$1.$ Document d:$$ rapid phone mobile phone

Query q:$$ inexpensive mobile phone

N$=1000000$ documents

df$($rapid$)=5000$

df$($mobile$)=15000$

df$($phone$)=2000$

df$($inexpensive$)=300002.$ Given a set of data points D $($on a plane$)$ and a query point Q $,$ the approach of using cluster pruning to determine the closest point in D to Q may result in an incorrect answer when two clusters $($with two leaders$)$ are used. Explain how this incorrect result is possible $($how it occurs$).$

$3.$ Regarding evaluation methods, explain how R$-$precision differs from Mean Average Precision $($MAP$),$ and what advantages each has.

$4.$ Using the Kappa measure for Inter$-$judge agreement $(0$ for chance agreement, $1$ for total agreement$),$ find the proportion of time the judges agree $\backslash ($ P$($A$)\backslash ),$ what agreement would be by chance $\backslash ($ P$($E$)\backslash )$ and the Kappa measure K for the following judgement statistics: $5.$ Using the Rocchio Algorithm and the following information, what is the vector for

$\backslash (\backslash$mathrm$\{$a$\}\_\{\backslash$mathrm$\{$m$\}\}\backslash )?$ Hint: Refer to the example from Lecture $8-1.$

$\backslash (\backslash$mathrm$\{$q$\}$: $\backslash )$ dependable RAM dependable ROM very dependable ROM

d$1$: dependable ROM interface dependable RAM

d$2$: dependable RAM socket

Relevant: d$1$

Nonrelevant: d$2$

Weights: tf $($no normalization$)$

Constants: $\backslash (\backslash$alpha$=1,\backslash$beta$=0\mathrm{.}75,\backslash$mathrm$\{$y$\}=0\mathrm{.}25\backslash )$

$6.$ Estimate $($by finding the RSV coefficients$)$ the probability that the following documents are relevant to the query by using a contingency table. These are the only $4$ documents in the collection. Assume that documents $1$ and $2$ are relevant and documents $3$ and $4$ are nonrelevant.

Query: administration tax plan

Document $1$: tax plan administration costs will rise

Document $2$; administration politicians discuss plans to tax citizens much more

Document $3$: administration plans to take recess

Document $4$: plan to pay taxes this year

$7.$ Which of the following two unigram models M$1$ and M$2$ has the higher probability of generating the string: the turtle ran the rabbit

Model M$1$

$0\mathrm{.}3$ the

$0\mathrm{.}1$ a

$0\mathrm{.}02$ rabbit

$0\mathrm{.}01$ turtle

$0\mathrm{.}02$ ran

$0\mathrm{.}05$ quicker

Model M$2$

$0\mathrm{.}2$ the

$0\mathrm{.}2$ a

$0\mathrm{.}01$ rabbit

$0\mathrm{.}02$ turtle

$0\mathrm{.}01$ ran

$0\mathrm{.}03$ quicker