## A Guide to the Built-In Examples

### Smily Face

This example generates a smily face out of points. It demonstrates the creation of points sets and the use of affine transformations to define a scene. Using concepts demonstrated here, a great variety of data sets can be generated.

### L1 Depth Flaws

The L1 Depth Measure is generally biased. Dimensions are not evenly considered when computing depth, leading to overly round depth contours when the underlying distribution is less round.

### Using PCA

Principal Component Analysis allows us to determine the primary direction of a data cloud. This allows us to align primary dimensions with the X and Y axis before scaling.

### L1/PCA-L1 Comparison

This examples shows how PCA-Scaling L1 Depth improves upon L1 depth in many cases.

### Multimodal Distrobutions

Many conventional depth measures fail to capture multimodality in their depth value assignments. This is an example of a bimodal set and the deepest half of points are highlighted using Convex Hull Peeling Depth. Note how points between the two clouds are highlighted. These points are in fact, the deepest points in the data set according to this depth measure. This is one of the problems that motivated our study of Proximity Depth.

### Proximiy Trees

This example illustrates how Proximity Depth is computed. First the data set is Delaunay Triangualted, and that graph is shown in light grey. Second depth values for each point are computed according to the minimum number of edges that are required to traverse in order to reach a point on the convex hull of the set. This is what produces these red trees.

### Proximity Depth Comparison

This example revisits the previous multimodal example, but shows how Proximity Depth does, in fact, recognize the bimodality of the set. The deepest points are in the centers of the two clouds.