WindMine: Fast and Effective Mining of Web-click Sequences Yasushi - - PowerPoint PPT Presentation

WindMine: Fast and Effective Mining

• f Web-click Sequences

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Yasushi Sakurai (NTT) Lei Li (Carnegie Mellon Univ.) Yasuko Matsubara (Kyoto Univ.) Christos Faloutsos (Carnegie Mellon Univ.)

Introduction

Web-click sequence applications

Web masters and web-site owners

• Capacity planning
• Intrusion detection
• Advertisement design

Goal

• Find meaningful patterns for web-click data

(e.g., the lunch-break trend, huge spike, anomalies)

• Find periodicity (daily and/or weekly, etc)
• Determine suitable window sizes automatically

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Introduction

Examples

access count from a business news site

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Original web-click sequence

Problem definition

Web-click sequences of m URLs:

(X1 , … , Xm)

Web-click sequence X of duration n : X = (x1 ,…, xt ,…, xn) Local Component Analysis: Given m sequences of duration n, (X1 , … , Xm)

• Find patterns, main components of the sequences
• Find the ‘best window’ size w for the analysis

Final challenge: scalable algorithm for the local component analysis

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Background

Independent component analysis (ICA)

• PCA vs. ICA

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1 PC 2 PC 1 IC 2 IC

Why not ‘PCA’?

Example of component analysis

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Source Mix

Why not ‘PCA’?

Example of component analysis

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ICA recognizes the components successfully and separately

PCA ICA

Main idea (1)

Multi-scale local component analysis

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Divide a sequence into subsequences of length w Compute the local components from the window matrix

a b c d e f g h

window matrix ˆ X B local components

a b c d e f g h

w = 2

a b c d e f g h

X

time

• riginal sequence

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Main idea (2)

Best window size selection Proposed criterion: CEM (Component Entropy Maximization)

• Estimate the optimal number of w for the sequence set
• Compute the entropy of the weight values of the mixing

matrix A

• ‘popular’ (widely-used) components show high CEM scores

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Q : How to estimate a ‘good window size’ automatically when we have multiple sequences?

Main idea (2)

CEM criterion:

• CEM score of the j-th component for the window size w
• Probability for the j-th component (size of the j-th

component’s contribution to each subsequence)

• Normalized weight values for each subsequences
• Mixing matrix

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k: # of components M: # of subsequences

å

• =

i j i j i j w

p p w C

, , ,

log 1

å

¢ ¢ =

i j i j i j i

a a p

, , ,

å

= ¢

j j i j i j i

a a a

2 , , ,

] [

, j i w

a A =

) , , 1 ; , , 1 ( k j M i ! ! = =

WindMine-part

Efficient solution Hierarchical partitioning approach: WindMine-part

• Partition the original window matrix into sub-matrices
• Extract local components each from the sub-matrices
• Reuse the local components for the component analysis on

the higher level

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Q : How do we efficiently extract the best local component from large sequence sets?

WindMine-part

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X :original sequence

...

local components window matrix sub-matrices

partition

:

ICA partition ICA

: :

Level 1 Level 2

Experimental Results

Experiments with real and datasets

Ondemand TV, WebClick, Automobile, Temperature, Sunspots

Evaluation

Accuracy for pattern discovery Accuracy for the best window size Computation time

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Pattern discovery

Ondemand TV

access count of users

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Original sequence

PCA: failed Anomaly spikes Weekly pattern Daily pattern

Pattern discovery

WebClick

Q & A site

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Weekly pattern Low activity during sleeping time Dip at dinner time Increase from morning to night and reach a peak

Pattern discovery

WebClick

job-seeking site

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High activity on week days (daily access decreases as the weekend approaches) Workers arrive at their office Job seeking during a short break Large spike during the lunch break

Pattern discovery

WebClick

• ther websites

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Educational site for kids (they visit here after school, 3pm) Website for baby nursery (the main users will be their parents, rather than babies!) High activity 8am-11pm, weekday (business purposes)

Pattern discovery

WebClick

• ther websites

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The users visit three times a day (early morning, noon, early evening) The users rarely visit here late in the evening (which is indeed good for their health!) Access count is still high in the night, 0am-1am (healthy diet should include an earlier bed time!) Access count increases after meal times

Pattern discovery

Generalization of WindMine

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Choice of best window size

CEM score for various window sizes

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Computation time

Wall clock time vs. # of subsequences

• Up to 70 times faster

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Computation time

Wall clock time vs. duration

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Conclusions

Scalable pattern extraction and anomaly detection in large web-click sequences

• 1. Scalable, parallelizable method for breaking

sequences into a few, fundamental ingredients

• 2. Linearly over the sequence duration, and

near-linearly on the number of sequence

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