Using Manhattan distance, we will apply the $k-$means algorithm. Choose the

points $D$ and $H$ as the initial centroids $(k=2).$ Find the coordinates of the

centroids after one iteration. Notice that the $h$ th coordinate of the centroid for

cluster $i$ is updated by

tilde$(x{)}_h^{(i)}=[\frac{1}{|C_i|}{\displaystyle \underset{ain{C}_i}{\overset{?}{}}}{x}_{ah}]$

$,$ where $\text{'}y\text{'}$ symbol indicates the nearest integer to $y($rounding $y).$ Consider two objects $x_i$ and $x_j$ in a $p-$dimensional space where the data

including those is normally distributed with the variance$-$covariance matrix $.$

Performing PCA using this data would produce $y_i$ and $y_j$ in the $p-$

dimensional principal components space, which are corresponding to $x_i$ and

$x_j$ respectively. Note that the length of $y_i$ and $y_j$ is $p,$ meaning that the data

of principal component scores has the same dimension with the original data.

Let $MD(a,b)$ be the Mahalanobis distance between a and $b.$ Which of the

following is true?

$(1)MD(x_i,x_j)>MD(y_i,y_j)$

$(2)MD(x_i,x_j)=MD(y_i,y_j)MD(x_i,x_j)$

$(3)MD(x_i,x_j)=MD(y_i,y_j)$

$(4)$ None $of$ the above. $We$ cannot compare. Each dataset shown below contains $1,000$ items and $10,000$ transactions. Dark

cells indicate ones $($presence of items$)$ and white cells indicate zeros $($absence of

items$).$ We will apply the apriori algorithm to extract frequent itemsets with

minsup $=10\%($i$.$e$.,$ itemsets must be contained in at least $1,000$

transactions.$).$ Which of the following correctly lists the dataset producing the

fewest number of frequent itemsets and the dataset producing the frequent

itemset with highest support? Sequentially type two alphabet letters. Consider a transactional database where $1,2,3,4,5,6,7$ are items. Suppose

that we set minsup $=0\mathrm{.}5.$

What is the total number of frequent $2-$itemsets that can be extracted?

$(1)3$

$(2)4$

$(3)5$

$(4)6$Let $c_1,c_2,$ and $c_3$ be the confidence values of the rules $\{a\}\{b\},\{a\}$

$\{b,c\},$ and $\{a,c\}\{b\}$ respectively. Assume that the rules have identical

support. Which of the following is true?

$(1)c_1{c}_2$

$(2)c_1{c}_3$

$(3)c_2{c}_3$

$(4)$ None of above