Question $4$

Recommender System

Consider a table with $4$ user ratings on $8$ items as shown below.

userID$/$game

WatchDog

GTAV

PUBG

StarCraft

CallOfDuty

FIFA

WOW

MineCraft

firechicken

$3$

$3$

$4$

$4$

$2$

$3$

mike$0702$

$3$

$5$

$4$

$3$

$3$

$4$

zephyros

$4$

$5$

$2$

$1$

dadvador

$2$

$4$

$4$

$4$

$5$

Treating the utility matrix as boolean $($buy or not buy$),$ compute the Cosine distance between firechicken and zephyros. Please answer to three decimal places.

Note: It is possible to solve this question mathematically, but it may be easier to solve this question programmatically.