LSA-BASED SEMANTIC REPRESENTATION OF ACTION
GAMES
Katia Lida Kermanidis and Kostas Anagnostou
Department of Informatics, Ionian University, 7 Tsirigoti Square, Corfu 49100, Greece
Keywords: Player modeling, Action games, Latent semantic analysis, Knowledge representation, Semantic similarity.
Abstract: Modeling the semantic space of a complex dynamic domain, like an action game, by automatically
identifying the relations governing the game’s concepts, entities, actions and other features, is a challenging
research objective. In this paper we propose modeling the semantic space of the action game SpaceDebris,
in order to identify semantic similarities between players’ gaming styles. To this end we employ Latent
Semantic Analysis and attempt to identify latent underlying semantic information governing the various
gaming techniques. The several challenging research issues that arise when attempting to apply Latent
Semantic Analysis to non-textual data describing a complex dynamic problem space (defining the semantic
vocabulary and “word” utterances, deciding upon the dimensionality reduction rate, etc.) are addressed, and
the framework of the proposed experimental setup is described. The extracted similarities are further
employed for player modelling, i.e. grouping players according to their playing styles.
1 INTRODUCTION
Representing the knowledge of a specific domain,
i.e. identifying the concepts that carry units of
meaning related to it (domain “words”), as well as
the semantic relations governing those concepts, is a
wide and popular research area. Modeling domain
knowledge is essential for developing expert
systems, for intelligent prediction and decision
making, for intelligent tutoring, user modeling,
complex problem solving, reasoning etc. Mastering
the semantics of a domain is to learn the “language”
of the domain (Lemaire, 1998), i.e. to become
exposed to various sequences of domain “words” in
numerous contexts. This is similar to the way a
foreign language learner learns vocabulary usage by
reading, listening to, and writing texts in that
language.
There are two possible ways for supplying
domain knowledge (Lemaire, 1998): by hand,
making use of domain experts’ know-how, and
automatically, by deriving the semantics from large
corpora of “word” sequences. The first approach is
more accurate, but domain-dependent, while the
second is useful when no hand-crafted knowledge is
available.
A widely used method for representing domain
knowledge by statistical analysis of word usage is
Latent Semantic Analysis (LSA). LSA is adopted
from the field of Information Retrieval (Landauer et
al., 1998) and improves retrieval performance by
taking into account automatically detected polysemy
and synonymy relations between words. LSA
identifies these underlying semantic relations by
exploiting the occurrence statistics of the words
throughout the document collection. By reducing the
dimensionality of the initial term-document matrix
(the matrix with rows representing index terms and
columns representing documents; each cell contains
the number of occurrences of a term in a document),
hidden semantic similarities between words,
between documents, and between words and
documents surface, linking together words that may
not even appear in the same document, or documents
that may not share any common words.
LSA has been applied with significant success to
other domains, like essay assessment in language
learning (Haley et al., 2005), intelligent tutoring
(Graesser et al., 2007), text cohesion measurement
(McCarthy et al., 2007, summary evaluation
(Steinberger and Jezek, 2004), text categorization
(Nakov et al., 2003). Although all previously
mentioned LSA applications have been performed
on text corpora, some approaches have proposed its
use in different non-textual knowledge domains like
board game player modeling (Zampa and Lemaire,
218
Kermanidis K. and Anagnostou K..
LSA-BASED SEMANTIC REPRESENTATION OF ACTION GAMES.
DOI: 10.5220/0003082602180223
In Proceedings of the International Conference on Knowledge Engineering and Ontology Development (KEOD-2010), pages 218-223
ISBN: 978-989-8425-29-4
Copyright
c
 2010 SCITEPRESS (Science and Technology Publications, Lda.)

2002), complex problem solving (Quesada et al.,
2001), gene function prediction (Done et al., 2010;
Dong et al., 2006; Ganapathiraju et al., 2005), web
navigation behavior prediction (van Oostendorp and
Juvina, 2007), collaborative filtering (Hofmann,
2004), semantic description of images (Basili et al.,
2007).
In this paper a work in progress is described, that
proposes (for the first time to the authors’
knowledge) the application of LSA to a new domain,
namely digital action games, in order to identify
similarities among the playing techniques of various
players. Action games have properties that resemble
those of complex dynamic environments: causality
relations (actions or decisions often affect
subsequent actions or decisions), time dependence
(the environmental circumstances that affect actions
and decisions vary over time), and latent, implicit
relations between domain properties that are not
straightforward. Identifying the domain vocabulary,
as well as well-formed sequences of “words” that
constitute complete descriptions of actions or
context conditions is of significant research interest.
Throughout the remainder of the paper we will
address the research challenges that emerge when
attempting to represent the semantics governing the
SpaceDebris action shooting game (Anagnostou and
Maragoudakis, 2009). The proposed use of the
representation is player modeling: unsupervised
grouping of players with similar gaming manners.
Section 2 provides a bibliographic review of player
modeling and categorization. Section 3 presents the
basic properties of Latent Semantic Analysis, section
4 introduces the action game SpaceDebris, and
finally section 5 describes the cognitive modeling
process of the game domain, as well as its use for
modeling players.
2 PLAYER MODELING
Several game designers have recently been shifting
their focus to the player rather than the game itself.
Numerous attempts have been made to identify the
gaming technique of each player (e.g.
(in)experienced, aggressive, tactical, action player),
aiming to adapt the game features to his individual
preferences and needs. By personalizing the features
of the game, the designer hopes to provide increased
satisfaction and entertainment.
Player modeling has been performed within an
interactive storytelling game and the use of machine
learning techniques (Thue et al., 2007; Roberts et al.,
2007), by estimating the statistical behavior
(distribution) of player actions (Thawonmas and Ho,
2007), by using graphical knowledge representation
schemata like influence diagrams (Shahine and
Banerjee, 2007) and Bayesian networks (He et al.,
2008). Further references to player modeling can be
found in (Geisler, 2002). In (Anagnostou and
Maragoudakis, 2009) SpaceDebris players are
grouped into two clusters, using unsupervised
learning, according to their playing style (aggressive
or tactical).
Unlike previous approaches that either assign
one of a set of predefined profiles to a player, or
explore explicit actions and decisions made by the
player, the present work proposes a knowledge
model that attempts to
- identify the vocabulary of the game domain,
- represent complicated game states (action
game states are hard to represent, as their
definition is not straightforward like in
board games), and
- detect hidden, underlying semantic relations
between decisions made and actions taken
and their context, as well as among domain
“words”.
3 LATENT SEMANTIC ANALYSIS
As mentioned earlier, LSA is a
mathematical/statistical method initially proposed
for reducing the size of the term-document matrix in
information retrieval applications, as the number of
lexicon entries may reach several thousand, and the
document collection may contain tens of thousands
of documents or more. LSA achieves dimensionality
reduction through Singular Value Decomposition
(SVD) of the term-document matrix. SVD
decomposes the initial matrix A into a product of
three matrices and “transfers” matrix A into a new
semantic space:
A = T S D
T
(1)
T is the matrix with rows the lexicon terms, and
columns the dimensions of the new semantic space.
The columns of D represent the initial documents
and its rows the new dimensions, while S is a
diagonal matrix containing the singular values of A.
Multiplication of the three matrices will reconstruct
the initial matrix. The product can be computed in
such a way that the singular values are positioned in
S in descending order. The smaller the singular
value, the less it affects the product outcome. By
maintaining only the first few of the singular values
LSA-BASED SEMANTIC REPRESENTATION OF ACTION GAMES
219

and setting the remaining ones to zero, and
calculating the resulting product, the initial matrix
may be approximated as a least-squares best fit. The
dimensions of the new matrix are reduced and equal
to the number of selected singular values.
As an interesting side effect, dimensionality
reduction reduces or increases the frequency of
words in certain documents, or may even set the
occurrence of words to higher than zero for
documents that they initially did not appear in.
Thereby semantic relations between words and
documents are revealed that were not apparent at
first (latent). It needs to be noted that LSA is fully
automatic, i.e. the latent semantic relations are
learned in an unsupervised manner. Another
significant property is that LSA does not take into
account the ordering of words within their context;
documents are considered “bags of words”.
Extensive information on LSA can be found in
(Landauer et al., 1998).
4 SPACEDEBRIS
The videogame used for the purposes of data
collection is based on SpaceDebris (Anagnostou and
Maragoudakis, 2009). The action takes place within
the confines of a single screen, with alien ships
scrolling downwards. There are two types of enemy
spaceships (next referred to as enemy 1 and enemy
2), the carrier which is slow and can withstand more
laser blasts, and a fighter which is fast and easier to
destroy. The player wins when he has successfully
withstood the enemy ship waves for a predetermined
time. The game environment is littered with floating
asteroids which in their default state do not interact
(i.e. collide) with any of the game spaceships. In
order to do so, an asteroid has to be “energized” (hit
by player weapon). Also floating are shield and life
power-ups which the user can use to replenish his
ship’s shield and remaining lives. The player’s ship
is equipped with a laser cannon which he can use to
shoot alien ships. The laser canon is weak and about
4-5 successful shots are required to destroy an
enemy ship (except for the boss which requires
many more). The laser can also be used to
“energize” an asteroid and guide it to destroy an
enemy ship.
5 MODELING SPACEDEBRIS
Several research challenges need to be addressed
when attempting to model the domain of an action
game like SpaceDebris using LSA.
5.1 Vocabulary Identification
In board-like games, like tic-tac-toe or chess,
domain “words” are easy to identify. Boards may be
viewed as grids of cells and each cell state (e.g. “X”,
“O” or empty in tic-tac-toe) constitutes a “word”
(Lemaire, 1998). In action video games “words” are
harder to identify. Should they represent player
actions, enemy actions, the state of the context,
scoring results, spare lives or ammunition, time
parameters? In the firefighting microworld of
(Quesada et al., 2001) “words” are actions like
appliance moves, or water drops. The definition of a
game “word” depends on the intended use of the
model. If the intended use is behavior prediction, a
“word” needs to model a player’s action, as the
player’s sequence of actions (in a given context)
defines his behavior.
Table 1: The total number of distinct cell states.
Distinct cell states
The cell contains an asteroid
The cell contains an “energized” asteroid
The cell contains the player’s ship
The cell contains the player’s ship being hit by enemy 1
The cell contains the player’s ship being hit by enemy 2
The cell contains the player’s ship being destroyed
The cell contains the player’s ship firing a laser
The cell contains enemy 1
The cell contains enemy 1 being hit by a laser
The cell contains enemy 1 being hit by an asteroid
The cell contains enemy 1 firing a laser
The cell contains enemy 1 being destroyed
The cell contains enemy 2
The cell contains enemy 2 being hit by a laser
The cell contains enemy 2 being hit by an asteroid
The cell contains enemy 2 firing a laser
The cell contains enemy 2 being destroyed
The cell contains a player laser
The cell contains an enemy 1 laser
The cell contains an enemy 2 laser
The cell contains a life upgrade
The cell contains a life upgrade hit by laser
The cell contains a shield upgrade
The cell contains a shield upgrade hit by laser
Empty cell
In the present work, two approaches to
representing “words” are considered. In the first
approach, the game terrain is considered a grid, and
a “word” is formed by two parts. The first part is the
string that derives from the concatenation of the
states of each cell in the grid. The state of each cell
is determined by several factors, depending on the
state of each game entity. Table 1 shows all 25
KEOD 2010 - International Conference on Knowledge Engineering and Ontology Development
220

distinct cell states. A cell might also be in a state that
combines a number of states such as those described.
The second part models further out-of-the-grid
(non-spatial) information, like score, number of
available life upgrades, number of available shield
upgrades. The values of these features are
concatenated to form an out-of-the-grid string, that
is then attached to the cell-states string to constitute
a complete “word”.
In this “grid” representation, player or enemy
actions are modelled implicitly (indirectly) through
the related cell states. For example, a player laser
appearing in the cell right above the player ship
indicates that the ship fired in the recent game
history.
The grid cell size is of importance, as it affects
the level of granularity. The smaller the cell size is,
the more “generic” the “words” are, and the fewer
the combinations of states each cell may appear in.
We will experiment with grid sizes 11x8 and 12x6,
the first corresponding to a cell size equal to the
player ship’s size and the second to a cell size equal
to the largest enemy ship size, with a screen
resolution of 1024x768 pixels.
Vocabulary size using this representation reaches
2212 with a grid size of 11x8 and 1728 with a grid
size of 12x6. Vocabulary size is important, as too
many “words” may result to too few co occurrences
and LSA will not work. On the other hand, too small
a vocabulary may lead to too few similarities and,
again, the method will not work (Lemaire, 1998).
Optimal vocabulary size is an open research issue
and depends on the domain.
The second approach to defining the vocabulary
is more “holistic” and resembles in part that of
(Quesada et al., 2001). Each “word” represents a
player action, like move to a location or fire.
However, unlike (Quesada et al., 2001), each action
in a “word” is accompanied by a concatenation of
features that represent the state of the context in
which the action took place. Thereby causality
relations (the reasoning behind the player’s action)
are clearly identifiable. The context features taken
into account are
- the number of enemies very close to the
player (denoting imminent threat)
- the number of enemies close to the player
(denoting danger)
- the total number of enemies on screen
- the number of player lasers fired
- the number of enemy 1 lasers fired
- the number of enemy 2 lasers fired
- the position of the player
- the number of life upgrades performed
- the number of shield upgrades performed
- the number of hit asteroids
- the number of visible asteroids
- the number of hit enemy 1 ships
- the number of hit enemy 2 ships
- the score value
- the number of the player’s available life
upgrades
- the number of shields available to the player
“Word” examples using an NxM grid (example
1) and the “holistic” (example 2) approach are
shown below. The first part (up to X
NM
) of the string
in example 1 consists of tokens that stand for each
cell state (tokens are concatenated together with
underscores). The second part (after X
NM
) encodes
out-of-the-grid information, as explained earlier. We
use 16bit numbers, to denote the presence (1 or 0) of
one of the 9 game entities (player, 2 types of
enemies, 3 types of lasers, 2 types of upgrades,
asteroid). So, each “word” is a sequence of numbers
that describe the state of the corresponding cell,
while the last three tokens stand for the score, the
number of spare lives and spare shields respectively.
In this example the first cell contains a life upgrade,
the second an asteroid, the third is empty etc. In
example 2 the first token is the player’s action (the
player moves to location with coordinates (-286, -
133)). Each of the following concatenated tokens is
a value for each of the features listed above (e.g. 1
enemy is very close, 3 are close, there are 9 enemies
on-screen, player has fired a laser, enemies have
fired 3 lasers etc.).
2_1_0_..._X
NM
_1000_3_100 (ex. 1)
move-286-133_1_3_9_1_3 _...._X (ex. 2)
The “grid” representation takes into account
long-distance semantic dependencies, i.e. the
semantics of each cell (no matter how distant)
participates in the domain knowledge. The “holistic”
representation, on the other hand, detects causality
relations between the environment and the player’s
reaction to it in a more straightforward way, while
the “grid” approach “mines” these causality relations
implicitly.
5.2 Game Session Representation
Game sessions play the role of documents in
Information Retrieval. As documents are sequences
of words that convey a specific meaning and are
considered to satisfy a certain information need,
game sessions are well-formed sequences of
LSA-BASED SEMANTIC REPRESENTATION OF ACTION GAMES
221

“words” in the game domain. Each sequence
describes a path to a goal: the end of a game. Each
“word” constitutes a complete description of a
player’s action or of a description of the context
(game environment) at a given moment.
One way to represent a game session is to take a
sample of the game state at constant pre-defined
time intervals (e.g. every 500 msecs) and register the
sequence of “words” (“words” are defined using
either the grid or the holistic approach) that describe
the sample. Each sample represents a game state at
the specified time point. The duration of the
sampling time interval is very important. Small
intervals may lead to consecutive states that are
semantically identical (i.e. the player has not had
enough time to make a decision or act, or the state of
the context has not changed). Long intervals may
lead to the loss of semantic information (i.e. player’s
actions that occurred between the samples may be
missed). We will experiment with various interval
sizes in order to find the “optimal” sampling rate.
Another way to represent game sessions is
through sampling events that are dynamically
triggered by player’s actions. Instead of sampling
with a static rate, sampling may be event-driven.
Every time the player acts, a game state sample is
taken, and the player’s action and game context are
recorded. Event-driven sampling will record
information that is more related to the player’s
actions and disregard irrelevant and superfluous
semantic information that is not important for the
goal of the session.
5.3 Reduction Rate
The rows of the resulting term-document matrix
represent the “words”, and the columns represent
game sessions. Each cell contains the frequency of
occurrence of the “word” in the row in the column
session. Applying LSA to the matrix, another
research question arises: What is the optimal number
of singular values that should be maintained? In
Information Retrieval the number of dimensions of
the latent semantic space is usually between 100 and
300 (Lemaire, 1998). More research work needs to
be done in order to determine the appropriate
number of dimensions when it comes to non-textual
domains. Our proposal includes the experimentation
with various dimension numbers and the research of
their impact on modeling performance.
5.4 Experimental Setup for Measuring
Semantic Similarity
As mentioned earlier, the extracted model will be
used for identifying similar gaming techniques
among players. A group of players will play the
game for a given time frame. Players will at first be
asked to familiarize themselves with the game by
playing off the record for 4-5 minutes. After this
introductory phase, game sessions will be recorded
for every player. Each game session lasts an average
of 3 minutes, and players will be asked to complete a
specific number of games. The number of games
needed for successfully identifying the player’s
gaming style will be experimentally explored. Each
game session will constitute a feature vector, which
is formed by the set of “words” representing it.
Feature vectors both before and after LSA will be
stored for comparative analysis of results.
To identify similar gaming techniques, the
distance between vectors needs to be computed.
Though several distance metrics have been
experimented with, pairwise cosine similarity is the
most popular measure (Lemaire, 1998). Cosine
similarity will link the most semantically similar
vectors together, forming clusters of similar gaming
techniques. Clustering evaluation may be performed
in two ways. Players may be asked to answer a short
questionnaire before playing, where they will
characterize their individual gaming style, choosing
one or more from a set of pre-defined styles.
Another way is to ask a game expert to identify the
style of each individual player by looking at his
actions and decisions throughout the game sessions.
The matching degree of the cosine similarity and the
expert’s decision (and/or the player’s questionnaire
answers) will be measured before and after applying
LSA, for detecting its impact.
6 CONCLUSIONS
In this paper we have described a proposal for
modeling, in a novel way, the semantic space of a
complex non-textual problem, i.e. an action game,
using LSA. While the application of LSA to textual
data is fairly straightforward, several research issues
arise when the data involved are not textual, but
represent players’ actions and environmental
(contextual) conditions. These research issues have
been addressed and an experimental setup has been
proposed for the novel use of the extracted model to
player modeling.
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