Sequence Classification Using Statistical Pattern Recognition

José Antonio Iglesias, Agapito Ledezma and Araceli Sanchis Sequence Classification Using Statistical Pattern

Recognition

Sequence Classification Using Statistical Pattern Recognition

José Antonio Iglesias, Agapito Ledezma, and Araceli Sanchis

Computer Science Department Universidad Carlos III de Madrid

Avda. de la Universidad, 30. 28911 Leganés, Spain{jiglesia, ledezma, masm}@inf.uc3m.es

.


Recognition

Motivation and Introduction Sequence classification Our approach

Library Creation Classification

Target Environment Description Experiments and Results

Conclusions and Future Works

OutlineOutline

.

1


Recognition

Motivation and IntroductionMotivation and Introduction Sequence classification Our approach


Target Environment Description Experiments and Results


1

OutlineOutline


Recognition

Opponent behavior Modelling / Classification(Environment: soccer simulation domain)

MotivationMotivation

.

2

Opponent Modeling

Pattern Recognition

Off-Line Analysis

No-Pattern LogFile

Pattern LogFile

Base Estrategy

Pattern

Recognized Patterns

On-Line Comparing Method

Pattern Detection

On-Line Detection

Environment Information Advices to

Players

RoboCup Soccer Server

Pattern Recognized


Recognition

Behavior ClassificationBehavior Classification

Behavior as sequence of elements

Sequence ClassificationSequence Classification

IntroductionIntroduction

.

3

SequenceSequence::

“set of elements ordered so that they can be labelled with the positive integers” (Merriam-Webster Dictionary)


Recognition

Motivation and Introduction

Sequence classificationSequence classification Our approach


Target Environment Description Experiments & Results


4

OutlineOutline


Recognition

• Given:

Classes = {cClasses = {c11, c, c22, … c, … cnn}}

Sequence E = {eSequence E = {e11, e, e22, … e, … enn}}

• Determine: Which class ci Є C does the sequence E belong to.

Sequence classificationSequence classification

5


Recognition

Motivation and Introduction Sequence classification

Our approachOur approach Library Creation Classification



.

6

OutlineOutline


Recognition

Our approachOur approach

pwd

fs

fg

…

vi

man

ls

…

…finger

more

ls

...Sequence 1

Class 1Sequence 2

Class 2Sequence n

Class n

Pattern 1 Pattern 2 Pattern 3

…

Pattern Library


vi

more

ls

…Pattern to classify

Sequence to classify

Compare_Patterns

Compare_Patterns

Compare_Patterns

…

On-Line Sequence

Classification

SEQUENCE CLASS

Classification Result

.

7


Recognition


Our approachOur approach Library CreationLibrary Creation Classification



8

OutlineOutline


Recognition

Library CreationLibrary Creation

.

TrieTrie (re (retrietrieval)val) data structure data structure::

Special search tree used for storing elements and its prefixes.Special search tree used for storing elements and its prefixes.

Every node: Every node: – represents an element– stores useful information (times appeared,…)

9


Recognition

Library Creation - Library Creation - An example trieAn example trie

Sequence to insert initially in the trie: {pwd vi pwd vi pwd ls}

pwd

vi

pwd

vi

pwd

ls

Sequence

10


Recognition


Sequence to insert initially in the trie: {pwd vi pwd vi pwd ls}

Sub-sequence length: 3Sub-sequence length: 3 {pwd vi pwd vi pwd ls}

Sub-sequences to insert in the trie: {pwd vi pwd} and {vi pwd ls}

pwd

vi

pwd

vi

pwd

ls

Sequence

10


Recognition

Library CreationLibrary Creation - - An example trieAn example trie

Sub-sequences to insert in the trie: {pwd pwd vi vi pwd pwd} and {vi pwd ls}

Root

11


Recognition


Sub-sequences to insert in the trie: {pwd pwd vi vi pwd pwd} and {vi pwd ls}

Root

pwd [1]

vi [1]

pwd [1]

11


Recognition


Sub-sequences to insert in the trie: {pwd vi vi pwd pwd} and {vi pwd ls}

Root

pwd [1]

vi [1]

pwd [1]

vi [1]

pwd [1]

11


Recognition


Sub-sequences to insert in the trie: {pwd vi vi pwdpwd} and {vi pwd ls}

Root

pwd [2]

vi [1]

pwd [1]

vi [1]

pwd [1]

11


Recognition



Root

pwd [2]

vi [1]

pwd [1]

vi [2]

pwd [2]

ls [1]

11


Recognition



Root

pwd [3]

vi [1]

pwd [1]

vi [2]

pwd [2]

ls [1]

ls [1]

11


Recognition



Root

pwd [3]

vi [1]

pwd [1]

vi [2]

pwd [2]

ls [1]

ls [1]

ls [1]

11


Recognition


{pwd vi vi pwd pwd vi pwd ls}

Root

pwd [3]

vi [1]

pwd [1]

vi [2]

pwd [2]

ls [1]

ls [1]

ls [1]

11

pwd

vi

pwd

vi

pwd

ls


Recognition

Evaluate the relation/dependence between an element and its prefix

Two approaches:

– Frequency-based method. Statistical dependence method.

Our approach: Statistical Value used: Chi-square value.

This value is stored in every node of the trie

Library Creation - Library Creation - Evaluating DependencesEvaluating Dependences

12


Recognition

EventDifferent

eventTotal

Prefix O11 O12 O11 + O12

Different Prefix

O21 O22 O21 + O22

Total O11+ O21 O12+ O22

O11 + O12+

O21 + O22

O11: How many times the current node/element is followed by its prefix.

O12: How many times the current node/element is followed by a different prefix.O21: How many times a different prefix (of the same length) is followed by the same node.O22: How many times a different prefix (of the same length) is followed by a different node.

Expected (Eij)= (Rowi Total x Columnj Total)

Grand Total

X2 = ∑ ∑(Oij - Eij ) 2

Eiji=1

r k

2 x 2 Contingency Table


j=1

.

13


Recognition


.

pwd [3]

vi [1] [5.1][5.1]

pwd [1] [4.3][4.3]

vi [2]

pwd [2] [3.5][3.5]

ls [1] [4.3][4.3]

ls [1] [4.3][4.3]

ls [2]

Sequence Pattern Trie

Root

A Sequence Pattern Trie is created for each class.

14


Recognition


Our approachOur approach Library Creation ClassificationClassification



15

OutlineOutline


Recognition

ClassificationClassification

pwd

fs

fg

…

vi

man

ls

…

…

finger

more

ls

...Sequence 1

Class 1Sequence 2

Class 2Sequence n

Class n

Pattern 2 Pattern 3

…

Pattern Library

Classification

vi

more

ls

…


Compare_Patterns

Compare_Patterns

…

On-Line Sequence

Classification

ONLINE SEQUENCE

CLASS

.

Library Creation

Pattern to classify

TestingTesting TrieTrie

Pattern 1

Compare_Patterns

ClassClass TrieTrie

16


Recognition

.

17

pwd [3]

vi [1] [5.1][5.1]

who [1] [4.3][4.3]

vi [2]

who [2] [3.5][3.5]

Root

Classification – Comparing ProcessClassification – Comparing ProcessClass Trie Testing Trie

pwd [3]

vi [1] [7.1][7.1]

pwd [1] [[7.3]7.3]

vi [2]

pwd [2] [1.5][1.5]

ls [1] [0.3][0.3]

ls [2]

Root

…

If the node (and its prefix) are in both Tries:

If ( abs(chi2TestingTrie – chi2

ClassTrie) ≤ ThresholdValue ):

SimilaritySimilarity between both tries.

Result [ElementTestingTrie, PrefixTestingTrie, ChiChi22TestingTrieTestingTrie]


Recognition

.

17

pwd [3]

vi [1] [5.1][5.1]

who [1] [4.3][4.3]

vi [2]

who [2] [3.5][3.5]

Root


pwd [3]

vi [1] [7.1][7.1]

pwd [1] [[7.3]7.3]

vi [2]

pwd [2] [1.5][1.5]

ls [1] [0.3][0.3]

ls [2]

Root

…

If the node (and its prefix) are in both Tries:

If (abs(5.1 – 7.1) ≤ ThresholdValue ):

SimilaritySimilarity between both tries.

Result [vi , pwd, 5.15.1]


Recognition

.

17

pwd [3]

vi [1] [5.1][5.1]

who [1] [4.3][4.3]

vi [2]

who [2] [3.5][3.5]

Root


pwd [3]

vi [1] [7.1][7.1]

pwd [1] [[7.3]7.3]

vi [2]

pwd [2] [1.5][1.5]

ls [1] [0.3][0.3]

ls [2]

Root

…

If the node (and its prefix) are only in the Testing Trie:

DifferenceDifference between both tries.

Result Result [Element [ElementTestingTrieTestingTrie, Prefix, PrefixTestingTrieTestingTrie, , (Chi(Chi22TestingTrieTestingTrie * -1) * -1)]]


Recognition

.

17

pwd [3]

vi [1] [5.1][5.1]

who [1] [4.3][4.3]

vi [2]

who [2] [3.5][3.5]

Root


pwd [3]

vi [1] [7.1][7.1]

pwd [1] [[7.3]7.3]

vi [2]

pwd [2] [1.5][1.5]

ls [1] [0.3][0.3]

ls [2]

Root

…



Result Result [who, pwd [who, pwd vi, vi, (-4.3)(-4.3)]]


Recognition

.

17

pwd [3]

vi [1] [5.1][5.1]

who [1] [4.3][4.3]

vi [2]

who [2] [3.5][3.5]

Root


pwd [3]

vi [1] [7.1][7.1]

pwd [1] [[7.3]7.3]

vi [2]

pwd [2] [1.5][1.5]

ls [1] [0.3][0.3]

ls [2]

Root

…



Result Result [who, vi, [who, vi, (-3.5)(-3.5)]]


Recognition

ResultResult:[Element1, Prefix1, ValueValue11]

[Element2, Prefix2, ValueValue22]



…

[Elementn, Prefixn, ValueValuenn]

Each comparison (ClassTrie, TestingTrie):

A comparision value

.

Comparison Value

18

Classification – Comparing ProcessClassification – Comparing Process


Recognition

ResultResult:[vi, pwd, + 5.1+ 5.1]

[who, pwd vi, - 4.3- 4.3]

[who, pwd, - 3.5- 3.5]

.

- 2.7

18

Classification – Comparing ProcessClassification – Comparing Process

Comparison Value


Recognition


pwd

fs

fg

…

vi

man

ls

…

…

finger

more

ls

...Sequence 1

Class 1Sequence 2

Class 2Sequence n

Class n


…

Pattern Library


vi

more

ls

…Pattern

to classify


…

ONLINE SEQUENCE

CLASS

On-Line Sequence

Classification

Compare_Patterns

Compare_Patterns

Compare_Patterns

comparision value

comparision value

comparision value

.

19


Recognition

comparision value

comparision value

comparision value


pwd

fs

fg

…

vi

man

ls

…

…

finger

more

ls

...Sequence 1

Class 1Sequence 2

Class 2Sequence n

Class n


…

Pattern Library


vi

more

ls

…Pattern to classify


Compare_Patterns

Compare_Patterns

Compare_Patterns

…

ONLINE SEQUENCE

CLASS

On-Line Sequence

Classification

Greatest Comparison

Value

.

20


Recognition

Motivation and Introduction Sequence classification Our approachOur approach


Target EnvironmentTarget Environment DescriptionDescription Experiments & Results


21

OutlineOutline


Recognition

Environment –Environment – UNIX command line sequences UNIX command line sequences

# Start session 1# Start session 1 cd ~/private/docs ls -laF | more cat foo.txt bar.txt zorch.txt > a.txt exit# End session 1# End session 1

# Start session 2 cd ~/games/ xquake & fg …

**SOF****SOF**cd<1>ls-laF|morecat<3>><1>exit**EOF****EOF**…

one "file name" argument

three "file name" arguments

one "file name" argument

Command histories of 9 UNIX computer usersUNIX computer users at over 2 yearsUCI Repository of ML Database [Newman C., Hettich S., Merz, C. (1998)]

22


Recognition



Target EnvironmentTarget Environment Description Experiments & ResultsExperiments & Results


23

OutlineOutline


Recognition

9 files (users) containing from about 10.000 to 60.000 commands each. 1. 1. Extracting Patterns:Extracting Patterns: A trie is created for each user Pattern Library

Experiments Experiments – – UNIX command line sequencesUNIX command line sequences

.

24


Recognition



.

24

2. 2. Classification Algorithm:Classification Algorithm: Sequence to classify (sequences of very different sizes) Classified in the class with the greatest value (result value).


Recognition



.

24

2. 2. Classification Algorithm:Classification Algorithm: Sequence to classify (sequences of very different sizes) Classified in the class with the greatest value (result value).

3. 3. Evaluating the result:Evaluating the result: Calculate:

difference between the greatest value and the second greatest value (+)(+)x difference between the real classification value and the greatest value (-)(-)

(The greater the difference, the better the classification)


Recognition

Results Results – – UNIX command line sequencesUNIX command line sequences

Unix Commands Classification – User 6

.

average of 25 simulation results

25

Cla

ssif

icat

ion

Val

ue

Length of the Sequence to classify


Recognition

Results Results – – UNIX command line sequencesUNIX command line sequences

Minimum length for classifying a UNIX Computer User correctly

.

26

Unix Computer User (Class)

Len

gth

of

the

Seq

uen

ce t

o c

lass

ify


Recognition




Conclusions and Future WorksConclusions and Future Works

27

OutlineOutline


Recognition

A threshold must be found

Long time for creating the tries

Results depend on the length of the sub-sequences used to create the trie

ConclusionsConclusions

28


Recognition

Effective method to classify UNIX users

If a behavior can be represented by sequences,

the proposed classification method can be used

If a new class is added, only its trie must be created (the others are not modified)

This method could be used for other tasks:

sequence prediction, sequence clustering…

RoboCup Coach 2006 Competition (succesfully results)

ConclusionsConclusions

29


Recognition

Pattern Library One Trie for all classes (users).

Classification method without threshold value

Analysis comparing our approach to others (HMMs)

Future WorksFuture Works

30


Recognition





.

Thank you!Thank you!


Recognition





.

QuestionsQuestions


Recognition




Avda. de la Universidad, 30. 28911 Leganés, Spain{ jiglesia, ledezma, masm}@inf.uc3m.es

.

Related to Questions...Related to Questions...

29


Recognition


**SOF****SOF**cd<1>ls-laF|morecat<3>>……

Pattern/Class User0

**SOF****SOF**ls<1>exit<1>ls-laFxquake&fg……

**SOF****SOF**vi<1>vi<3>ls-lacat<2>……

USER 0

Class0

USER 1

Class1

USER 8

Class8

…

…

Pattern Library

**SOF****SOF**ls-laF|Morecd<4>

…Test User

Sequence ClassificationPattern/Class

User1Pattern/Class

User8

User On-Line

Є Class c

User On-Line vs Class User0 21






User On-Line vs Class User6 -1



ClassUser1


Recognition



Pattern/Class User0



USER 0

Class0

USER 1

Class1

USER 8

Class8

…

…

Pattern Library


…Test User


User1Pattern/Class

User8

User On-Line

Є Class c


User On-Line vs Class User1 User On-Line vs Class User1 49 49








ClassUser1


Recognition



Pattern/Class User0



USER 0

Class0

USER 1

Class1

USER 8

Class8

…

…

Pattern Library


…Test User


User1Pattern/Class

User8

User On-Line

Є Class c










ClassUser1

Correctly ClassifiedCorrectly Classified


Recognition



Pattern/Class User0



USER 0

Class0

USER 1

Class1

USER 8

Class8

…

…

Pattern Library


…Test User


User1Pattern/Class

User8

User On-Line

Є Class c










ClassUser1

Correctly ClassifiedCorrectly Classified

20


Recognition



Pattern/Class User0



USER 0

Class0

USER 1

Class1

USER 8

Class8

…

…

Pattern Library


…Test User


User1Pattern/Class

User8

User On-Line

Є Class c










ClassUser2


Recognition



Pattern/Class User0



USER 0

Class0

USER 1

Class1

USER 8

Class8

…

…

Pattern Library


…Test User


User1Pattern/Class

User8

User On-Line

Є Class c










NO Correctly NO Correctly ClassifiedClassified

ClassUser2


Recognition



Pattern/Class User0



USER 0

Class0

USER 1

Class1

USER 8

Class8

…

…

Pattern Library


…Test User


User1Pattern/Class

User8

User On-Line

Є Class c










NO Correctly NO Correctly ClassifiedClassified

- 40

ClassUser2

Sequence Classification Using Statistical Pattern Recognition

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