Description
Question 1 [20 marks] Data Mining in an Online Game
In this problem we examine data from Magic League, an online role-playing game (RPG), where
each player assumes a virtual identity, aims to advance in a virtual landscape, and earn scores
by defeating virtual monsters. Even for the most prolific geeks, spending hours shooting virtual
monsters can get lonely. Therefore, game developers have introduced online multiplayer options, in
which gamers register accounts, they chat with other users, they form online alliances and clans,
and they share virtual quality moments together fending minions.
Your mission is to study the user and games data and help improve the social aspect of undead
shooting. The user data is stored in the following tables:
1. Accounts. These include: information about each user such as their screen name, chosen
character, date they sign up, best scores, unlocked achievements, held artifacts, experience
level and hit points.
2. Alliances. This database includes information about user alliance composition, recording for
each alliance the id of its members.
3. User Interactions. This table contains information about user-to-user interactions. The
information include: the time of the interaction, id of the two users involved in the interaction,
the type and attribute of the interaction (e.g., artifact exchange, fight, or chat).
4. Battle Sessions. This contains information about each game session. Including: the time
that a user logs in; the time the session starts and ends; each user’s actions, losses and
achievements; and the outcome of the battle.
Your overall task is to build a data warehouse from these databases to analyse user behaviour, with
the goal of building a game that is even more fun to play.
(a) A gamer, Tintin, logs into his account and together with a few friends from his alliance started
to conquer a forest occupied by monsters. In this battle, Tintin was bitten by a unicorn and
temporarily lost his ability to fight. He recovered by drinking a life potion offered by an ally,
Pinocchio. The battle ended with the alliance taking control of the forest. Which databases
tables (among 1–4 above) are changed during this session? And if changed, are entries added
or updated? Please indicate your answer by circling the appropriate option for each DB below.
[4 marks]
DB(1) Accounts: Changed / Unchanged; (if changed) Added / Updated
DB(2) Alliances: Changed / Unchanged; (if changed) Added / Updated
DB(3) User interactions: Changed / Unchanged; (if changed) Added / Updated
DB(4) Battle sessions: Changed / Unchanged; (if changed) Added / Updated
(b) Tintin and Pinocchio’s team needs to assign a team member to fight a new monster, Basilisk,
in the reptile category. You need to supply a function that helps them decide who has had
the most number of wins against reptiles. Which database(s) do you need to use to get the
information? [2 marks]
(c) What is metadata of a database? Please provide a brief description. Also give two examples
of metadata about the Battle Sessions database above. [4 marks]
(d) You are to generate a data warehouse, containing the average number of battles users participated in, and the average number of logins they made of in May 2014; tabulated by the
alliances they are in, and the year they signed up for the game (2011, 2012, 2013). Draw a
star schema of this table. Clearly annotate where each measure and each dimension come
from in databases (1–4). [4 marks]
(e) You analysed the game achievements versus user interactions for a number of prominent
alliances in May 2014. Compute the average size of alliances in this sample. [1 mark]
Alliance Name Size Number of Monsters Chat Messages Exchanged
(# Members) Defeated per Member per Member
Justice League 7 150 2.5
Gryffindor 150 4.2 300
Dumbledore’s Army 12 83.0 18.5
Fellowship of the Ring 6 0.0 260
Southern Airbenders 45 23.5 25
(f) In the game achievements table in the previous part, how does the average number of defeated
monsters related to the average number of chat messages exchanged? Answer this question
by computing the Pearson correlation coefficient of these two quantities. Show your workings.
[3 marks]
(g) Assuming the data in part (e) is collected correctly, what do you think could lead to the
observed behaviour in each alliance? Provide one example reason. [2 marks]
Question 2 [10 marks] Understanding User Data
Consider the following set of 6 game users.
ID Name Gender Age Skill Level Motto
u001 Harry Male 17yrs Black “Never tickle a sleeping dragon”
u002 Hermione Female 16.5yrs Brown “When in doubt, go to the library”
u003 Katara Female 15yrs Black “Never turn my back on people who need me”
u012 Frodo Male 16yrs Green “One ring to rule them all”
u011 Superman Male 25yrs Black “An acceptable face of invading realities”
u066 Astro Male 15mo Doggy “Happiness is a warm puppy”
(a) What is the number of datum n and the number of attributes p in this table? [2 marks]
(b) Among the p different attributes, identify one binary and one numeric attribute. [2 marks]
(c) You need to apply a data mining algorithm which only accepts binary attributes on this user
profile dataset. Explain how the age and skill level variables can be transformed into a binary
attribute, or a set of binary attributes without loosing any information contained the
original dataset. Write out the transformed binary attributes for the skill level attribute
for each user. [6 marks]
Question 3 [12 marks] Constructing User Graphs
We construct two graphs among these six users, by making an (unweighted) edge between two users
when they have exchanged at least 5 messages in May 2014 (on the left, the Chat graph); and when
they have exchanged at least 5 virtual artifacts in May 2014 (on the right, the Artifact Exchange
graph).
Chat Artifact Exchange
Harry
Hermione
Katara
Frodo Astro Superman Harry
Hermione
Katara
Frodo Astro Superman
(a) How many edges are there in each graph? [2 marks]
(b) Which node(s) have the highest degree in each graph? [2 marks]
(c) Which node(s) have the second highest degree in each graph? [2 marks]
(d) What is the closeness centrality of Frodo in each graph? [2 marks]
(e) What is the (un-normalized) betweenness centrality of Katara in the Chat graph? i.e. the
number of shortest paths from all users to all others users that pass through Katara. Is this
the same with her betweenness centrality in the Artifact Exchange graph, why or why not?
[4 marks]
Question 4 [8 marks] Data cubes and OLAP
The Magic League game provides a feature for users to build virtual pets, take them along as battle
companions, or give to each other as gifts.
1. Species ten possible values: Dog, Cat, Pig, Lizard, Horse, Stag, Otter, Swan, Hare, Phoenix.
2. Gender two possible values: Male/Female.
3. Color seven different values.
4. Size five different values.
5. Intelligence, five different values.
You are to study users pet-keeping behaviour.
(a) The first task is to construct a data cube. How many cells are in the base cuboid? [3 marks]
(2 marks for working, 1 mark for the correct final answer)
(b) How many cells are there in total if you were to compute all cuboids? [3 marks]
(c) One summary measure in the datacube is the number of pets. Given a cuboid with dimensions
Species, Colour and Intelligence, what OLAP operations do you use to get the number
of pets that is purple, and tabulated by their Intelligence? [2 marks]
Question 5 [15 marks] Structure of a Network
Consider the set of 18 Web pages drawn in the following figure, whose links forming a directed
graph.
Figure 1: A directed network of 18 web pages.
(a) Which nodes constitute the largest strongly connected component (SCC) in this graph? Taking this as the giant SCC, which nodes then belong to the sets IN and OUT as defined in
the lectures? Which nodes belong to the tendrils of the graph? Explain all of your answers.
[9 marks]
(b) As new links are created and old ones are removed among an existing set of Web pages, the
pages move between different parts of the bow-tie structure.
Name an edge you could add or delete from the graph in the above figure so as to increase
the size of the largest strongly connected component. Explain why you named this edge.
[3 marks]
(c) Name an edge you could add or delete from the graph in the above figure so as to increase
the size of the set IN. Explain why you named this edge. [3 marks]
Question 6 [15 marks] Chi-Square Test
Hogwarts owlry keeps a large number of owls with varying magic capacity. We examine their feather
colour – black or white; and beak colour – red or yellow, along with a critical magic property: ability
to locate the recipient – strong or weak. The table below contains the number of owls that possess
two qualities simultaneously, e.g. there are 10 black-feathered owls that have strong localization
ability.
black feather white feather red beak yellow beak
weak localization 45 30 60 15
strong localization 10 15 20 5
(a) How many owls have black feather? white feather? How about red or yellow beak? [4 marks]
(b) Is the magic localization ability correlated with feather colour or beak colour? Which feather
or beak colour seems to produce highly capable owls? Answer this question by manually
computing χ
2
tests on feather/beak colours and localization ability. Show all of your workings.
[7 marks]
(c) If there is a third attribute, having sulphur crest, found to be highly correlated with strong
localization ability in owls, with χ
2 = 20. Is it correct to say that sulphur crest causes
improved localization ability? Why or why not? [4 marks]
Question 7 [20 marks] Hands-on Analysis of a Real-World Dataset
Take the UCI Energy efficiency dataset http://archive.ics.uci.edu/ml/datasets/Energy+efficiency,
complete the following analysis and compute the designated metrics.
(a) Draw a boxplot of dimension y1: heating load, annotate all key landmarks on the box plot.
What is the median of y1, what is the mean of y1, what are the values of Q1 and Q3, how
large is the inter-quartile range, are there any outliers?
[8 marks]
(b) Draw a scatter plot of dimension Y 1: heating load vs Y 2: cooling load. What is the
minimum and maximum of Y 1 and Y 2, respectively? Are Y 1 and Y 2 positively correlated,
negatively correlated, or appear to be un-correlated?
[5 marks]
(c) Compute the Pearson correlation of the 8 attributes X1 . . . X8 with Y 1 heating load.
[4 marks]
(d) Rank the attributes with respect to their strength of correlation with y2 cooling load –
from the least to the most correlated.
[3 marks]
