## 3 Analyzing HCAHPS Data
### Salient Feature Extraction
each cluster centroid are calculated. If a record's distance from a cluster centroid is within one standard deviation from the mean, then it is considered an in-pattern record of that cluster. Otherwise, it is an out-pattern record of the cluster. Suppose that there are nine records in the dataset. Table 5 shows the distance of each record to all three cluster centroids as well as the mean and standard deviation of each cluster. The in-pattern records of each cluster are shown in bold. After tagging the records in a cluster as in-pattern and out-pattern, the mean of in-pattern records and out-pattern records in each cluster are calculated. Table 6 shows the difference factors of each feature in all three clusters along with the mean and standard deviation of the difference factors of each cluster. The salient features are highlighted in bold. For example, D3 (pain management) and D4 (cleanliness of the hospital) are salient features of cluster 1 while D2 (communication with Nurse) and D5 (quietness) are salient features of cluster 2. The positive values of significant difference factors show high frequency of dichotomous variables and high values for other categorical and continuous variables. Similarly, negative values show a low frequency for dichotomous variables and low values for other categorical and continuous variables. For instance, D3 (pain management) has negative difference factor for cluster one which shows low values of this variable, so the satisfaction with pain management is generally low in this cluster. Similarly, a high satisfaction with pain management can be inferred from cluster three. The salient features of each cluster are presented in Table 7, along with the range of that value or frequency of dichotomous value (High/Low) next to each of them. The salient features with the range of their values are a representation of the cluster, which will be used to create associations. \begin{table}
\begin{tabular}{c c c c} \hline \hline _Features_ & \(\mathbf{C1}\) & \(\mathbf{C2}\) & \(\mathbf{C3}\) \\ \hline D1 & \(-0.03037039\) & \(1.18199255\) & \(\mathbf{-1.22503855}\) \\ D2 & \(0.04416163\) & \(\mathbf{-0.20817361}\) & \(-0.02380192\) \\ D3 & \(\mathbf{-1.537553}\) & \(1.033197\) & \(\mathbf{1.041475}\) \\ D4 & \(\mathbf{-1.554513}\) & \(1.045382\) & \(\mathbf{1.047448}\) \\ D5 & \(-0.06825377\) & \(\mathbf{-0.03673413}\) & \(-0.03182003\) \\ \(\mu\) & \(-0.6293057\) & \(0.6031327\) & \(0.1616524\) \\ \(\Sigma\) & \(0.7493974\) & \(0.5972044\) & \(0.8430252\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Difference Factor of each Feature in each Cluster. Bold numbers are salient features which are out of range of 1 standard deviation from mean. \begin{table}
\begin{tabular}{c c c} \hline \hline _Records_ & \(\mathbf{C1}\) & \(\mathbf{C2}\) & \(\mathbf{C3}\) \\ \hline R1 & \(\mathbf{1.967133}\) & \(0.7958750\) & \(\mathbf{1.3957300}\) \\ R2 & \(2.121455\) & \(\mathbf{1.6483554}\) & \(0.9116866\) \\ R3 & \(\mathbf{1.675209}\) & \(\mathbf{1.5959835}\) & \(\mathbf{1.7050408}\) \\ R4 & \(\mathbf{1.518996}\) & \(\mathbf{1.6174912}\) & \(\mathbf{1.5210744}\) \\ R5 & \(\mathbf{1.697462}\) & \(\mathbf{1.0558556}\) & \(2.1432977\) \\ R6 & \(\mathbf{1.843458}\) & \(0.8124378\) & \(\mathbf{1.1173187}\) \\ R7 & \(1.191784\) & \(2.2571117\) & \(\mathbf{1.3717867}\) \\ R8 & \(2.266916\) & \(0.7501202\) & \(\mathbf{1.4390353}\) \\ R9 & \(\mathbf{1.706186}\) & \(\mathbf{1.6242395}\) & \(\mathbf{1.709041}\) \\ R10 & \(1.107229\) & \(2.0101626\) & \(\mathbf{0.7544890}\) \\ \(\mu\) & \(1.687192\) & \(1.367895\) & \(1.367732\) \\ \(\sigma\) & \(0.3833892\) & \(0.4231975\) & \(0.4307547\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Distance of records from centroid. Bold numbers denote in-pattern records which are in range of one standard deviation from the mean.