Partitions—Defining new dimensions
Antaeus lets you define a new dimension from any scatter plot. A dimension is defined from the subdivision of records, represented as data points in the scatter plot, into two or more mutually exclusive sets of records. By working from a scatter plot, 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 this functionality, 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.
In Antaeus, the Partition Measures SV (SynchroView) is used to partition a scatter plot by using a "divider diagram" to divide the scatter plot into individual parts. The divider diagram is positioned over the plot, which causes groups of data points to fall into one of the regions demarcated by the diagram. There are four basic divider diagrams, each of which can be modified to divide the plot in specific ways. Once the scatter plot is partitioned in the desired manner, a new dimension can be created that uses the parts defined by the diagram as its values.
The best way to clarify this concept is to show examples. Two are shown below which will demonstrate the use of two of the four divider diagrams. The starting point for defining a partition is an unseparated scatter plot. Here is one from the College Data demo cube, taken from the Single Scatter Plot SV. This cube is installed with Antaeus:
Below, diagram 4 is positioned over the same scatter plot in the Partition Measures SV so that the plot is divided into four distinct quadrants:
The dimension, named HighAndLow, created from this partition contains the values "High Apps" (green), "High Tuition" (red), "Both High" (black), and "Both Low" (blue). The Colleges Data cube contains 1,302 records, but 39 of these records are not represented by this scatter plot. When records are not represented by a partitioned scatter plot due to missing or invalid values in one or both of the plotted measures, those records are automatically assigned to an additional value which is given the default name "Unassigned", which can be changed. In the case of this plot, 39 records are left unassigned.
Once a dimension has been created from a partitioned scatter plot, it can be separated like any other dimension. This is how the HighAndLow dimension looks when separated in other plots:
In these four plots from the Scatter Plot Array SV, "Others" (gray) refers to those records that were left unassigned when the dimension was created.
In order to more fully understand and appreciate this functionality, we'll look at the same process using a different divider diagram. Again, we'll start with another unseparated scatter plot:
This time, diagram 1 is used to divide the plot into three regions which arrange the records according to low, median, and high SAT scores:
This scatter plot contains 777 data points, so this means there are 525 records not represented in the plot. As with the previous example, these are automatically assigned to a part which given the default name of "Unassigned". When the dimension, MathVerbalScores, is created from this partition, the three parts shown above become the three values "Low" (black), "Median" (red), and "High" (blue), with the 525 unassigned records assigned to the value "Others".
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 MathVerbalScores 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 such dimensions can be used to ask new questions about your data.