deletions | additions       diff --git a/Decision_threshold.tex b/Decision_threshold.tex  index 43ea005..678cecb 100644  --- a/Decision_threshold.tex  +++ b/Decision_threshold.tex 
...
Each clustering step includes the calculation of two internal validation metrics which statistically evaluate how well the k-means algorithm was able to create distinct groups of daily profiles, the silhouette coefficient and the sum of square error. The silhouette coefficient score is a measurement of the inter-cluster cohesiveness and intra-cluster separation; a score of 1 is best and -1 is the worst. The coefficient is calculated with the following equation\cite{Rousseeuw:1987wr}:  \begin{equation}  s = \frac{b - a}{\max{(a,b)}}  \label{eq:silhouette_eq}