PREDICTING WEB REQUESTS EFFICIENTLY USING A
PROBABILITY MODEL
Shanchan Wu, Wenyuan Wang
Department of Automation, Tsinghua University, Beijing 100084, P.R.C.
Ke
ywords: data mining, web mining, probability model, prediction
Abstract: As the world-wide-web grows rapidly and a user's browsing experiences are needed to be personalized, the
problem of predicting a user's behavior on a web-site has become important. In this paper, we present a
probability model to utilize path profiles of users from web logs to predict the user's future requests. Each of
the user's next probable requests is given a conditional probability value, which is calculated according to
the function presented by us. Our model can give several predictions ranked by the values of their
probability instead of giving one, thus increasing recommending ability. Based on a compact tree structure,
our algorithm is efficient. Our result can potentially be applied to a wide range of applications on the web,
including pre-sending, pre-fetching, enhancement of recommendation systems as well as web caching
policies. The experiments show that our model has a good performance.
1 INTRODUCTION
Data mining is a process of discovering implicit and
useful knowledge from large datasets [Fayyad, et al,
1996]. It is first motivated by the decision support
problem faced by many large retail organizations.
Now with the development of information
technology revolution, we have witnessed an
explosive growth in the information available on the
World Wide Web (WWW).
Web mining is the application of data mining
technology to huge Web data repositories. Basically,
there are two domains that pertain to Web mining:
the content mining and Web usage mining. The
former is the process of extracting knowledge from
the content of Web sites, and the latter, also known
as Web log mining, is the process of extracting
interesting patterns in Web access logs. The purpose
of this paper is to explore ways to exploit the
information from web logs for predicting users’
actions on the web.
There has been an increasing amount of work on
prediction models on the web. In the past, web-log
based inference has been focused on prediction
models that make best guesses on the users next
actions based on their previous ones. Almost all of
them only give one best guess when given a
sequence of previous requests. In this paper, we
present a probability model to predict the user’s next
request. From a sequence of previous requests,
instead of giving only one prediction, we can give
several predictions ranked by the values of their
probability. We present a function to calculate the
values of their conditional probability and present an
efficient algorithm to implement it. Our algorithm is
based on the compact web access pattern tree
(WAP-tree) (J.Pei, 2000) structure.
We discuss related work in section 1.1 and
discuss preprocessing task in section 2. We describe
construction of WAP-tree (J.Pei, 2000) structure in
section 3, and introduce our probability model and
describe the algorithm of prediction in section 4. In
section 5, we evaluate our experiments and provide a
summary of this work.
1.1 Related Work
WebWatcher(T. Joachirms, 1997), acts like a web
tour guide assistant, it guides the user along an
appropriate path through the collection based on the
past experiences of the visitor. It accompanies users
from page to page, suggests appropriate hyperlinks
and learns from experience to improve its advice
giving skills.
Syskill & Webert (M. Pazzani, 1996) is designed
to help users distinguish interesting web pages on
a particular topic from uninteresting ones.
WebTool, an integrated system (F. Masseglia,
1999), is developed for mining either association
rules or sequential patterns on web usage mining to
48
Wu S. and Wang W. (2004).
PREDICTING WEB REQUESTS EFFICIENTLY USING A PROBABILITY MODEL.
In Proceedings of the Sixth International Conference on Enterprise Information Systems, pages 48-53
DOI: 10.5220/0002622000480053
Copyright
c
 SciTePress

provide an efficient navigation to the visitor. When
the navigation matches a rule, the hypertext
organization of the document requested is
dynamically modified.
WhatNext (Z. Su, 2000) is focused on path-
based prediction model inspired by n-gram
prediction models commonly used in speech
processing communities. The algorithm build is n-
gram prediction model based on the occurrence
frequency. Each sub-string of length n is an n-gram.
The algorithm scans through all sub-strings exactly
once, recording occurrence frequencies of the next
click immediately after the sub-string in all sessions.
The maximum occurred request is used as the
prediction for the sub-string.
In (R. R. Sarukkai, 2000), the authors proposed
to use Markov chains to dynamically model the
URL access patterns that are observed in navigation
logs based on the previous state. In (Xing Dongshan,
2002), a new a new Markov model is presented.
Another prediction system proposed in (J.
Pitkow, 1999) is based on the assumption of mining
longest repeating subsequences to predict surfing. In
(Xin Chen, 2003), the authors use a popularity-based
prediction model for web pre-fetching.
2 PREPROCESSING
There are three main tasks for performing Web
Usage Mining or Web usage Analysis:
Preprocessing, Pattern Discovery, Pattern Analysis
(J.Srivasta, 2000). As Preprocessing is the first step
for our task and it is very important, we discuss it in
this session.
Preprocessing consist of converting the usage,
content, and structure information into the data
abstractions necessary for pattern discovery.
Typically, only the portion of each user session that
is accessing a specific site can be used for analysis,
since the access information is not publicly available
from the vast majority of Web servers. There are
two ways (KhuResearch) to identify server sessions:
(1) IP address associated with a time range:
We assume that from this period of the time, all
accesses from a specific machine (unique IP
address) belong to a specific user.
(2) Cookie associated with a time range:
After reconfigure the server, whenever a new
visitor comes in, he/she will be set with a cookie.
When he/she revisits the server, we could identify
him/her by the cookie.
A thirty minute timeout is often used as the
default method of breaking a user’s click-stream into
sessions. Clearing the useless information in the
Web logs is needed.
After preprocessing is applied to the original
Web log files, pieces of Web logs can be obtained.
Each piece of Web log is a sequence of events from
one user or session in timestamp ascending order,
i.e. the events happened early goes before the events
happened late. We use a single letter or a single
letter with a number subscript to denote one event,
and a sequence of event can be denoted as a
sequence of letters or letters with number subscripts.
For example, let E be a set of events. A Web log
piece or (Web) access sequence
n
eeeS L
21
=
)( Ee
i
∈
for
)1( ni ≤≤
is a sequence of events,
while n is called the length of the access sequence.
Because one can access the same web page more
than one time during a single access to the web site,
it is not necessary that
ji
ee ≠
for
)( ji ≠
in an
access sequence S.
3 CONSTRUCT THE WAP-TREE
As our algorithm is based on the compact web
access pattern tree (WAP-tree) (J.Pei, 2000)
structure, in this section, we introduce how to
construct a WAP-Tree, which is previously
presented by J.Pei et al. Due to different purpose,
our WAP-Tree has some difference. In order not to
lose information, we do not do any truncation to
WAP-Tree during construction.
The compactness of the WAP-Tree comes from
the fact that if two access sequences share a common
prefix P, the prefix P can be shared in the WAP-
Tree.
The WAP-Tree can be defined as follows (J.Pei,
2000). The only difference from (J.Pei, 2000) is that
we use the complete sequences.
1. Each node in a WAP-Tree registers two pieces
of information: label and count, denoted as label:
count. The root of the tree is a special virtual node
with an empty label and count 0. Every other node is
labeled by an event in the event set E, and is
associated with a count which registers the number
of occurrences of the corresponding prefix ended
with that event in the Web access sequence database.
2. The WAP-Tree is constructed as follows: for
each access sequence in the database, insert them
into WAP-Tree. The insertion of sequences is started
from the root of WAP-Tree. Considering the first
event, denoted as e, increment the count of child
node with label e by 1 if there exist one; otherwise
create a child labeled by e and set the count to 1.
Then, recursively insert the rest of the sequence to
the sub tree rooted at that child labeled e.
3. Auxiliary node linkage structures are
constructed to assist node traversal in a WAP-Tree
as follows. All the nodes in the tree with the same
PREDICTING WEB REQUESTS EFFICIENTLY USING A PROBABILITY MODEL
49

label are linked by shared-label linkages into a
queue, called event-node queue. The event-node
queue with label
i
e is also called e
i
-queue. There is
one header table H for a WAP-Tree, and the head of
each event-node queue is registered in H.
The specific process of the algorithm of
construction of WAP-Tree can be referred in (J.Pei,
2000). We can also build our WAP-tree from
frequent sequences which are mined from original
sequences with minimum support. This method will
reduce applicability (applicability is defined in
session 5), but it will also increase precision and
reduce the time consumed in the predicting process.
We will discuss this in session 5.
4 PREDICT FUTURE REQUESTS
Using the previous requests to predict the next can
be treated as a problem to find the maximum
conditional probability. Let E be the set of web
pages, and
121 −n
eee L be the previous requests.
Our target is to find
m
e which satisfy the following
equation:
Ee
eeeepMaxeeeep
i
nninnm
∈
=
−−−−
,)}|({)|(
121121
LL
Where
)|(
121
eeeep
nni
L
−−
is the conditional
probability of request for page
i
e at the next step.
Suggest the user will request
n
e at the next step. It
is not guaranteed that
n
e equals
m
e , but for all
pages in E, from the above equation,
n
e is most
probably equal to
m
e .
Practically, it is not easy to find the ideal
maximum probability
)(
max i
eP for a certain user,
because there are many facts which affect the
probability and some of which are difficult to get
and describe in math form. For example, different
user has different interests and so requests in
different mode, and for different request time, the
mode will also alter. Here we use the user’s previous
requests in the same session to predict the next
request, without taking personal information into
account, which is needed for Syskill & Webert (F.
Masseglia, 1999). Comparing to well known
WebWatcher (T. Joachirms, 1997), we also do not
require the web site link structure. We only use the
logs of web site. This greatly simplifies the process
of prediction and without losing much accuracy, and
even sometimes may increase it.
What we need to do is to find the maximum
conditional probability
)}|({
121
eeeepMax
nni
L
−−
from the web logs. How to find
)}|({
121
eeeepMax
nni
L
−−
is the problem we
will discuss below.
4.1 Model of Prediction
The previous requests
121
,,,
−− nn
eee L have
different influences to the prediction of the future
request
n
e . We suppose that the most recent request
has the strongest influence, and in most the fact is
so. This assumption is useful for prediction.
To extend this, we give a coefficient to weigh
the influence of every item in the user’s previous
request. Let
nn
bbbbB
121 −
= L denote the n-
sequence gotten from web logs,
B
f denote the
support of sequence B,
121
,,,
−− nn
eee L denote the
user’s previous request,
k
C denote the coefficient
called weight here of k’s event in the user’s previous
requests, and
i
Ω denote the collection of all n-
sequences in web logs which satisfy
in
eb = . In
addition, we define
)(
k
b ω as following:
⎩
⎨
⎧
≥∀=
≥≠∃
=
kjeb
kjeb
b
jj
jj
k
,1
,0
)(
ω
We calculate the probability value of
i
e to
appear at the next step by the following equations:
∑∑
Ω∈
−
=
−−
⎭
⎬
⎫
⎩
⎨
⎧
⎟
⎠
⎞
⎜
⎝
⎛
⋅
+
=
i
B
n
k
kk
B
B
nni
Cb
Mf
f
eeeeQ
1
1
121
)()|( ω L
M
is a constant (1)
)2(
)|(
)|(
)|(
121
121
121
∑
∈
−−
−−
−−
=
Ek
nnk
nni
nni
eeeeQ
eeeeQ
eeeeP
L
L
L
We use the following rule to
k
C .
1,,3,2
1
−=⋅=
−
nkCC
kk
L α ,
α
is a constant. (3)
Function (3) guarantees that no matter what
1−n
C is, the result will not change if only
α
is the
same. Simply, we set
1
1
=
−n
C , then
kn
k
C
−−
=
1
α .
In order to find the maximum value
of
)|(
121
eeeeP
nni
L
−−
, We only need to find the
maximum value of
)|(
121
eeeeQ
nni
L
−−
. We
calculate
)|(
121
eeeeQ
nni
L
−−
efficiently basing
on the WAP-tree (J.Pei, 2000). For convenient
statement, we also mark
)|(
121
eeeeQ
nni
L
−−
as
i
e
Q . We give an example to illustrate our predicting
process below and then in the session 4.2 we will
generalize our algorithm.
Example 1. Let
{} fedcba ,,,,, be a set of
events. From the Web log, we get the Web access
sequence as table 1.
From the above Web access sequences, we
construct the WAP-tree (J.Pei, 2000) as figure 1.
ICEIS 2004 - ARTIFICIAL INTELLIGENCE AND DECISION SUPPORT SYSTEMS
50

User
ID
Web Access
Sequence
User
ID
Web Access
Sequence
1 abcf 7 fbce
2 abcea 8 bca
3 abcf 9 fbfb
4 abcea 10 fbfb
5 abcea 11 fbfb
6 bca
Table 1: A database of Web access sequences.
Figure 1: The WAP-tree in Table 1
Suppose a user request the web site in the
sequence abc, and we want to predict the next
request. Based on function (1), if a sequence in the
web tree hasn’t the node c, it has no contribution to
Q value. This reduces much of the work of
calculation. Let
α
in function (3) equal 2, and
M
in function (1) equal 3. Then the process of
calculating
Q in function (1) is as follows.
First, from the header table of the WAP-tree, all
of the nodes with c label in the tree is easily reached,
which are recorded one after one in the Header
Table. The first node labeled c we get is (c: 5). Its
parent node (b: 5) is labeled b which is the same as
the second event of sequence
abc . Moreover, the
parent node of node (b: 5) is labeled a which is the
first event of sequence
abc . So
71)(
2
3
1
1
1
=++==
∑∑
=
−
=
ααω
k
k
n
k
kk
CCb
. We create a set L to
hold the optional events. Each node in the set has its
event label and the event’s Q value. The child nodes
of (c: 5) are (f: 2) and (e: 3). Now since event f and
event e haven’t existed in the set L, two new nodes
are created into the set labeled f and e respectively.
According to function (1), set their Q values as
follows (the Q values would probably be updated
during the future steps):
8.27
32
2
3
0
3
1
=⋅
+
=
⎟
⎠
⎞
⎜
⎝
⎛
+
+=
∑
=k
k
f
f
f
C
f
f
Q
5.37
33
3
3
0
3
1
=⋅
+
=
⎟
⎠
⎞
⎜
⎝
⎛
+
+=
∑
=k
k
e
e
e
C
f
f
Q
The second node labeled c in the Header Table
of the WAP-tree is (c: 2). Its parent node (b: 2) is
labeled b which is the second event of sequence
abc. In addition, the parent node of node (b: 2) is
the root of the tree without label a. So in the function
(1),
0)(,1)()(,1)()(
123
===== bbbcb ωωωωω
,
31)(
1
1
=+=
∑
−
=
αω
n
k
kk
Cb
. There is only one child
node of node (c: 2). The label of the child node is a,
which does not exist in the set L. Then a new node
labeled a is created into the set L. Its Q value is set
as follow (the Q value would probably be updated
during the future steps):
2.13
32
2
)(
3
0
1
1
=⋅
+
=
⎟
⎠
⎞
⎜
⎝
⎛
+
+=
∑
−
=
n
k
kk
a
a
a
Cb
f
f
Q
ω
The last nod labeled c in the header table is (c:
1). Its parent node is (b: 4) and the parent node of
(b:4) is (f:4) which label is not the same as the first
event in the sequence
abc. Similar to the above we
can get
31)(
1
1
=+=
∑
−
=
αω
n
k
kk
Cb
. The node (e: 1)
is the only child node of node (c: 1). As the label e
has existed in the set L, a new node isn’t needed to
created. What is needed to do is just to update the Q
value of node e in the set L.
75.03
31
1
)(
3
0
1
1
=⋅
+
=
⎟
⎠
⎞
⎜
⎝
⎛
+
′
′
+=∆
∑
−
=
n
k
kk
e
e
e
Cb
f
f
Q ω
25.475.05.3 =+=∆+=
′
eee
QQQ
′
e
Q is the new value of
e
Q . Set
25.4=
e
Q
to the
node e in the set
L
.
Now in the set L there are three nodes {f, Q =
2.8}, {e, Q = 4.25}, {a, Q = 1.2}. The maximum
value of Q is 4.25. Then we predict the user’s next
request would be event (page) e.
PREDICTING WEB REQUESTS EFFICIENTLY USING A PROBABILITY MODEL
51

4.2 Prediction Algorithm
Algorithm 1 (Predicting users’ future requests with
WAP-tree by calculating the values of conditional
probability)
Input: a WAP-tree constructed from web logs, a
user’s previous request sequence
121
,,,
−− nn
eee L , constant M and
α
, and number
n.
Output: the n events of the user’s most probable
requests at the next step.
Method:
(1). Initialize optional events set
φ
=L .
(2). Following
1−n
e ’s node-queue of the Header
Table of the tree., for each node (marked as
Θ ) in
the
1−n
e ’s node queue,
(a) initialize
0=
λ
, 1=
β
, node Θ
′
= Θ ,
event
1−
=
′
n
ee .mark the parent node of node
Θ
′
as parent ( Θ
′
), and mark the event
exactly before event
e
′
as parent (e
′
).
(b) following node
Θ ’s links in the tree from
child to parent.
while (the label of node Θ
′
is the same as
event
e
′
)
β
λ
λ
+← ,
α
β
β
⋅←
)(Θ
′
←Θ
′
parent , )(eparente
′
←
′
end while
(c) for each child node of node Θ ,
mark the count value of the child node as
f ,
then
λ ⋅
+
=∆
Mf
f
Q
If the label of the child node hasn’t existed
in the optional events set
L
, create a new item
with the label that is the same as that of the
child, and set it’s
QQ ∆← .
Otherwise, update
Q value of the item with
the same label in the set
L
, QQQ ∆+← .
(3) For all items in the optional set
L
, select the n
top ones with largest
Q values, return their labels,
which denote the events.
The algorithm shows that we only need to scan
part of the tree once. In addition, the tree isn’t
needed to be constructed again when making
another prediction. Generally, we can put the tree
in the memory, and according to the algorithm of
constructing WAP-tree, it can be updated easily.
We just need to put the user’s new sequence to the
tree according to the rule of construction.
5 EXPERIMENTAL EVALUATION
AND CONCLUSIONS
In the evaluation of the algorithm, we use the
following measures. Let
},,{
21 n
SSSS L= be the
set of sequences in a log file. We build WAP-tree
Models on a subset of these sequences, known as the
training sequences. The remaining is used as testing
sequences. If the returned n top events from the
algorithm contain the factual next request, we say
that it is a correct prediction. Let
+
P
be correct
predictions,
−
P
be set of incorrect predictions, and
R be the set of all requests. For some requests our
algorithm can’t give prediction (in the case that in
the end the optional set
L
is empty), so
normally
|| RPP ≠+
−+
. We use the following
measures (Z. Su, 2000):
P
precision
P
P
+
+−
=
+
,
|
|
P
P
applicability
R
+−
+
=
We use Microsoft anonymous web data as
experimental data. The data records the use of
www.microsoft.com by 38000 anonymous,
randomly-selected users visiting in a one-week
timeframe in February 1998. It can be downloaded
from the website (MSWeb).
As we use the original sequences to build our
WAP-tree, almost all the testing requests can be
given predictions. In other words, in the end the
optional set
L
isn’t empty. So in our experiments,
applicability = 1. If our WAP-tree is built from
frequent sequences, then applicability will decrease,
but
precision
will increase.
As applicability = 1, here we only need to
analyze
precision
.
Let
50=M , 2=
α
, and we change
parameter n which denotes the returning quantity of
predicting events from 1 to 10. The value
of
precision
percentage is shown as figure 2:
Further, we get different events predicting ability
as figure 3. Figure 3 explains that for the n returned
events, the greater Q value of one event, the greater
probable precision the event can be. This means that
Q can approximately represent the actual conditional
probability.
As we can see, the event with the greatest Q value
still hasn’t very great precision percentage. There
are some reasons. The important one is that,
different users have different request sequences, and
even the same user in the different time the
request sequence will also change. We can reduce
ICEIS 2004 - ARTIFICIAL INTELLIGENCE AND DECISION SUPPORT SYSTEMS
52

applicability to increase precision. As we say
previously, we can first mine the web logs to collect
frequent sequences with certain minimum support
Figure 2: A curve showing the change of precision
according to different quantity of returning events.
Figure 3: Precision of top events ranked by Q values.
Each histogram represents the precision percentage of the
event with a certain rank.
and build WAP-tree from the frequent sequence
instead of from original sequences. This method not
only increase precision, but also decrease the time
consumed in prediction. One shortage of this method
is that for some previous sequences, it can not give
predictions (optional set in our algorithm is finally
empty), or we say that applicability will decrease to
less than 1. There exists contradiction between
applicability and precision. To let applicability equal
1 or approximately equal 1 and still need high
precision, we can use n top ones instead of the
greatest one. In some cases, we need to compromise
between precision and applicability. This is very
useful in recommendation systems.
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