Task $1$: Design a BM$25-$based IR model $($BM$25)$ that ranks documents in each data collection

using the corresponding topic $($query$)$ for all $50$ data collections.

Inputs: $50$ long queries $($topics$)$ in the$50$Queries.txt and the corresponding $50$ data collections

$($Data$\_$C$101,$ Data$\_$C$102,...,$ Data$\_$C$150).$

Output: $50$ ranked document files $($e$.$g$.,$ for Query R$107,$ the output file name is

$$BM$25\_$R$107$Ranking.dat$)$ for all $50$ data collections and save them in the folder

$$RankingOutputs$.$

For each long query $($topic$)$ Q$,$ you need to use the following equation to calculate a score for

each document D in the corresponding data collection $($dataset$)$:

$\backslash$sum$\_\{$i $\backslash$in Q$\}\backslash$log $\backslash$left$(\backslash$frac$\{($r$\_$i$+0\mathrm{.}5)/($R$-$r$\_$i$+0\mathrm{.}5)\}\{($n$\_$i$-$r$\_$i$+0\mathrm{.}5)/($N$-$n$\_$i$-$R$+$r$\_$i$+0\mathrm{.}5)\}\backslash$right$)\backslash$cdot $\backslash$frac$\{($k$\_1+1)$f$\_$i$\}\{$k$\_1+$f$\_$i$\}\backslash$cdot $\backslash$frac$\{($k$\_2+1)$q f$\_$i$\}\{$k$\_2+$q f$\_$i$\}$

where Q is the title of the long query, k$1=1\mathrm{.}2,$ k$2=500,$ b $=0\mathrm{.}75,$ K $=$ k$1*((1-$b$)+$ b$*$dl $/$avdl$),$ dl

is document D$$s length and avdl is the average length of a document in the dataset, the base of

the log function is $10.$ Note that BM$25$ values can be negative, and you may need to update the

above equation to produce non$-$negative values but keep the resulting documents in the same

rank order.

Formally describe your design for BM$25$ in an algorithm to rank documents in each data

collection using corresponding query $($topic$)$ for all $50$ data collections. When you use the BM$25$ score to rank the documents of each data collection, you also need to answer what the

query feature function and document feature function are.

Use Python to implement: BM$25,$ For each long query, your python programs will produce ranked resultsand save them into $.$dat files. For example, for query R$107,$ you can save the ranked results of

thee models into $$BM$25\_$R$107$Ranking.dat$,$ by using the following format, where the firstcolumn is the document id $($the itemid in the corresponding XML document$)$ and the secondcolumn is the document score $($or probability$).$

OUTPUT for BM$25$ Model

Query$101($DocID Weight$)$:

$...$

$...$

Query$107($DocID Weight$)$:

$515762\mathrm{.}765639300454872$

$711572\mathrm{.}386400256599359$

$779362\mathrm{.}273108908141271$

$799502\mathrm{.}144090202267175$

$592441\mathrm{.}8983172340327779$

$671071\mathrm{.}6074284655326316$

$674111\mathrm{.}6074284655326316$

$864591\mathrm{.}128090008008347$

$314040\mathrm{.}5807469321665876$

$417910\mathrm{.}56351553901341$

$693770\mathrm{.}5625603334593126$

$373300\mathrm{.}5584756327943026$

$182970\mathrm{.}5497333978620387$

$185290\mathrm{.}548367073995152$

$781640\mathrm{.}5467090324257456$

$...$

Query$109($DocID Weight$)$:

$169531\mathrm{.}7689441459684538$

$260731\mathrm{.}64507953070341$

$615401\mathrm{.}6346667531459578$

$49331\mathrm{.}4873010135488298$

$644761\mathrm{.}4002858970645484$

$165751\mathrm{.}3834259539490046$