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Clayton Miller deleted multi_variate_comparison.tex
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The \emph{DayFilter} process is univariate in this analysis, however the clusters can be visualized as compared to distributions of potential influencing external variables using box plots. Figure \ref{fig:boxplots} illustrates this visualization. Figure \ref{fig:boxplots}a shows the distributions of daily cooling energy according to cluster, producing intuitive results of consecutively increasing, tight clusters due to utilization of this variable as the clustering target. The discord candidates span most of the cooling consumption range and include quite a few high consumption outliers as compared to the characteristic clusters. Figure \ref{fig:boxplots}b illustrates the chilled water plant efficiency distributions which vary slightly in mean but are quite different in variance and outliers. It is interesting to observe the difference in variance between the clusters, with some exhibiting very small ranges (Cluster 3) and others showing much larger ranges (Cluster 1). This insight could be further investigated with respect to cooling system control. The discord candidates actually exhibit a tight range of cooling system efficiency. Figure \ref{fig:boxplots}c shows the cluster distribution according to outside ambient dry bulb temperature. This result shows how consistent the chiller plant output is over the operating range with respect to weather conditions.