.
The Graph Data Editor toolbar provides various buttons for applying brushing actions to selected data points. That is, you can mark, label, etc., selected data points (or unmark, unlabel, etc.) in the Graph Data Editor using the toolbar buttons. You can also toggle the display of brushed data points using additional toolbar buttons.
Typical applications of animated brushing are in exploratory data analysis using matrix plots, where instead of brushing consecutive ranges of a variable (to explore the influence of various sections of its distribution), you can invoke an automatic movement of the brush (Box, Lasso, Slice X, Slice Y, Slice Z, or Cube) and watch the "results."
Specifically, a brushing region is defined in one subgraph in the matrix and is automatically moved across the subgraph (horizontally, vertically, or both). As the brushing region passes over groups of points in the subplot, corresponding points in all other plots are highlighted.
For example, in the illustration below, the rectangular region can be advanced automatically across groups of points in the Income, and the corresponding points will be highlighted in plots of the other three variables. The speed and direction of the movement can be interactively controlled in the Animation dialog.
The Animate button is available on the Interactive tab of the Brushing dialog whenever the Draggable Brush check box is marked and the Box, Lasso, Cube, Slice X, Slice Y, or Slice Z brush is selected.
Draggable brush. A user-controlled animation. Note that when the Draggable Brush check box is selected on the Interactive tab of the Brushing dialog, you can select cases via any of the six shape defining brushing tools (i.e., Box, Lasso, Cube, Slice X, Slice Y, or Slice Z), and then drag that shape to any position on the graph, thus animating the selection manually. Note that the Draggable Brush check box must be selected before you make your selection in order to use the animated brushing facilities described above.
Identifying all points of a plot. In the (default) pointing mode (when the point tool is enabled), click on any point that belongs to the specific plot and all points of that plot will become highlighted. They will stay highlighted for as long as you keep pressing the mouse button. If there are many plots in the graph, and their respective point markers are small and difficult to identify, then you can click on the legend. This will also highlight all points that belong to the respective plot.
Identifying individual points of a plot. If you need to identify values of specific points in the graph, use the Brushing Tool.
Graphs menu graphs offer facilities to define subsets of cases to be identified in graphs. User-defined "multiple-subset" definitions of such subsets can be entered as logical case selection conditions of virtually unlimited complexity using facilities identical to those illustrated in producing categorized graphs.
These subset identification facilities are supported in many types of Graphs menu graphs, including 2D scatterplots, 3D scatterplots, 3D trace plots, matrix plots, icon plots, and other graphs.
Here are examples of matrix and icon plots:
Subsets can also be identified on the Extended tab of the Brushing dialog. This facility offers a wide variety of methods to identify subsets of data (which can be considered a "command driven" brushing). On this tab, you can select ranges of values for the variables in the plot and examine their relations to other variables (for example, in a matrix plot; note that the layout of this dialog is somewhat different depending on the current type of graph).
Yes, by marking them in the Graph Data Editor or by labeling them selectively.
2D graphs. When the brushing facility has been activated for a 2D graph such as a matrix scatterplot, available brush types in the Selection Brush group box in the Brushing dialog include Slice X and Slice Y. When one of these is selected, the brushing tool can be used to define a vertical (Slice X) or horizontal (Slice Y) rectangle or "slice" of variable width on any of the individual graphs.
All of the point markers within the rectangular slice will become highlighted, and the corresponding point markers on the remaining matrix scatterplots will also be highlighted. Corresponding data will also be highlighted in the Graph Data Editor.
If the Auto Animate check box on the Interactive tab of the Brushing dialog is selected, and the Animate button on the dialog is clicked, the slice will move back and forth on the x-axis (Slice X) or up and down on the y-axis (Slice Y) successively highlighting points that fall within the slice on all the graphs. The movement of the slices is controlled by the options in the Animation dialog that is displayed when the animation begins.
If the Slice X selection brush was chosen, the X Step slider will control the increments at which the slice moves across the x-axis. The Y Step slider will control increments at which the slice moves on the y-axis if the Slice Y selection brush was chosen. The automatic pause between successive incremental movements of the slice is controlled by the setting of the Waiting time slider. The Pause button located near the top of the Animation dialog can be toggled to start and stop the animation, and a Reset button is available to start the animation over at the location on the graph where the slice was originally defined.
3D graphs. The slicing tools discussed above can also be applied in 3D graphs such as 3D scatterplots. In this context, the individual slice tools define a rectangular prism on the graph. All of the points within the prism will be highlighted, as well as corresponding points in the Graph Data Editor. In 3D graphs, slices can be defined for X, Y, or Z axes, and the prisms can be automated in a manner analogous to that described above for slices on 2D graphs. Note that in 3D graphs, a Cube selection brush is also available to define a 3D prism of any size within the graph. This tool performs in a manner analogous to the Box tool in 2D graph brushing, and it can be animated to move incrementally within the body of the graph in the x, y, and z directions.
Click the 3D Rotation control button on the graph Tools toolbar to access the interactive rotation control facility (i.e., the Point of View Settings and Exploratory Spin dialog), or select Graph: Point of View in the tree view of the Graph Options dialog to access options to enter specific viewpoint parameters controlling the position of the imaginary viewpoint against the 3D object.
Click the 3D Rotation control toolbar button to display the Point of View Settings and Exploratory Spin dialog, which contains options used for rotation, spinning, and interactive adjustment of the point of view for three-dimensional displays for analytic or exploratory purposes. Click the Analytic exploratory spin options button to set the display into continuous rotation in clockwise or counter-clockwise directions.
Note that specific adjustments of the viewpoint and perspective (e.g., for an exact reproduction of a display) can also be made in the Graph: Point of View options pane of the Graph Options dialog.
You can change the aspect ratio for both 2D and 3D graphs in the Documents: Graphs - Settings options pane of the Options dialog (accessible by selecting Options from the Tools menu). For 3D graphs, use the options in the 3D graphs axis proportions group box.
Note that the adjustment does not modify the proportions of the graph window; only the axis proportions of the graph are modified.
For example, the default proportions of the axes in the graph above are 1:1:1 (i.e., the proportions of the X, Y, and Z sides are of equal length and form a regular cube). By changing the respective values, you can "flatten" (e.g., increase the proportions of the x- and y-axes compared to the z-axis: 1:1:.5)
or "stretch" (e.g., increase the relative length of just the z-axis: 1:1:2)
the 3D box in any direction. To change the axis proportions for a specific graph (i.e., locally), select Graph: Layout in the tree view of the Graph Options dialog.
The primary controls for defining contour intervals for 3D surface or contour plots are accessed on the Surface Specifications dialog obtained by clicking the Surface specs button in the Plot: Fitting options pane of the Graph Options dialog. (Display the Graph Options dialog by double-clicking on the outer background area of the graph.)
The number of color levels placed on the graph is determined by default by the number of minor tickmarks spanned by the surface on the Z axis of the plot. This default option is in the Get shading levels from box at the top of the Surface Specifications dialog. Note that other options for determining the number of contour levels to place on the graph include Major tickmarks, Custom tickmarks, and combinations of Custom with Major or Minor tickmark options.
To control the numeric values that divide contours, select Axis: Custom Units in the tree view of the Graph Options dialog to specify as custom tickmarks the values corresponding to boundaries between contours. Then select Custom tickmarks from the Get shading levels from box at the top of the Surface Specifications dialog (available by clicking the Surface specs button in the Plot: Fitting options pane).
The primary controls for defining colors for 3D surface or contour plots are accessed on the Surface Specifications dialog obtained by clicking the Surface specs button in the Plot: Fitting options pane of the Graph Options dialog. (Display the Graph Options dialog by double-clicking on the outer background area of the graph.)
On 3D XYZ surface plots (or contour plots, which are projections of 3D surfaces onto a 2-dimensional plane), STATISTICA uses a default color palette consisting of 10 colors ranging from dark green through light greens, yellows, and oranges to shades of red. This color palette can be viewed in the Defining colors area of the Surface Specifications dialog. The number of colors in the palette can be set in the range of 2 to 11 in the Number of defining colors box, and the individual color blocks can be changed by clicking the arrow at the right side of each color window. Note that you can make global changes to the color palette in the Documents: Graphs - Display options pane of the Options dialog.
The number of color levels required (as determined in the Surface Specifications dialog) is compared by STATISTICA against the number of color levels available in the defined palette. The colors to be applied are then picked across the range of the palette by interpolation between the specified defining colors.
To select a cube in a 3D graph, click the zoom in button and drag the cursor across the portion of the graph you want to select. A cube will be drawn, and its sides will be reflected on the three axis. You can fine-tune the sides of the cube by dragging any of resizing handles on the side reflections (the cursor will change to a double headed arrow when the handle is selected). You can also move the cube to another location on the graph, by dragging any of the side reflections (the cursor will change to a four headed arrow when the procedure is possible).
To zoom in on the selected cube, double-click on the cube. Note that if you have selected Clone graph on zoom from the View menu, the selected cube will be redrawn in a separate graph window.