Download Self-Organising Maps for User Communities

SELF-ORGANISING MAPS FOR USER
COMMUNITIES
Sennaike O. A., Ojo A. K. and Sofoluwe A. B.
Abstract
User communities are usually constructed from user data which are fairly static.
However, these data are usually explicitly acquired from the user. Usage data,
on the other hand, is very dynamic and can be acquired unobtrusively but
presents a number of challenges including processing of sequential data.
We propose the use of Self Organising Maps (SOM) in constructing user
communities based on usage data. We also introduce use of the transition
matrix for the representation of usage data. We further show the applicability of
our approach by applying it to call data from a mobile telecommunications
network operator.
1 Introduction
Recent advances in information technology have made collection and storage of
data commonplace. However, obtaining information from the collected data is
becoming increasingly difficult due to both the huge amount of data available,
and the diversity in the background and interests of users, making conventional
information retrieval systems rather inefficient.
Also, a lot of systems are built with a lot of functionality for users with various
background and interests. Such systems tend to either be quite complex for
casual users or inadequate for expert users. For these complex software
systems to be usable, it is important for the systems to be able to identify the
user interacting with it and be able to provide functionalities only relevant to the
present needs of the user. User models and user modeling are attempts to make
good predictions about the users of a system and the use to which such a
system will be put.
In this paper, we propose a methodology for constructing user communities from
unobtrusively acquired user interaction data (usage data). Constructing user
communities from usage data introduces a number of issues as opposed to user
data. User data are fairly static and is not structured and can be easily be used
in available clustering/classification algorithms with little or no data
transformation. Usage data, on the other hand, is very dynamic and structured
(Hierarchical, sequences, time series, etc) with variable length of interaction
history. Available clustering/classification algorithms are not able to process
these forms of data without extensive data transformation. Our methodology
employs the transition matrix for representing usage data and subsequently
using SOM in discovering the user communities.
This research was partly supported by CRC No 99/2000/02 of University of
1
Lagos, Akoka, Nigeria.
The rest of this section gives an insight to some important concepts used in our
work including user modeling and Self-Organising Maps. Section 2 discusses
our SOM based approach to constructing user communities. In section 3, we
present a case study of mobile phone subscribers and use our approach in
discovering user communities. In section 4, our conclusions are presented and
current research effort is discussed.
1.1 User Modeling
User models attempt to provide a model of a user. The different kinds of data in
a user model can be classified as user data, usage data and environment data
[Kobsa et al 01]. User data comprise the various characteristics of the user.
This includes demographic data, user knowledge, user skills and capabilities,
user interests and preferences, user goals and plans [Kobsa et al 01]. Usage
data is related to data about user interaction with the system. As noted in [Kobsa
et al 01], there are potential overlaps between usage data and user data. User
data can be inferred from usage observation. In particular, Brusilovsky limits
usage data to comprise data about user interaction with the systems that can not
be resolved to user characteristics but can still be used to make adaptation
decisions. Environment data relates to data about the user’s environment that
are not related to users themselves. This is particularly relevant to web-based
systems where the range of different hardware and software is very diverse.
Furthermore, location information is also important to some applications
[Brusilovsky 01].
User modeling can be viewed as the process of constructing and applying (often
computer based) models of individuals and (or) groups of users. User Modeling
Systems consists of components that provide user modeling facilities to other
systems. They provide three (3) essential facilities [Kass et al 88]: acquisition,
representation and maintenance, and access facilities. An extension of these
requirements is presented in [Kobsa 01a] with a number of services listed as
being required of user modeling systems.
It is desirable that initial user groups in the domain in question be identified.
These groups share the same interests according to a set of criteria [Benaki et al
97] and are referred to as stereotypes. Stereotypes are organized in a singlerooted hierarchical structure, with a stereotype being able to inherit information
from several immediate subsumers as in a Lattice [Kass et al 88]. An individual
user model is thus represented as a leaf node in the hierarchy. Users can be
assigned to one or more stereotype with the users inheriting the characteristics of
these stereotypes [Kass et al 88].
Some problems associated with stereotypes are listed below [Paiva 95]:
It is difficult to determine what stereotypes to define for a certain applications.
It is difficult to establish the boundaries between stereotypes
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The information created needs to be constantly revised in order to maintain the
consistency of the models
The inferences are too general to be used in fine-grained models.
Further, the user classifications of the stereotyping method are ad hoc and unprincipled and they can be exploited by the adaptive system only after a large
number of trials by various kinds of users.
1.2 User Communities
The concept of user communities refers to explicitly clustering users with similar
behaviour through the users’ interaction with the system. The idea of user
communities was introduced by Jon Orwant in the user modeling system called
Doppelganger
[Orwant 93]. The idea of user communities is similar to stereotypes in that they
permit prediction of default values for the user model. They differ from the
stereotypes in that they are defined from a collection of user models and are
dynamic, being recomputed periodically. Perhaps, more significantly, a user had
probabilistic membership, matching some communities better than others.
The Doppelganger system employed the ISODATA clustering algorithm to
generate its communities. Other approaches, COBWEB and ITERATE, based
on conceptual clustering technique has also been applied [Paliouras et al 98],
[Paliouras et al 99].
Some other approached that have been employed in the construction of User
communities include Quinlan's C4.5 [Quinlan, 1987], Feedforward NN, ART
(Adaptive Resonance Theory), SOM, Watkin's Q Learning algorithm [Watkins
1989] and Case based Reasoning
1.3 Self-Organising Maps
The Self-Organising Map (SOM) was developed by Teuvo Kohonen in the early
1980's [Kohonen 00]. This artificial neural network tries to emulate the
development of topological maps in the brain using locally interconnected
networks and an algorithm based on local neighborhoods. The cerebral cortex of
the brain is arranged as a two-dimensional plane of units and spatial mappings
are used to model complex data structures. This means that topological
relationships in external stimuli are preserved and complex multi-dimensional
data can be represented in a lower (usually two) dimensional space. Kohonen
also uses two-dimensional networks where the units are arranged on a flat grid
using a regular topology (e.g. rectangular, hexagonal).
The SOM projects a high dimensional input data into a two-dimensional layer
which preserves order, compacts sparse data, and spreads out dense data. In
other words, if two input vectors are close, they will be mapped to processing
elements that are close together in the two-dimensional Kohonen layer that
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represents the features or clusters of the input data. Thus, the SOM is used to
visualize topologies and hierarchical structures of higher-order dimensional input
spaces and to discover patterns in a pool of data.
The learning model adopted by Kohonen’s self-organising Maps is a variation of
the competitive learning. The SOM consists of (usually) two-dimensional array of
identical neurons (nodes). This array of neurons can attain a regular topology
(e.g., rectangular or hexagonal) or irregular. Every node has, associated with it,
a reference vector (also called codebook or model vector) m i = [i1, i2, ……..,
in]T  n, where ij represent scalar weights. The codebook vectors are
initialized to random numbers. n is the set of all possible n-tuples of real
numbers, each of which is from the interval (-, +).
The input vector x = [1, 2,…………, n]T  n is connected to all neurons in
parallel via variable scalar weights ij. Note that the scalar weights are initialized
to random values thus they are in general different for different neurons. The
input x is then compared with all the codebook vectors mi and the location of the
best match in some metric is defined as the location of the “response”. In many
practical applications, the smallest of the Euclidean distances ||x – mi|| can be
made to define the best-matching node (the winning node), signified by the
subscript c:

c  arg min x  m i

which means the same as
i
x  mc  min  x  mi 
(1)
i
where the Euclidean distance x  mi is defined as


  j  ij
n
j 1

2
The weights of the nodes that are topographically close in the array up to a
certain geometric distance (neighborhood) to the winning node are then adjusted
(relaxed). A continuous local relaxation or smoothening effect on the weight
vectors of neurons in this neighborhood leads to global ordering. The relaxation
process, which is the learning process, can be represented as:
mi(t + 1) = mi(t) + hci(t) [x(t) – mi(t)]
(2)
where t = 0, 1, 2, ……… is an integer, the discrete-time coordinate.
In the relaxation process, the function hci(t) acts as the neighborhood function, a
smoothing kernel defined over the lattice points. For convergence, it is
necessary that hci(t)  0 when t  . Usually hci(t) = h(||rc – ri||, t) where rc  2
and ri  2 are the location vectors of nodes c and i, respectively, in the array.
With increasing ||rc – ri||, hci  0. The average width and form of hci define the
4
“stiffness” of the “elastic surface” to be fitted to the data points.
neighborhood functions are discussed in [Kohonen 01]
Some
After presenting the input samples and the codebook vectors have converged to
practically stationary values, the map is calibrated. Calibration of the map is
done to locate images of different input data items on it. In practical applications,
for which such maps are used, it may be self-evident how a particular input data
set ought to be interpreted and labeled. By inputting a number of typical,
manually analysed data sets, looking where best matches on the map lie, and
labeling the map units correspondingly, the map becomes calibrated. Since the
mapping is assumed to be continuous along a hypothetical “elastic” surface, the
closest reference vectors approximate the unknown input data.
It must be noted that the order resulting in the Self-Organising Map always
reflects the properties of the probability density function p(x). A number of ways
of improving the performance of the SOM algorithm and a number of variants of
the SOM is presented in [Kohonen 01].
2 Construction of User Communities from
Usage data
A user classification serves as a basis for an adaptive system; it saves and
analyzes the data pertaining to each particular user and makes available
information relevant to the program’s adaptation to the user in each successive
stage. User communities basically capture generalizations about large classes
of users. Thus, given incomplete information on a user, the user community the
user belongs to will help in eliciting and filling the missing information.
2.1 Why SOM?
Our proposed approach is based on SOM, an unsupervised learning technique
which automatically discovers hidden (implicit) relationships in data. It is also
able to identify clusters in data making it a natural candidate for the automatic
construction of user communities.
The fact that SOM preserves topological
order inherent in the data makes it a particularly attractive approach since users
with similar characteristics automatically become neighbours on the SOM grid.
2.2 Methodology
The processes involved the construction of our user communities are outlined as
follows:
2.2.1 Data collection
Usage data may be extracted from an existing database, through some empirical
research, sensors, or from some other means. Usage data is collected in an
unobtrusive manner. Our data set thus consists of usage data of different users.
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We refer to each user’s usage data as data item. Each data item is a series of
ordered vectors. Data items may have varying lengths.
2.2.2 Feature Extraction
With usage data available, we need to decide on a representation of the data
items and subsequently the metric to be used. The representation chosen will
determine the structure that will eventually be discovered. The metric used will
depend on (or sometimes inform) our representation decision. A number of
metrics for different representations is presented in [Kohonen 01].
It may also be important to scale the selected features before applying the SOM
algorithm. If knowledge of the relative importance of the components of the data
items is available, the corresponding dimensions of the input space can be
scaled according to this information [Kaski 97].
2.2.3 The transition matrix representation
We employ the use of the transition matrix for representing data. This matrix
keeps a count of the number of transitions between states. For a problem with
one variable and N states, we have a two dimensional N X N matrix. An element
a(i,j) in the matrix will indicate the number of transitions from state i to state j.
In general, for a problem with k variables and N1, N2, N3, ……, Nk states (where
Nk is the states for variable k), we will need 2k dimensional matrix. The first k
dimensions will represent the source states while the last k dimensions will
represent the destination states.
The definition of the states for each variable will usually depend on the nature of
the data. With the states defined, each data point is categorised into its
constituent state(s) and the transition matrix is constructed.
For a one variable problem, it is easy to visualize the two dimensional transition
matrix. However, for problems with more than one variable, it becomes quite
complex to visualize.
To give a visual example of a problem with more than one variable, we give a
hypothetical example for a 2 variable problem, say, colour and temperature. We
define the states as follows:
Color = {Black, Red, White}
Temperature = {Hot, Cold}
We further give the following ordered data as observed in a hypothetical
experiment:
(Red, Hot), (Black, Cold), (Black, Cold), (White, Hot), (Red, Hot)
The transitions can be outlined as follows:
Transition A: (Red, Hot), (Black, Cold)
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Transition B: (Black, Cold), (Black, Cold)
Transition C: (Black, Cold), (White, Hot)
Transition D: (White, Hot), (Red, Hot)
The transitions are visualized below:
Black
Red
Hot
Black
Hot
Cold
B
Hot
Red
Hot
Cold
Hot
White
Cold
Cold
A
Hot
Cold
Hot
Cold
Cold
Hot
Cold
Hot
Cold
Hot
Hot
Cold
Hot
Cold
Hot
Cold
White
Cold
C
Hot
Cold
Hot
Cold
Hot
Cold
Hot
D
Cold
Hot
Cold
Table 1: Four dimensional Transition matrix
The labels (A, B, C, D) in the example above are for illustration only. In practice,
the entries will be a count of the number of transitions from one state to the other.
Each transition matrix constructed is subsequently transformed into a vector
which is used as input for the construction the SOM. This transformation can
simply be achieved by listing the elements of each dimension of the transition
matrix in order.
2.2.4 Determining the states
For some problems, states may not be easily identifiable. Sometimes states may
be defined using some form of heuristics. Defining states is usually dependent
on the problem at hand and guided by experience. Too many states will result in
an unnecessarily large feature vector resulting in a longer processing time. On
the other hand, too few states will result in loss of information.
2.2.4.1 Construction of Maps
The construction of the maps follows from the SOM algorithm presented earlier.
Appropriate speed up techniques and guidelines for the construction of good
maps are presented in [Kohonen 01]. While the SOM can be of any dimension,
the two dimensional SOM is usually preferred because it makes it easy to build
efficient visualizations and user interfaces. After learning the data are projected
onto a two dimensional map surface.
7
A number of maps can be generated for the same data set. Since the SOM
algorithm is a stochastic process, the maps generated will be different. A
number of techniques that can be used to determine the best map is presented in
[Kaski 97], [Honkela 97], [Vesanto 00] and [Ypma et al 97].
During the construction of the map, each data point is labeled so that the training
data example can easily be referenced.
2.2.4.2 Interpretation and use of map
On visual inspection of the resulting map, clusters are usually noticed. Data
points that are close on the map are more similar than ones that are far apart. In
many applications, it may be necessary to identify and label these clusters.
Identification of the clusters may be done manually through visual inspection. A
number of techniques for cluster visualization have been presented [Merkl et al
97]. However, automated approaches to cluster identification have also been
researched into. See
[Siponen et al 01] and
[Galliat et al 00].
In this research, we are interested in attaching default properties to a new user
given that we have incomplete information on the user. Identifying and labeling
the clusters of the resulting SOM is not required since we are interested in the
winning node for a particular input data.
When presented with user data, the SOM may present a number of scenarios.
The winning node may have zero, one or more training examples attached to it.
Different strategies can be adopted here.
When there are no training examples attached to the winning node, the nearest
neighbor (with the smallest distance) can be considered. For winning nodes with
one training data, the values are derived directly from the associated exemplary
data. For winning nodes with more than one training data, an ‘average’ measure
can be defined which is used to select the default value.
Another possible strategy is to associate the default values to the reference
vectors when the maps are initially constructed with a similar strategy to the one
proposed in the preceding paragraph. Missing values from the user data can
then be inferred directly from the reference vector of the winning node.
It should be pointed out that communities, unlike stereotypes, are constructed
from actual (rather than potential) user data, are dynamic and will require
periodic re-computation as user data becomes available.
8
2.2.4.3 Soft bounded user communities
One of the problems identified in [Paiva 95] is that it is difficult to establish
boundaries between stereotypes. Rather than trying to define distinct boundaries
between our user communities, we propose soft boundaries between our user
communities. This means that we do not strictly define boundaries for our user
communities. Since the main aim of identifying a user’s community is to be able
to predict default values for missing information in the user model, defining hard
boundaries between our user communities is of little or no value. In fact,
allocating users to hard bounded user communities tends to limit the generality of
predicted values in the user model. Doppelganger tried to introduce some
generality by assigning a user probabilistic membership, matching some
communities better than others.
3 The Call Data Example
3.1 Background
The telecommunications industry is a rapidly expanding and highly competitive
industry. The industry generates and stores a large amount of intrinsically
multidimensional data which is difficult to process manually. These data include
call detail data, which describes the calls that traverse the
telecommunication networks. This is also referred to as call data records
(CRDs) and includes caller number, receiver's number, date, startingending time, call duration, location, etc.
network data, which describes the state of the hardware and software
components in the network.
customer data, which describes the telecommunication customers. This is
also referred to as contractual data and can include name of subscriber,
address, age, sex, occupation, phone number, payment type, contract
starting-ending date etc.
It is imperative that telecommunication companies develop strategies for
identifying market trends, detecting key characteristics and patterns for market
segments, improving the quality of products and services offered, detecting fraud
and insolvency early enough and focusing on customers likely to stay with the
company longer and profitable customers.
3.2 The Data
We collected call detail data from a mobile telecommunications operator that
consist of calls made by 500 subscribers over a period of six months. The
subscribers were all on “pay as you go” arrangement. Only selected fields in the
call detail database were extracted. For our experiment, we decided to
investigate only calls initiated from the network under consideration (originating
calls). The transaction type field for these calls has a value of 1.
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3.3 Preprocessing
In order to have the data in a form suitable for our purpose, a number of
preprocessing tasks were carried out. There were 808610 call records for the 6month period under consideration. Calls with third party present (conference
calls) were normalized. The normalization process removed the third party field
by creating an extra record with the same values in all the fields as the original
one except for the other party field which is replaced by the value in the third
party field. Thus all the records are now less by one field. The total number of
normalized calls was 853484.
Calls originating from the mobile phone operator in question totaled 227318. Of
these calls, records that had no other party field were removed reducing the
number of call records to 225292.
For simplicity, we select one variable, the duration of the call. The date and time
the call was made provided us with information about the order in which the calls
were made.
3.3.1 Feature extraction
The resultant data after preprocessing were records with variable lengths which
will result in variable length feature vectors. The next task is to generate the
fixed length feature vector for each subscriber while keeping information about
the order in which the calls were made. To achieve this, we employ the use of a
state transition matrix.
We define the states (using heuristics) for call duration as follows:
State 1:
State 2:
State 3:
State 4:
State 5:
Call duration less than 10sec
Call duration from 10 seconds to 39 seconds
Call duration from 30 seconds to 59 seconds
Call duration from 60 seconds to 120 seconds
Call duration from 120 seconds and above
We then construct a 5 X 5 transition matrix to represent the each user’s call
record. The transition matrix is then transformed into a vector with 25 features
for each user.
3.4 Construction of the Maps
Two kohonen maps were constructed, a two-dimensional network with the units
arranged on a flat grid using a regular rectangular topology, and another network
arranged in a regular hexagonal topology. The maps were trained using the
standard SOM algorithm [Kleiweg 01]. The maps generated are shown in the
appendix below.
10
3.5 Visualizing the maps
The visualization method used here employs the use of color to indicate the
similarity between adjacent nodes. For the rectangular grid network, the square
difference between neighboring units on the trained map is calculated and the
value is used to color the edged separating the units. Dark lines are used
indicate strong difference, and light lines to indicate strong resemblance. The
results show that the fact that nodes are close together does not necessarily
indicate strong similarity.
3.6 The user communities
We will not attempt to define hard boundaries for our user communities since it is
of no value for our purpose. We will define soft bounded communities based on
a neighbourhood definition.
Given an exemplar caller with incomplete
information, we can easily identify the community as the winning node and nodes
within its neighbourhood. This community is used to predict the missing values.
The closer a node is to the winning node, the stronger the influence it has in
predicting the missing information of the exemplar caller.
3.7 Conclusions
We have been able to represent usage data (call profile) of a user with a
transition matrix. The use of the transition matrix helps to preserve important
information on the temporal nature of the usage data. Based on the transition
matrix, we generated map (using kohonen SOM) that automatically defined soft
bounded user communities on the given data set.
It is also desirable to be able to characterize a group of users based on their
usage profile rather than individual users.
4 Conclusion
4.1 Discussion
User modeling offers a cheap way of tailoring applications to meet the needs of
diverse users. In order to fully achieve its potentials, a lot of research effort has
to go into developing standards, techniques and methodologies in the area of
user model acquisition, representation and inferencing, and communication
between user modeling systems and other with external systems.
We have presented a Kohonen SOM based approach that can be employed in
some defining user communities based on usage data.
11
4.2 Research Directions
There are a number of issues that still need attention in our proposed use of
SOM in discovering user communities. These issues are presented in the
following sections.
4.2.1 Determining States
In our approach, determining the states inherent in data is done using heuristics.
The nature of the problem at hand and experience usually come to play. There
is need to investigate more rigorous approaches to determining the states
inherent in data.
4.2.2 Associating raw data with identified communities
In its current form, our approach does not associate raw data directly with its
identified user community. Rather it associates the feature vectors (which
resulted from a transformation of the raw data) with the user community.
However, a more robust approach will have to provide a way in which raw data
can be directly associated with the identified user community without having to
go through the transition matrix transformation process and the
learning/clustering process. A possible approach to this is to build a feed forward
neural network to learn the association between raw data and the
classes/categories that evolve in the data.
4.2.3 Feature selection
The features that are selected to represent our feature space will determine the
quality of our results. Wrong set of feature may lead to misleading results.
Determining the salient features to use in representing our problem space is very
important. Including all the available features may lead to including a lot of
redundant features. Too few features may lead to loss of relevant information.
The features to be selected in a particular situation are usually dependent on the
nature of the problem being considered. There is need to investigate and
establish general factors and techniques that can be used in eliciting salient
features in a given data set.
4.2.4 Variants of SOM
In our proposal for the use of SOM in user modeling, the basic SOM algorithm
was assumed. However, where there are some specific additional requirements
(e.g., need for a hierarchical structure) there may be need for an appropriate
variant of the SOM (e.g. hierarchical SOM) to be implemented.
4.2.5 Improving the SOM algorithm
The dynamic nature of communities require frequent computation these
communities.
This is usually done periodically because the process is
computationally intensive (e.g., Doppelganger does it every night
12
[Orwant 93]). However, we acknowledge the fact that some applications may
require that communities be recomputed more often. There is need for more
research effort in this direction.
4.3 Concluding Remarks
This paper proposed a novel methodology for constructing user communities
using usage data. In order to preserve important temporal information on the
usage data, we employed the use of a transition matrix to represent usage data.
This matrix was then used as an input to the Kohonen SOM to generate soft
bounded user communities. We demonstrated the applicability of our
methodology by successfully applying it to call data from a mobile
telecommunications network operator.
Appendix
Sample subscriber record
CallDate
CallDuration
09/04/2003
11:55
7
21/04/2003
14:18
57
23/04/2003
09:30
109
24/04/2003
18:12
9
29/04/2003
09:30
5
30/04/2003
09:26
53
05/05/2003
13:48
112
08/05/2003
15:05
94
09/05/2003
14:25
26
21/05/2003
18:02
7
27/05/2003
18:31
6
28/05/2003
09:24
26
29/05/2003
10:21
64
CallDate
26/06/2003
17:38
06/07/2003
16:55
07/07/2003
10:06
07/07/2003
10:07
14/07/2003
13:42
16/07/2003
17:37
22/07/2003
12:44
23/07/2003
08:35
23/07/2003
08:44
29/07/2003
12:32
29/07/2003
17:40
04/08/2003
09:13
04/08/2003
10:34
CallDuration
1
10
6
79
44
48
16
27
6
60
17
62
47
13
29/05/2003
13:03
29/05/2003
14:00
29/05/2003
16:08
29/05/2003
16:34
04/06/2003
18:46
06/06/2003
09:13
10/06/2003
13:56
11/06/2003
09:24
19/06/2003
18:25
19/06/2003
18:31
22/06/2003
13:52
25/06/2003
17:38
11
66
19
7
52
7
55
20
242
25
6
33
04/08/2003
19:09
04/08/2003
19:09
06/08/2003
14:44
06/08/2003
20:50
06/08/2003
20:59
06/08/2003
21:07
20/08/2003
16:04
22/08/2003
10:53
17/09/2003
09:56
18/09/2003
18:05
26/09/2003
16:18
28/09/2003
15:46
13
64
43
228
202
21
2
89
28
30
29
17
Sample transition matrix vector
22530
62141
24121
15310
02001
Sample feature vector
2, 2, 5, 3, 0, 6, 2, 1, 4, 1, 2, 4, 1, 2, 1, 1, 5, 3, 1, 0, 0, 2, 0, 0, 1
Sample normalized feature vector
0.16667, 0.16667, 0.41667, 0.25, 0.00, 0.42857, 0.14286, 0.07143, 0.28571,
0.07143, 0.2, 0.4, 0.1, 0.2, 0.1, 0.1, 0.5, 0.3, 0.1, 0.00, 0.00, 0.66667, 0.00, 0.00,
0.33333
Sample Maps constructed from the same subscriber training data.
14
15
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