How Depth Explorer Works

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Depth Explorer enables automatic generation of data sets and transformation or composition of existing data sets. For each data set, Depth Explorer can quickly visualize the behavior of the depth measure on the data. Data sets are defined using a hierarchical representation of the scene (the render-tree) in an XML file. Clicking a toolbar button switches to "live" view and renders the scene to the screen. The user can then switch back into XML editor mode to adjust the scene and then re-render. The changes are almost instantly re-rendered into the window, allowing for interactive experimentation. Generated PDF files can be saved to the filesystem.

Data generation, transformations and visualizations are specified hierarchically using XML tags in the render tree. The tree is rendered starting from the leaf nodes and moving up. Each node is a C++ module that, given the output of its children nodes, modifies or appends the data, then passes it to its parent. Ultimately, the root node, called the canvas node describes the dimensions and scale of the PDF output file and renders its childrens' data onto the PDF document. The leaf nodes are data sources, either CSV files with a data set, or a random cloud generator with a set of points. Depth Explorer can currently create Gaussian clouds with any number of points with standard deviation 1, as well as uniformly distributed clouds on the range (-1,-1) to (1,1).

Non-leaf nodes modify data or add visualizations. Depth Explorer supports affine transformation nodes that can scale, rotate or translate nodes below them. With affine transformations and any number of randomly generated clouds, a broad spectrum of data sets can be generated to test statistical methods.

Visualizations include the display of the alpha contour by highlighting the alpha-% deepest points. If the set is dense enough this serves as a good visual approximation to the alpha / 100 central region. Depth Explorer displays the convex hulls enclosing the 20%, 40%, 60%, 80% and 100% deepest points, to visualize a subset of the depth contours, under the assumption that the underlying distribution is elliptic and the convex hull containing the alpha-% deepest points is a simplified sample estimate of the boundary of the contour. Note that the resulting contour may contain shallower data points, that are not the alpha-% deepest points.

As Depth Explorer uses a modular, tree-based renderer, it is trivial to combine visualizations, even at different points in the hierarchy. By viewing two visualizations on the same data, it is possible to compare depth measures or convey two concepts in one image.

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© 2006 John Hugg, Tufts University