Partitions—Defining new dimensions
As of release 2.3, Antaeus lets you define a new dimension from one or more scatter plots. A dimension is defined from the subdivision of records, represented as datapoints in a scatter plot, into two or more mutually exclusive sets of records. By working from scatter plots, you can be fully oriented as you define this subdivision. See Dimensions and Separation for a more detailed discussion about dimensions and how they can be used.
Think about dividing a pile of pebbles into two or more smaller piles. This is the fundamental operation addressed by Antaeus, with the cube's records in the role of pebbles. This means that each dot in a scatter plot can be thought of as a pebble. Each subdivided pile of pebbles is called a part and is given a name. The entire collection of parts is called a partition. The end result is a new dimension with an array of unique values, defined by the partition. We call this process partitioning.
There are two ways to define parts in Antaeus. The first is to pick out one or more rectangular regions in the scatter plot by using a selection box that can be moved and resized. The second way is to specify any subset of the cube. Antaeus lets you define subsets very precisely, so this method can be exact.
The best way to clarify this concept is to show examples. We'll begin with the first method. The starting point for defining a partition is an unseparated scatter plot. Here is one from the College Data demo cube, installed with Antaeus:
In this scatter plot below, the selection box is used to define four parts: "High Apps" (black), "High Tuition" (blue), "Both High" (green), and "Both Low" (red). The first three are defined using the selection box, the last is defined by assigning all remaining records:
The Colleges Data cube contains 1,302 records, so 39 records are not represented by this scatter plot, but since all 1,263 records represented in this plot are assigned to parts, the plot is completely partitioned.
Once a scatter plot is completely partitioned, it can be used to define a new dimension, in which the name of each part becomes a value of the dimension. The scatter plot itself may not represent all the records in the cube, due to missing or invalid data as is the case with the above plot. If records exist outside the partition defined by the current plot when a new dimension is created, these will be automatically assigned to a part named "Unassigned". When a new dimension is created from the above partition, named HighAndLow, and subsequently separated, this is the effect on other plots in the cube:
In these four plots from the Scatter Plot Array SV (SynchroView), "Others" (gray) refers to those records that were left unassigned when the dimension was created.
In order to most fully understand and appreciate the concepts discussed here, we'll also look at how a partition is defined using subsets, the second method. Any number of subsets can be defined in Antaeus, and any of these can be used to define a part. We'll start with another unseparated scatter plot:
In this scatter plot, as shown below, subsets is used to define four parts. The subsets themselves are defined by a function-measure (See Functions) named MathVerbalDiff, which was created by subtracting the values of Verbal SAT from Math SAT (plotted here) to find the differences. The four parts are:
| Name | Color | Defined by |
| "X <= 25" | black | subset defined as MathVerbalDiff LESS THAN 25 |
| "X >= 75" | blue | subset defined as MathVerbalDiff GREATER THAN 75 |
| "25 thru 49" | green | subset defined as MathVerbalDiff BETWEEN 25 AND 49 |
| "49 thru 75" | red | all remaining records |
Because the subsets used to define these parts are themselves defined by a function-measure which was created from the measures plotted here, exactly 777 records are partitioned. There remain 525 records not represented in this scatter plot, which are automatically assigned to a part named "Unassigned" when the new dimension, MathVerbalDiff, is created. Consider once again the effects that separating this dimension has on another set of plots:
New dimensions not only provide you with new ways to separate records in scatter plots, as demonstrated above, they also provide you with new ways to define subsets, which can be used as brushes. To illustrate this, here is a scatter plot separated by the MathVerbalDiff dimension defined above, but brushed with a subset defined by the "Both High" value of the HighAndLow dimension (large yellow dots):
Of course new dimensions must be defined with some knowledge about the data in mind. This requires the intuition, intellect, and ingenuity of the human brain, which nothing can replace. Thus it is with this combination of reason and understanding that new dimensions can be used to learn new things about the same data.