# Molecular Subtyping and Outlier Detection in Human Disease Using the Paralique Algorithm
## 3 Experimental Results
### Alignment with Previously Known Subtypes
#### 3.3.3 Comparison with Other Methods  
We sought to compare this basic and untuned version of the paraclique algorithm with well-known strategies such as k-means and hierarchical clustering, as implemented in core-R through the functions _kmeans_ ( ) and _hclust_ ( ).  
Results for the k-means method were mixed. It proved extremely successful on the gastric cancer data. There it divided samples into two subsets of size 26 and 44. All but one of the invasive samples were placed in the first cluster, while all of the proliferative and all but one of the metabolic samples were placed in the second. However, k-means failed completely on the non-small cell lung cancer data. Samples were divided into subsets of  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{6}{c}{**Paraclique Results**} \\ \hline \multicolumn{6}{c}{**Gastric Cancer**} & \multicolumn{6}{c}{**NSCLC**} \\ \hline \multicolumn{6}{c}{**Paraclique Sizes**} \\ \cline{2-7}  & 29 & 16 & & 26 & 12 & 8 \\ \hline \multicolumn{6}{c}{**Subtype**} \\ \hline proliferative & 1 & 12 & AC & 23 & 0 & 8 \\ invasive & 19 & 1 & SCC & 3 & 12 & 0 \\ metabolic & 9 & 3 & & & & \\ \hline \multicolumn{6}{c}{**k-Means Results**} \\ \hline \multicolumn{6}{c}{**Gastric Cancer**} & \multicolumn{6}{c}{**NSCLC**} \\ \hline \multicolumn{6}{c}{**Cluster Sizes**} \\ \cline{2-7}  & 26 & 44 & & 28 & 30 \\ \hline \multicolumn{6}{c}{**Subtype**} \\ \hline proliferative & 0 & 29 & AC & 18 & 22 \\ invasive & 25 & 1 & SCC & 10 & 8 \\ metabolic & 1 & 14 & & & \\ \hline \multicolumn{6}{c}{**Hierarchical Clustering Results**} \\ \hline \multicolumn{6}{c}{**Gastric Cancer**} & \multicolumn{6}{c}{**NSCLC**} \\ \hline \multicolumn{6}{c}{**Cluster Sizes**} \\ \hline \multicolumn{6}{c}{**Cluster Sizes**} \\ \cline{2-7}  & 33 & 37 & 9 & 49 \\ \hline \multicolumn{6}{c}{**Subtype**} \\ \hline \multicolumn{6}{c}{**Subtype**} \\ \hline \multicolumn{6}{c}{proliferative} & 0 & 29 & AC & 0 & 40 \\ invasive & 22 & 4 & SCC & 9 & 9 \\ metabolic & 11 & 4 & & & \\ \hline \hline \end{tabular}
\end{table}
Table 4: Cluster compositions based on known subtypes. Shown is a breakdown of the subtypes obtained from datasets with best available ground truth for paraclique, k-means, and hierarchical clustering.  
size 28 and 30, with both the adenocarcinoma and the squamous cell carcinoma samples spread almost evenly across these two clusters. The hierarchical approach was also a rather uneven performer. On the gastric cancer data, it divided samples into two subsets of size 33 and 37. While all of the proliferative samples found their way to the second cluster, the first contained 84% of the invasive and about 73% of the metabolic. On the non-small cell lung cancer data, it divided samples into subsets of size 9 and 49. All the adenocarcinoma samples were admirably grouped in the second cluster, but the squamous cell carcinoma samples were not convincingly stratified at all, with exactly half placed in each cluster. These results are also summarized in Table 4.  
As demonstrated by these experiments, the paraclique methodology can provide excellent patient stratification, further motivating the use of graph theoretical methods to differentiate samples based on their underlying genetic signatures. Such stratification is not perfect, of course, nor should we expect it to be given data limitations and biological variability. Moreover, unlike techniques such as k-means and hierarchical clustering, patients are not forced into a cluster under paraclique, as is evidenced by the 25 samples it left unclassified in the gastric cancer data. We suggest therefore that the tools we have described here may be best suited to fast screening tasks, for example, when transcriptomic data are relatively easy to obtain. Once clinical and/or additional forms of data have been collected, histological and other more laborious techniques will likely help provide more comprehensive subtyping of entire patient populations.