Question $3$: $(25$ Marks$)$

$($a$)$ Given the data in the following table, use PCA to reduce the dimension from $2$ to $1$ :

$\backslash$table$[[$Feature$,$Example $1,$Example $2,$Example $3,$Example $4],[x_1,4,8,13,7],[x_2,11,4,5,14]]$

$(13$ Marks$)$

$($b$)($i$)$ Assume the following: A database contains $80$ records on a particular topic of which $55$ are relevant to a certain investigation. A search was conducted on that topic and $50$ records were retrieved. Of the $50$ records retrieved, $40$ were relevant. Construct the confusion matrix for the search and calculate the precision and recall scores for the search.

$($ii$)$ Using the confusion matrix obtained in $($i$),$ compute the accuracy, error rate, sensitivity$,$ specificity and the F$-$measure.

$(6+6$ Marks $)$

Question $4$: $(25$ Marks$)$

$($a$)$ Find the quadratic regression model for the following data:

$\backslash$table$[[x,3,4,5,6,7],[y,2\mathrm{.}5,3\mathrm{.}2,3\mathrm{.}8,6\mathrm{.}5,11\mathrm{.}5]]$

$(10$ Marks$)$

$($b$)$ Define the following concepts alongside the schematic representation, if any:

$($i$)$ Artificial neuron

$($ii$)$ Activation function

$($iii$)$ Perceptron

$(9$ Marks$)$

$($c$)$ Write down the perceptron learning algorithm.

$(6$ Marks$)$