$[3+3+1=7$ Marks$]$

Use case: Committee of experts convene every year to nominate literary works to become eligible for the award of highest category by assessing the works on multiple parameters. Below is one subset of such features. Categorizing the works phvides a transparent & streamlined way of nomination process. Consider all the below literary work data and answer all the following sub questions sequentially to detect patterns.

Note: Use only the Manhattan distance for calculation. Use the given data as is$.$ ie$.,$ No scaling or normalization is needed.

$\backslash$table$[[$Literature ID$,\backslash$table$[[$Readership$],[$Base$]],\backslash$table$[[$Writer$\text{'}$s Reputation$],[$spread in other$],[$countries$]],\backslash$table$[[$Distinctiveness$],[$in Style$]]],[$L$1,5,10,5],[L2,10,20,0],[L3,10,5,5],[L4,50,5,10],[$LS$,10,15,0],[$L$6,20,25,5]]$

$\backslash$table$[[$Literature ID$,\backslash$table$[[$Readership$],[$Base$]],\backslash$table$[[$Writer$\text{'}$s Reputation$],[$spread in other$],[$countries$]],\backslash$table$[[$Distinctiveness$],[$in Style$]]],[$L$1,5,10,5],[$L$2,10,20,0],[$L$3,10,5,5],[$L$4,50,5,10],[$L$5,10,15,0],[$L$6,20,25,5]]$

A$.$ Detect outlier in given data using the technique of DBSCAN algorithm using minPts $=3$ and epsilon $=45.$ Note: No need to show the step by step working of DBSCAN.

B$.$ Remove the detected outlier if any found from the result of part A$)$ and Cluster the remaining literary works using single linkage algorithm and show the dendogram with step by step merges.

C$.$ From the results of part B$),$ comment on the significance of the cophenetic distances with justification and suggest the most suitable dendogram cut range to create two meaningful clusters.