TABLE $1$: Test Variables

$4$ patients are tested using $9$ different testing protocols. Test labels are recorded as columns $1$ to $9($Col$1-$Col$9)$ where: columns $2,5$ and $8$ have continuous scores; columns $1,3,4$ and $9$ have binary values; and columns $6$ and $7$ are categorial values. Table $1$ shows the number of categorical variables as $3$ for both columns $6$ and $7,$ and the ranges for the continuous variables. As the continuous variables are similar, assume that no form of normalisation is required for these values.

TABLE $2$: Patient Test Results

Table $2$ shows the test results for $4$ anonymous patients listed as $\backslash ($ A$,$ B$,$ C $\backslash )$ and $\backslash ($ D $\backslash ).$ Assume the binary variables are treated as asymmetric. You are required to determine which $2$ patients are most likely to have the same medical condition. Answer parts a$)$ to d$)$ to demonstrate your approach to this problem.

Q $1($a$)$

Using only continuous variables, which $2$ patients are most similar in terms of their medical tests?

Use the manhattan function and explain how you compute the distance scores.

Q $1($b$)$

$[6$ Marks$]$

Using only binary variables, which $2$ patients are most similar in terms of their medical tests?

Explain the distance function you used in this part of the question and show the results.

Q $1($c$)$

$[6$ Marks$]$

Using only discrete variables, which $2$ patients are most similar in terms of their medical tests?

Explain the distance function you used in this part and show the results.

Q $1($d$)$

$[7$ Marks$]$

When comparing the entire record of all patients, which $2$ are most similar and which two are least similar?

How did you compute the final result?

$[$End of Question $1]$