Mining Weighted Browsing Patterns with Linguistic Minimum Supports

Submitted manuscript

Mining Weighted Browsing Patterns with Linguistic

Minimum Supports

Tzung-Pei Hong†_{*, Ming-Jer Chiang}‡ _{and Shyue-Liang Wang}‡

†_{Department of Electrical Engineering}

National University of Kaohsiung Kaohsiung, 811, Taiwan, R.O.C.

tphong@nuk.edu.tw

‡_{Graduate School of Information Engineering}

I-Shou University Kaohsiung, 840, Taiwan, R.O.C.

ndmc893009@ yahoo.com.tw, slwang@ isu.edu.tw

Abstract

World-wide-web applications have grown very rapidly and have made a significant impact on computer systems. Among them, web browsing for useful information may be most commonly seen. Due to its tremendous amounts of use, efficient and effective web retrieval has become a very important research topic in this field. Techniques of web mining have thus been requested and developed to achieve this purpose. All the web pages are usually assumed to have the same importance in web mining. Different web pages in a web site may, however, have different importance to users in real applications. Besides, the parameters set in most conventional data-mining algorithms are numerical. This paper thus attempts to propose a weighted web-mining technique to discover linguistic browsing patterns from log data in web servers. Web pages are first evaluated by managers as linguistic terms to reflect their importance, which are then transformed as fuzzy sets of weights. Linguistic minimum supports are assigned by users, showing a more natural way of human reasoning. Fuzzy operations including fuzzy ranking are then used to find linguistic weighted large sequences. An example is also given to clearly illustrate the proposed approach.

Keywords: browsing pattern, fuzzy set, web mining, weight.

--- * Corresponding author

1. Introduction

Knowledge discovery in databases (KDD) has become a process of considerable interest

in recent years as the amounts of data in many databases have grown tremendously large.

KDD means the application of nontrivial procedures for identifying effective, coherent,

potentially useful, and previously unknown patterns in large databases[17]. The KDD process

generally consists of three phases: pre-processing, data mining and post-processing [16, 29].

Among them, data mining plays a critical role to KDD. Depending on the classes of

knowledge derived, mining approaches may be classified as finding association rules,

classification rules, clustering rules, and sequential patterns [8], among others.

Recently, world-wide-web applications have grown very rapidly and have made a

significant impact on computer systems. Among them, web browsing for useful information

may be most commonly seen. Due to its tremendous amounts of use, efficient and effective

web retrieval has thus become a very important research topic in this field. Techniques of web

mining have thus been requested and developed to achieve this purpose. Cooley et. al. divided

web mining into two classes: web-content mining and web-usage mining [13]. Web-content

mining focuses on information discovery from sources across the world-wide-web. On the

from web servers [14]. In the past, several web-mining approaches for finding sequential

patterns and interesting user information from the world-wide-web were proposed [7, 9, 12,

13].

The fuzzy set theory has been used more and more frequently in intelligent systems

because of its simplicity and similarity to human reasoning [38, 39]. The theory has been

applied in fields such as manufacturing, engineering, diagnosis, and economics, among others

[19, 26, 28, 38]. Several fuzzy learning algorithms for inducing rules from given sets of data

have been designed and used to good effect with specific domains [2, 4, 15, 18, 20-24, 32-34].

Strategies based on decision trees were proposed in [6, 10-11, 30-32, 35-36], and based on

version spaces were proposed in [27]. Fuzzy mining approaches were proposed in [5, 25, 27,

37].

In the past, all the web pages were usually assumed to have the same importance in web

mining. Different web pages in a web site may, however, have different importance to users in

real applications. For example, a web page with merchandise items on it may be more

important than that with general introduction. Also, a web page with expensive merchandise

items may be more important than that with cheap ones. Different importance for web pages

confidence values in most conventional data-mining algorithms were set numerical. In [22],

we proposed a weighted mining algorithm for association rules using linguistic minimum

support and minimum confidence. In this paper, we further extend it to mining weighted

sequential browsing patterns from log data on web servers. The linguistic minimum support

values are given, which are more natural and understandable for human beings. The browsing

sequences of users on web pages are used to analyze the overall retrieval behaviors of a web

site. Web pages may have different importance, which is evaluated by managers or experts as

linguistic terms. The proposed approach transforms linguistic importance of web pages and

minimum supports into fuzzy sets, then filters out weighted large browsing patterns with

linguistic supports using fuzzy operations.

The remaining parts of this paper are organized as follows. Several mining approaches

related to this paper are reviewed in Section 2. Fuzzy sets and operations are introduced in

Section 3. The notation used in this paper is defined in Section 4. The proposed web-mining

algorithm for weighted browsing patterns with linguistic minimum supports are described in

Section 5. An example to illustrate the proposed web-mining algorithm is given in Section 6.

2. Review of related mining approaches

Agrawal and Srikant proposed a mining algorithm to discover sequential patterns from a

set of transactions [1]. Five phases are included in their approach. In the first phase, the

transactions are sorted first by customer ID as the major key and then by transaction time as

the minor key. This phase thus converts the original transactions into customer sequences. In

the second phase, the set of all large itemsets are found from the customer sequences by

comparing their counts with a predefined support parameter α. This phase is similar to the

process of mining association rules. Note that when an itemset occurs more than one time in a

customer sequence, it is counted once for this customer sequence. In the third phase, each

large itemset is mapped to a contiguous integer and the original customer sequences are

transformed into the mapped integer sequences. In the fourth phase, the set of transformed

integer sequences are used to find large sequences among them. In the fifth phase, the

maximally large sequences are then derived and output to users.

Besides, Cai et al. proposed weighted mining to reflect different importance to different

items [3]. Each item was attached a numerical weight given by users. Weighted supports and

weighted confidences were then defined to determine interesting association rules. Yue et al.

In this paper, we proposed a weighted web-mining algorithm to mine browsing patterns

with linguistic supports from log data on a web server. Different web pages have different

importance, which is evaluated by managers or experts. The fuzzy concepts are used to

represent importance of web pages and minimum supports. These parameters are expressed in

linguistic terms, which are more natural and understandable for human beings.

3. Review of related fuzzy set concepts

Fuzzy set theory was first proposed by Zadeh and Goguen in 1965 [39]. Fuzzy set theory

is primarily concerned with quantifying and reasoning using natural language in which words

can have ambiguous meanings. This can be thought of as an extension of traditional crisp sets,

in which each element must either be in or not in a set.

Formally, the process by which individuals from a universal set X are determined to be

either members or non-members of a crisp set can be defined by a characteristic or

discrimination function [39]. For a given crisp set A, this function assigns a value µA( )x to

_





µ

Thus, the function maps elements of the universal set to the set containing 0 and 1. This

kind of function can be generalized such that the values assigned to the elements of the

universal set fall within specified ranges, referred to as the membership grades of these

elements in the set. Larger values denote higher degrees of set membership. Such a function is

called the membership function,

µ

function is represented by

µ

where [0, 1] denotes the interval of real numbers from 0 to 1, inclusive. The function can also

be generalized to any real interval instead of [0,1].

Triangular membership functions are commonly used and can be denoted by A=(a, b, c),

where a≤ ≤b c (Figure 1). The abscissa b represents the variable value with the maximal

grade of membership value, i.e.

µ

Figure 1: A triangular membership function

There are a variety of fuzzy set operations. Among them, three basic and commonly used

operations are complement, union and intersection, defined as follows.

(1) The complement of a fuzzy set A is denoted by

¬

¬

µ

µ

∀ ∈

x X

(2) The intersection of fuzzy sets A and B is denoted by A I B and the membership

function of A I B is given by:

} ) ( , ) ( { ) (x Min _A x _B x B A

µ

µ

µ

(3) The union of fuzzy sets A and B is denoted by A U B and the membership function of A U B is given by: } ) ( , ) ( { ) (x Max x x B A B A

µ

µ

µ

Besides, fuzzy ranking is usually used to determine the order of fuzzy sets and is thus

quite important to actual applications. Several fuzzy ranking methods have been proposed in

the literature. The ranking method using gravities is introduced here. Note that other ranking

methods can also be used in our fuzzy algorithm.

The abscissa of the gravity of a triangular membership function (a, b, c) is stated as

follows.

)

(

3

1

)

(

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(

)

(

)

(

)

(

)

)

(

(

c

b

a

dx

a

b

a

x

dx

a

b

a

x

xdx

b

c

x

c

xdx

a

b

a

x

dx

x

dx

x

x

gravity

=

+

+

−

−

+

−

−

×

−

−

+

×

−

−

=

×

=

∫

∫

∫

∫

∫

∫

µ

µ

Let A and B be two triangular fuzzy sets. A and B can then be represented as follows:

B = (a_B, b_B, c_B). Let g(A) = 3 1 (a_A + b_A + c_A), and g(B) = 3 1 (a_B + b_B + c_B).

Using the gravity ranking method, we say _{A > B if g(A) > g (B).}

4. Notation

The notation used in this paper is defined as follows.

n: the total number of log records;

n’: the total number of browsing sequences;

m: the total number of web pages;

i

A : the i-th web page, 1≤i≤m;

k: the total number of managers;

j i

W_, : the transformed fuzzy weight for importance of PageAi, evaluated by the j-th

ave i

W : the fuzzy average weight for importance of PageAi;

s

W : the fuzzy weight for importance of sequential sequence s;

connti: the count of PageAi;

α

ave

I : the fuzzy average weight of all possible linguistic terms of importance;

wsupi: the fuzzy weighted support of Page Ai;

minsup: the transformed fuzzy set from the linguistic minimum support value

α

wminsup: the fuzzy weighted set of minimum supports;

Cr: the set of candidate sequences with r web pages;

r

L : the set of large sequences with r web pages;.

5. The proposed algorithm for linguistic weighted web mining

Log data in a web site are used to analyze the browsing patterns on that site. Many fields

exist in a log schema. Among them, the fields date, time, client-ip and file name are used in

the mining process. Only the log data with .asp, .htm, .html, .jva and .cgi are considered web

pages and used to analyze the mining behavior. The other files such as .jpg and .gif are

thus reduced. The log data to be analyzed are sorted first in the order of client-ip and then in

the order of date and time. The web pages browsed by a client can thus be easily found. The

importance of web pages are considered and represented as linguistic terms. Linguistic

minimum support value is assigned in the mining process.

The proposed web-mining algorithm then uses the set of membership functions for

importance to transform managers’ linguistic evaluations of the importance of web pages into

fuzzy weights. The fuzzy weights of web pages from different mangers are then averaged.

The algorithm then calculates the weighted counts of web pages from browsing sequences

according to the average fuzzy weights of web pages. The given linguistic minimum support

value is also transformed into a fuzzy weighted set. All weighted large 1-sequences can thus

be found by ranking the fuzzy weighted support of each web page with fuzzy weighted

minimum support. After that, candidate 2-sequences are formed from weighted large

1-sequences and the same procedure is used to find all weighted large 2-sequences. This

procedure is repeated until all weighted large sequences have been found. Details of the

proposed mining algorithm are described below.

The weighted web-mining algorithm:

managers, two sets of membership functions respectively for importance and

minimum support, and a pre-defined linguistic minimum support value

α

OUTPUT: A set of weighted linguistic browsing patterns.

STEP 1: Select the records with file names including .asp, .htm, .html, .jva, .cgi and closing

connection from the log data; keep only the fields date, time, client-ip and file-name.

STEP 2: Transform the client-ips into contiguous integers (called encoded client ID) for

convenience, according to their first browsing time. Note that the same client-ip with

two closing connections is given two integers.

STEP 3: Sort the resulting log data first by encoded client ID and then by date and time.

STEP 4: Form a browsing sequence for each client ID by sequentially listing the web pages.

STEP 5: Transform each linguistic term of importance for web page Ai, 1≤i≤m, which is

evaluated by the j-th manager into a fuzzy set Wi,j of weights, using the given

membership functions of the importance of web pages.

STEP 6: Calculate the fuzzy average weight W_iave of each web page Ai by fuzzy addition as:

ave i W =

∑

STEP 7: Count the occurrences (counti) of each web page Ai appearing in the set of browsing

sequences; if Ai appears more than one time in a browsing sequence, its count

addition is still one; set the support (supporti) of Ai as counti / n’, where n’ is the

STEP 8: Calculate the fuzzy weighted support wsupi of each web page Ai as: wsupi = ' n W count_i × _iave .

STEP 9: Transform the given linguistic minimum support value

α

using the given membership functions of minimum supports.

STEP 10: Calculate the fuzzy weighted set (wminsup) of the given minimum support value as:

wminsup = minsup × (the gravity of ave

I ), where m I I m j j ave ∑ = = 1 ,

with Ij being the j-th membership function of importance. Iave represents the fuzzy

average weight of all possible linguistic terms of importance.

STEP 11: Check whether the weighted support (wsupi) of each web page Ai is larger than or

equal to the fuzzy weighted minimum support (wminsup) by fuzzy ranking. Any

fuzzy ranking approach can be applied here as long as it can generate a crisp rank. If

wsupi is equal to or greater than wminsup, put Ai in the set of large 1-sequences L1.

STEP 12: Set r=1, where r is used to represent the number of web pages kept in the current

large sequences.

STEP 13: Generate the candidate set Cr+1 from Lr in a way similar to that in the aprioriall

algorithm [1]. Restated, the algorithm first joins Lr and Lr, under the condition that

permutations represent different candidates. The algorithm then keeps in Cr+1 the

sequences which have all their sub-sequences of length r existing in Lr.

STEP 14: Do the following substeps for each newly formed (r+1)-sequence s with web

browsing pattern

(

)

(a) Calculate the fuzzy weight W of sequence s as: s

ave s ave s ave s s W1 W 2 W r 1 W + = Λ ΛKΛ _, where ave si

W is the fuzzy average weight of web page s , calculated in STEP 6. _i

If the minimum operation is used for the intersection, then:

ave s r i s MinWi W 1 1 + = = .

(b) Count the occurrences (counts) of sequence s appearing in the set of browsing

sequences; if s appears more than one time in a browsing sequence, its count

addition is still one; set the support (supports) of s as counts / n’, where n’ is the

number of browsing sequences.

(c) Calculate the weighted support wsup of sequence s as: s

' n count W

wsup_s = s × s _.

(d) Check whether the weighted support wsup of sequence s is greater than or equal s

to the fuzzy weighted minimum support wminsup by fuzzy ranking. If wsup is s

greater than or equal to wminsup, put s in the set of large (r+1)-sequences Lr+1.

STEP 16: For each large r-sequence s (r > 1) with weighted support wsups, find the linguistic

minimum support region Si with wminsupi≤ wsups < wminsupi+1 by fuzzy ranking,

where:

wminsupi = minsupi × (the gravity of Iave),

minsupi is the given membership function for Si. Output sequence s with linguistic

support value Si.

The linguistic sequential browsing patterns output after Step 16 can serve as

meta-knowledge concerning the given log data.

6. An example

In this section, an example is given to illustrate the proposed web-mining algorithm. This

is a simple example to show how the proposed algorithm can be used to generate weighted

linguistic browsing sequential patterns for clients' browsing behavior according to the log data

Table 1: A part of the log data used in the example

DATE TIME CLIENT-IP SERVER-IP SERVER-PORT FILE-NAME 2001-03-01 05:39:56 140.127.194.127 140.127.194.88 21 Inside.htm … 2001-03-01 05:40:08 140.127.194.127 140.127.194.88 21 home-bg1.jpg … 2001-03-01 05:40:10 140.127.194.127 140.127.194.88 21 line1.gif … : : : : : : … 2001-03-01 05:40:26 140.127.194.127 140.127.194.88 21 person.asp … : : : : : : … 2001-03-01 05:40:52 140.127.194.82 140.127.194.88 21 cheap.htm … 2001-03-01 05:40:53 140.127.194.82 140.127.194.88 21 line1.gif … : : : : : : … : : : : : : … 2001-03-01 05:41:08 140.127.194.128 140.127.194.88 21 cheap.htm … : : : : : : … 2001-03-01 05:48:38 140.127.194.44 140.127.194.88 21 closing connection … : : : : : : … 2001-03-01 05:48:53 140.127.194.22 140.127.194.88 21 cheap.htm … : : : : : : … 2001-03-01 05:50:13 140.127.194.20 140.127.194.88 21 search.asp … : : : : : : … 2001-03-01 05:53:33 140.127.194.20 140.127.194.88 21 closing connection …

Each record in the log data includes fields date, time, client-ip, server-ip, server-port and

file-name, among others. Only one file name is contained in each record. For example, the

user in client-ip 140.127.194.127 browsed the file inside.htm at 05:39:56 on March 1st, 2001.

For the log data shown in Table 1, the proposed web-mining algorithm proceeds as follows.

Step 1: The records with file names being .asp, .htm, .html, .jva, .cgi and closing

kept. Assume the resulting log data from Table 1 are shown in Table 2.

Table 2: The resulting log data for web mining.

DATE TIME CLIENT-IP FILE-NAME

2001-03-01 05:39:56 140.127.194.128 inside.htm 2001-03-01 05:40:26 140.127.194.128 person.asp 2001-03-01 05:40:52 140.127.194.82 cheap.htm 2001-03-01 05:41:08 140.127.194.128 cheap.htm 2001-03-01 05:41:30 140.127.194.22 homepage.htm 2001-03-01 05:41:54 140.127.194.82 inside.htm 2001-03-01 05:42:25 140.127.194.82 cheap.htm 2001-03-01 05:42:46 140.127.194.128 search asp 2001-03-01 05:43:02 140.127.194.22 cheap.htm 2001-03-01 05:43:46 140.127.194.44 inside.htm 2001-03-01 05:44:06 140.127.194.44 search asp 2001-03-01 05:44:07 140.127.194.82 closing connection 2001-03-01 05:44:17 140.127.194.128 closing connection 2001-03-01 05:44:31 140.127.194.22 closing connection 2001-03-01 05:45:47 140.127.194.44 person.asp 2001-03-01 05:46:46 140.127.194.38 cheap.htm 2001-03-01 05:47:45 140.127.194.44 inside.htm 2001-03-01 05:47:53 140.127.194.38 inside.htm 2001-03-01 05:47:56 140.127.194.44 search.asp 2001-03-01 05:48:19 140.127.194.38 search.asp 2001-03-01 05:48:38 140.127.194.44 closing connection 2001-03-01 05:48:53 140.127.194.20 cheap.htm 2001-03-01 05:49:33 140.127.194.38 closing connection 2001-03-01 05:50:13 140.127.194.20 search.asp 2001-03-01 05:51:14 140.127.194.20 person.asp 2001-03-01 05:53:16 140.127.194.20 inside.htm 2001-03-01 05:53:33 140.127.194.20 closing connection

each client’s first browsing time. The transformed results for Table 2 are shown in Table 3.

Totally six clients logged on the web server and five web pages including homepage.htm,

longin.htm, search.asp, cheap.htm and person.asp were browsed in this example.

Table 3: Transforming the values of field client-ip into contiguous integers.

DATE TIME CLIENT ID FILE-NAME

2001-03-01 05:39:56 1 inside.htm 2001-03-01 05:40:26 1 person.asp 2001-03-01 05:40:52 2 cheap.htm 2001-03-01 05:41:08 1 cheap.htm 2001-03-01 05:41:30 3 homepage.htm 2001-03-01 05:41:54 2 inside.htm 2001-03-01 05:42:25 2 cheap.htm 2001-03-01 05:42:44 1 search asp 2001-03-01 05:43:02 3 cheap.htm 2001-03-01 05:43:46 4 inside.htm 2001-03-01 05:44:06 4 search asp 2001-03-01 05:44:07 2 closing connection 2001-03-01 05:44:17 1 closing connection 2001-03-01 05:44:31 3 closing connection 2001-03-01 05:45:47 4 person.asp 2001-03-01 05:46:46 5 cheap.htm 2001-03-01 05:47:45 4 inside.htm 2001-03-01 05:47:50 5 inside.htm 2001-03-01 05:47:56 4 search.asp 2001-03-01 05:48:19 5 search.asp 2001-03-01 05:48:38 4 closing connection 2001-03-01 05:48:53 6 cheap.htm 2001-03-01 05:49:33 5 closing connection 2001-03-01 05:50:13 6 search.asp 2001-03-01 05:51:14 6 person.asp 2001-03-01 05:53:16 6 inside.htm 2001-03-01 05:53:33 6 closing connection

Step 3: The resulting log data in Table 3 are then sorted first by encoded client ID and

then by date and time. Results are shown in Table 4.

Table 4. The resulting log data sorted first by client ID and then by date and time

DATE TIME CLIENT ID FILE-NAME

2001-03-01 05:39:56 1 inside.htm 2001-03-01 05:40:26 1 person.asp 2001-03-01 05:41:08 1 cheap.htm 2001-03-01 05:42:46 1 search asp 2001-03-01 05:44:17 1 closing connection 2001-03-01 05:40:52 2 cheap.htm 2001-03-01 05:41:54 2 inside.htm 2001-03-01 05:42:25 2 cheap.htm 2001-03-01 05:44:07 2 closing connection 2001-03-01 05:41:30 3 homepage.htm 2001-03-01 05:43:02 3 cheap.htm 2001-03-01 05:44:31 3 closing connection 2001-03-01 05:43:46 4 inside.htm 2001-03-01 05:44:06 4 search asp 2001-03-01 05:45:47 4 person.asp 2001-03-01 05:47:45 4 inside.htm 2001-03-01 05:47:56 4 search.asp 2001-03-01 05:48:38 4 closing connection 2001-03-01 05:46:46 5 cheap.htm 2001-03-01 05:47:53 5 inside.htm 2001-03-01 05:48:19 5 search.asp 2001-03-01 05:49:33 5 closing connection 2001-03-01 05:48:50 6 cheap.htm 2001-03-01 05:50:13 6 search.asp 2001-03-01 05:51:14 6 person.asp 2001-03-01 05:53:16 6 inside.htm 2001-03-01 05:53:33 6 closing connection

Step 4: The web pages browsed by each client are listed as a browsing sequence. For

convenience, simple symbols are used here to represent web pages. Let A, B, C, D and E

respectively represent homepage.htm, inside.htm, search.asp, cheap.htm and person.asp. The

resulting browsing sequences from Table 4 are shown in Table 5.

Table 5: The browsing sequences formed from Table 4.

CLIENT ID BROWSING SEQUENCES

1 B, E, D, C 2 D, B, D 3 A, D 4 B, C, E, B, C 5 D, B, C 6 D, C, E, B

Step 5: Assume the importance of the five web pages (A, B, C, D, and E) is evaluated by

three managers as shown in Table 6.

Table 6: The importance of the web pages evaluated by three managers

MANAGER Important Important Important E Very Unimportant Unimportant Unimportant D Important Important Ordinary C Important Important Very Important B Ordinary Ordinary Important A MANAGER 3 MANAGER 2 MANAGER 1 WEB PAGE MANAGER Important Important Important E Very Unimportant Unimportant Unimportant D Important Important Ordinary C Important Important Very Important B Ordinary Ordinary Important A MANAGER 3 MANAGER 2 MANAGER 1 WEB PAGE

Also assume the membership functions for importance of the web pages are given in

Figure 2.

Figure 2: The membership functions of importance of the web pages in this example

In Figure 2, the importance of the web pages is divided into five fuzzy regions: Very

Unimportant, Unimportant, Ordinary, Important and Very Important. Each fuzzy region is

represented by a membership function. The membership functions in Figure 2 can be

represented as follows:

Very Unimportant (VU): (0, 0, 0.25),

Unimportant (U): (0, 0.25, 0.5),

Ordinary (O): (0.25, 0.5, 0.75),

Important (I): (05, 075, 1), and

Very Important (VI): (0.75, 1, 1).

Weight Membership value 1 1 0.5 0.25 0.75 Very Unimportant Unimportant Important Very Important Ordinary 0 0 Weight Membership value 1 1 0.5 0.25 0.75 Very Unimportant Unimportant Important Very Important Ordinary 0 0

MANAGER WEB PAGE (0.5, 0.75, 1) (0.5, 0.75, 1) (0.5, 0.75, 1) E (0, 0, 0.25) (0, 0.25, 0.5) (0, 0.25, 0.5) D (0.5, 0.75, 1) (0.5, 0.75, 1) (0.25, 0.5, 0.75) C (0.5, 0.75, 1) (0.5, 0.75, 1) (0.75, 1, 1) B (0.25, 0.5, 0.75) (0.25, 0.5, 0.75) (0.5, 0.75, 1) A MANAGER 3 MANAGER 2 MANAGER 1 MANAGER WEB PAGE (0.5, 0.75, 1) (0.5, 0.75, 1) (0.5, 0.75, 1) E (0, 0, 0.25) (0, 0.25, 0.5) (0, 0.25, 0.5) D (0.5, 0.75, 1) (0.5, 0.75, 1) (0.25, 0.5, 0.75) C (0.5, 0.75, 1) (0.5, 0.75, 1) (0.75, 1, 1) B (0.25, 0.5, 0.75) (0.25, 0.5, 0.75) (0.5, 0.75, 1) A MANAGER 3 MANAGER 2 MANAGER 1

The linguistic terms for the importance of the web pages given in Table 6 are

transformed into fuzzy sets by the membership functions in Figure 2. For example, Page A is

evaluated to be important by Manager 1. It can then be transformed as a triangular fuzzy set

(0.5, 0.75, 1) of weights. The transformed results for Table 6 are shown in Table 7.

Table 7: The fuzzy weights transformed from the importance of the web pages in Table 6.

Step 6: The average weight of each web page is calculated by fuzzy addition. Take Page

A as an example. The three fuzzy weights for A are respectively (0.5, 0.75, 1), (0.25, 0.5, 0.75)

and (0.25, 0.5, 0.75). The average weight is then ((0.5+0.25+0.25)/3, (0.75+0.5+0.5)/3,

(1+0.75+0.75)/3), which is derived as (0.33, 0.58, 0.83). The average fuzzy weights of all the

Table 8: The average fuzzy weights of all the web pages

WEB PAGE AVERAGE FUZZY WEIGHT

A (0.333, 0.583, 0.833)

B (0.583, 0.833, 1)

C (0.417, 0.667,0.917)

D (0, 0.167, 0.417)

E (0.5, 0.75, 1)

Step 7: The appearing number of each web page is counted from the browsing sequences

in Table 5. If a web page occurs more than one time in a sequence, it is counted once for this

sequence. Results for all the web pages are shown in Table 9.

Table 9: The counts of all the web pages

WEB PAGE COUNT

A 1

B 5

C 4

D 5

E 3

Step 8: The weighted support of each web page is calculated. Take Page A as an example.

The average fuzzy weight of A is (0.333, 0.583, 0.833) and the count is 1. Its weighted

support is then (0.333, 0.583, 0.833) * 1/ 6, which is (0.056, 0.097, 0.139). Results for all the

Table 10: The weighted supports of all the web pages

WEB PAGE WEIGHTED SUPPORT

A (0.056, 0.097, 0.139)

B (0.486, 0.694, 0.833)

C (0.278, 0.444, 0.611)

D (0, 0.139, 0.347)

E (0.25, 0.375, 0.5)

Step 9: The given linguistic minimum support value is transformed into a fuzzy set of

minimum supports. Assume the membership functions for minimum supports are given in

Figure 3.

Figure 3: The membership functions of minimum supports

Also assume the given linguistic minimum support value is “Middle”. It is then

transformed into a fuzzy set of minimum supports, (0.25, 0.5, 0.75), according to the given

membership functions in Figure 3.

Minimum support Membership value 1 1 0.5 0.25 0.75

Very Low Low Middle High Very High

0 0 Minimum support Membership value 1 1 0.5 0.25 0.75

Very Low Low Middle High Very High

0 0

Step 10: The fuzzy average weight of all possible linguistic terms of importance in

Figure 2 is first calculated as:

Iave = [(0, 0, 0.25) + (0, 0.25, 0.5) + (0.25, 0.5, 0.75) + (0.5, 0.75, 1) +(0.75, 1, 1)]/5

= (0.3, 0.5, 0.7).

The gravity of Iave is then (0.3+0.5+0.7)/3, which is 0.5. The fuzzy weighted set of

minimum supports for “Middle” is then (0.25, 0.5, 0.75) × 0.5, which is (0.125, 0.25, 0.375).

Step 11: The weighted support of each web page is compared with the fuzzy weighted

minimum support by fuzzy ranking. Any fuzzy ranking approach can be applied here as long

as it can generate a crisp rank. Assume the gravity ranking approach is adopted in this

example. Take Page B as an example. The average height of the weighted support for Page B

is (0.486 + 0.694 + 0.833)/3, which is 0.671. The average height of the fuzzy weighted

minimum support is (0.125 + 0.25 + 0.375)/3, which is 0.25. Since 0.671 > 0.25, B is thus a

large weighted 1- sequences. Similarly, C and E are large weighted 1-sequences. These

1-sequences are put in L1.

large sequences.

Step 13: The candidate set Cr+1 is generated from Lr. C2 is then first generated from L1 as

follows: (B, B), (B, C), (B, E), (C, B), (C, C), (C, E), (E, B), (E, C) and (E, E).

Step 14: The following substeps are done for each newly formed candidate 2-sequence in

C2.

(a) The fuzzy weights of all the 2-sequences in C2 are calculated. Here, the minimum

operator is used for intersection. Take the 2-sequence (B, C) as an example. Its fuzzy weight is

calculated as min((0.583, 0.833, 1), (0.417, 0.667, 0.917)), which is (0.417, 0.667, 0.917). The

results for all the 2-sequences are shown in Table 11.

Table 11: The fuzzy weights of the 2-sequences in C2.

2-SEQUENCE FUZZY WEIGHT

(B, B) (0.583, 0.833, 1) (B, C) (0.417, 0.667,0.917) (B, E) (0.5, 0.75, 1) (C, B) (0.417, 0.667,0.917) (C, C) (0.417, 0.667,0.917) (C, E) (0.417, 0.667,0.917) (E, B) (0.5, 0.75, 1) (E, C) (0.417, 0.667,0.917) (E, E) (0.5, 0.75, 1)

(b) The count of each candidate 2-sequence is found from the browsing sequences. If a

2-sequence occurs more than one time in a browsing sequence, it is counted once for this

browsing sequence. Results for this example are shown in Table 12.

Table 12: The counts of the 2- sequences

2-SEQUENCE COUNT (B, B) 1 (B, C) 3 (B, E) 2 (C, B) 2 (C, C) 1 (C, E) 2 (E, B) 2 (E, C) 2 (E, E) 0

(c) The weighted support of each candidate 2-sequence is calculated. Take the sequence

(B, C) as an example. The minimum fuzzy weight of (B, C) is (0.417, 0.667, 0.917) and the

count is 3. Its weighted support is then (0.417, 0.667, 0.917) * 3 / 6, which is (0.208, 0.333,

Table 13: The weighted supports of the 2-sequences

2-SEQUENCE WEIGHTED SUPPORT

(B, B) (0.097, 0.139, 0.167) (B, C) (0.208, 0.333, 0.458) (B, E) (0.167, 0.25, 0.333) (C, B) (0.139. 0.222, 0.306) (C, C) (0.069, 0.111, 0.153) (C, E) (0.139, 0.222, 0.306) (E, B) (0.167, 0.25, 0.333) (E, C) (0.139, 0.222, 0.306) (E, E) (0, 0, 0)

(d) The weighted support of each candidate 2-sequence is compared with the fuzzy

weighted minimum support by fuzzy ranking. As mentioned above, assume the gravity

ranking approach is adopted in this example. (B, C), (B, E) and (E, B) are then found to be

large weighted 2-sequences. These 2-sequences are put in L2.

Step 15: Since L2 is not null in the example, r = r + 1 = 2. Steps 13 to 15 are repeated to

find L3. C3 is then generated from L2. There are no large 3-sequences in the example. L3 is

thus an empty set.

STEP 16: The linguistic support value is found for each large r-sequence s (r > 1). Take

the sequential browsing pattern (E, B) as an example. Its weighted support is (0.167, 0.25,

(0.25, 0.5, 0.75) and for “High“ is (0.5, 0.75, 1). The weighted fuzzy set for these two regions

are (0.125, 0.25, 0.375) and (0.25, 0.375, 0.5). Since (0.125, 0.25, 0.375) ≤ (0.167, 0.25, 0.333)

< (0.25, 0.375, 0.5) by fuzzy ranking, the linguistic support value for sequence (E, B) is then

“Middle”. The linguistic supports of the other two large 2-sequences can be similarly derived.

All the three large sequential browsing patterns are then output as:

1. B -> C with a middle support,

2. B -> E with a middle support,

3. E -> B with a middle support.

The three linguistic sequential patterns above are thus output as the meta-knowledge

concerning the given log data.

7. Conclusion and future work

In this paper, we have proposed a new weighted web-mining algorithm, which can

process web-server logs to discover useful sequential browsing patterns with linguistic

supports. The web pages are evaluated by managers as linguistic terms, which are then

are used to find weighted sequential browsing patterns. Compared to previous mining

approaches, the proposed one has linguistic inputs and outputs, which are more natural and

understandable for human beings.

Although the proposed method works well in weighted web mining from log data, and

can effectively manage linguistic minimum supports, it is just a beginning. There is still much

work to be done in this field. Our method assumes that the membership functions are known

in advance. In [20-21, 23], we proposed some fuzzy learning methods to automatically derive

the membership functions. In the future, we will attempt to dynamically adjust the

membership functions in the proposed web-mining algorithm to avoid the bottleneck of

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