Markov Models for Page Prediction: Understanding User Browsing Behavior, Slides of Fundamentals of E-Commerce

Download Markov Models for Page Prediction: Understanding User Browsing Behavior and more Slides Fundamentals of E-Commerce in PDF only on Docsity!

The Cockburn and McKenzie study

from 2002

The number of distinct pages visited versus page vocabulary size of eachof the 17 users in the Cockburn and McKenzie (2002) study

The Cockburn and McKenzie study

from 2002

The number of distinct pages visited versus page vocabulary size of eachof the 17 users in the Cockburn and McKenzie (2002) study (log-log plot)

Video-based analysis of Web usage

Byrne et al. (1999) analyzed video-taped recordingsof eight different users over a period of 15 min to 1hour

Audio descriptions of the users was combined withthe video recordings of their screen for analysis

Study found

users spent a considerable amount of time scrolling Webpages

users spent a considerable amount of time waiting forpages to load (~15% of time)

Probabilistic models of browsing

behavior

Useful to build models that describe thebrowsing behavior of users

Can generate insight into how we use Web

Provide mechanism for making predictions

Can help in pre-fetching and personalization

Markov models for page prediction

For simplicity, consider order-dependent, time-independentfinite-state Markov chain with M states

Let s be a sequence of observed states of length L. e.g. s =ABBCAABBCCBBAA with three states A, B and C. s

t

is state at

position t (1<=t<=L). In general,

Under a first-order Markov assumption, we have

This provides a simple generative model to producesequential data

=

−

=

L t

t

t^

s s s P s P s P

2

1

1

1

)

,...,

| ( ) ( ) (

∏

=

−

=

L t

t

t

s s P s P s P

2

1

1

) | ( ) ( ) (

Markov models for page prediction

If we denote T

ij

= P(s

t

j

|s

t-

i

), we can define a M x M

transition matrix

Properties

Strong first-order assumption

Simple way to capture sequential dependence

If each page is a state and if W pages, O(W

2

), W can be of the

order 10

5

to 10

6

for a CS dept. of a university

To alleviate, we can cluster W pages into M clusters, eachassigned a state in the Markov model

Clustering can be done manually, based on directory structureon the Web server, or automatic clustering using clusteringtechniques

Markov models for page prediction

First-order Markov model assumes that the nextstate is based only on the current state

Limitations

Doesn’t consider ‘long-term memory’

We can try to capture more memory with

k

th-order

Markov chain

Limitations

Inordinate amount of training data O(M

k

1

1

1

k t t t t t

s s s P s s s P

−

−

−

Fitting Markov models to observed

page-request data

Assume that we collected data in the form of Nsessions from server-side logs, where

i

th

session s

i

i

<= N, consists of a sequence of L

i

page requests,

categorized into M – 1 states and terminating in E.Therefore, data D = {s

, …, s

N

Let

denote the set of parameters of the Markov

model,

consists of M

-1 entries in T

Let

denote the estimated probability of

transitioning from state

i

to

j

ij