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Clayton Miller added sax_group_variance.tex
almost 10 years ago
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We investigate these scenarios further by taking the most frequent pattern found for each set of parameter inputs and using a box plot to visualize the statistical distribution of the days contained in each pattern according to different windows within the daily profile. Figure \ref{fig:Wmod_boxplot} shows this analysis for the $W$ window count input. A strong difference exists between the variability and, thus, the detail captured by the selection of this input. A relatively high variance is present for $W$=2 during occupied hours between 06:00 and 12:00. Values of $W$ of 8 and 4 created profiles of more similar distribution with slightly higher variance for the latter. These results reinforce the observation that smaller window sizes create more tightly grouped patterns, albeit with many more variations.
Figure \ref{fig:Amod_boxplot} illustrates the same process with the most frequent patterns from the SAX alphabet size, $A$, experiments. The alphabet size decision modulates the magnitude resolution available to the algorithm. Thus it is intuitive that the pattern has less variance as the value of $A$ increases. This observation is also apparent in this analysis where an alphabet size of 4 produces tighter distributions than a value of 2, in this case primarily during occupied hours as well.
