example two categorical dimensions

Nanocube internals with one spatial dimension and two categorical dimensions

Michael Thomas sent a message for the nanocubes discussion list asking for an example of a nanocube featuring two-categorical dimensions. Here is an example which appends one categorical dimension (language) to the example of Figure 2 in the nanocubes paper.

The schema and encoding of this example:

Dimension 1: location, 2-level-quad-tree
             (0=Bottom Left, 1=Bottom Right, 2=Top Left, 3=Top Right)

Dimension 2: device, categorical
             (0=Android, 1=iPhone)

Dimension 3: language, categorical
             (0=English, 1=Spanish)

Points in insertion Order:

1) { {2,1}, {0}, {0} }         { {TL,BR}, {Android}, {English} }
2) { {2,1}, {1}, {1} }         { {TL,BR}, {iPhone},  {Spanish} }
3) { {1,2}, {1}, {0} }    or   { {BR,TL}, {iPhone},  {English} }
4) { {3,0}, {0}, {1} }         { {TR,BL}, {Android}, {Spanish} }
5) { {1,3}, {1}, {0} }         { {BR,TR}, {iPhone},  {English} }

Before we present the images here are some observations on how to interpret them:

• The label of the leaves are simply {<point-id-1>:1,<point-id-2>:2,...,<point-id-n>:n}
• The label of the internal nodes are simply -
• Arrows point to the the root of a tree in the next dimension (every node has one outgoing arrow, except for the leaves)
• Non-arrows point to from a parent to a child bin in the same dimension and are labeled with the restriction name (e.g. in the figure below one 1 edge between two pink nodes is an iPhone constraint.
• Dashed lines represent shared connections (either non-arrows-parent-child, or arrows-next-dimension-tree).
• the first mustard-colored layer is the location one (a two-level-quadtree); the pink layer is the device categorical one, the bottom mustard-colored layer is the language categorical layer.
• For a vectorial high-quality version of the figures below download nanocubes-two-categorical-dimensions.pdf

After Points 1,2,3,4,5

5) { {1,3}, {1}, {0} }         { {BR,TR}, {iPhone},  {English} }

After Points 1,2,3,4

4) { {3,0}, {0}, {1} }         { {TR,BL}, {Android}, {Spanish} }

After Points 1,2,3

3) { {1,2}, {1}, {0} }    or   { {BR,TL}, {iPhone},  {English} }

After Point 1,2

2) { {2,1}, {1}, {1} }         { {TL,BR}, {iPhone},  {Spanish} }

After Point 1

1) { {2,1}, {0}, {0} }         { {TL,BR}, {Android}, {English} }