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MEMEA Novel Technique for Learning Rare A Novel Technique for Learning Rare

EventsEvents

Margaret H. Dunham, Yu Meng, Jie HuangMargaret H. Dunham, Yu Meng, Jie Huang

CSE DepartmentCSE Department

Southern Methodist UniversitySouthern Methodist University

Dallas, Texas 75275Dallas, Texas 75275

mhd@engr.smu.edu

This material is based upon work supported by the National Science This material is based upon work supported by the National Science Foundation under Grant No. Foundation under Grant No. IIS-0208741 IIS-0208741

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Objectives/Outline

Develop modeling techniques which can “learn/forget” past behavior of spatiotemporal events. Apply to prediction of rare events.

Introduction EMM Overview EMM Applications to Rare Event Detection Future Work

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Objectives/Outline

Develop modeling techniques which can “learn/forget” past behavior of spatiotemporal events. Apply to prediction of rare events.

Introduction EMM Overview EMM Applications to Rare Event Detection Future Work

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Spatiotemporal Environment

Events arriving in a streamCan not look at a snapshot of the data.At any time, t, we can view the state of the problem at a site as represented by a vector of n numeric values:

Vt = <S1t, S2t, ..., Snt>

V2 V2 … V2

S1 S11 S12 … S1q

S2 S21 S22 … S2q

… … … … …

Sn Sn1 Sn2 … Snq

Time

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Spatiotemporal Modeling

Example Applications: Flood Prediction Rare Event Detection – Network traffic,

automobile traffic Requirements

Capture Time Capture Space Dynamic Scalable Quasi-Real Time

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Technique

Spatiotemporal modeling technique based on Markov models.

However – Size of MM depends on size of dataset The required structure of the MM is not known at the

model construction time. As the real world being modeled by the MM changes,

so should the structure of the MM. Thus not only should transition probabilities change, but the number of states should be changed to more accurately model the changing world.

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MM

A first order Markov Chain is a finite or countably infinite sequence of events {E1, E2, … } over discrete time points, where Pij = P(Ej | Ei), and at any time the future behavior of the process is based solely on the current state

A Markov Model (MM) is a graph with m vertices or states, S, and directed arcs, A, such that:

S ={N1,N2, …, Nm}, and A = {Lij | i 1, 2, …, m, j 1, 2, …, m} and Each

arc, Lij = <Ni,Nj> is labeled with a transition probability Pij = P(Nj | Ni).

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Problem with Markov Chains

The required structure of the MC may not be certain at the model construction time.

As the real world being modeled by the MC changes, so should the structure of the MC.

Not scalable – grows linearly as number of events. Markov Property Our solution:

Extensible Markov Model (EMM) Cluster real world events Allow Markov chain to grow and shrink dynamically

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Objectives/Outline

Develop modeling techniques which can “learn/forget” past behavior of spatiotemporal events. Apply to prediction of rare events.

Introduction

EMM Overview EMM Applications to Rare Event Detection Future Work

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Extensible Markov Model (EMM)

Time Varying Discrete First Order Markov Model Nodes are clusters of real world states. Learning continues during application phase. Learning:

Transition probabilities between nodes Node labels (centroid/medoid of cluster) Nodes are added and removed as data arrives

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Related Work Splitting Nodes in HMMs

Create new states by splitting an existing state M.J. Black and Y. Yacoob,”Recognizing facial expressions in image sequences using local

parameterized models of image motion”, Int. Journal of Computer Vision, 25(1), 1997, 23-48. Dynamic Markov Modeling

States and transitions are cloned G. V. Cormack, R. N. S. Horspool. “Data compression using dynamic Markov Modeling,” The

Computer Journal, Vol. 30, No. 6, 1987.

Augmented Markov Model (AMM) Creates new states if the input data has never been seen in the

model, and transition probabilities are adjusted Dani Goldberg, Maja J Mataric. “Coordinating mobile robot group behavior using a model of

interaction dynamics,” Proceedings, the Third International Conference on Autonomous Agents (agents ’99), Seattle, Washington

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EMM vs AMMOur proposed EMM model is similar to AMM, but is more flexible: EMM continues to learn during the application (prediction, etc.) phase. The EMM is a generic incremental model whose nodes can have any

kind of representatives. State matching is determined using a clustering technique. EMM not only allows the creation of new nodes, but deletion (or

merging) of existing nodes. This allows the EMM model to “forget” old information which may not be relevant in the future. It also allows the EMM to adapt to any main memory constraints for large scale datasets.

EMM performs one scan of data and therefore is suitable for online data processing.

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EMM

Extensible Markov Model (EMM): at any time t, EMM consists of an MM and algorithms to modify it, where algorithms include:

EMMSim, which defines a technique for matching between input data at time t + 1 and existing states in the MM at time t.

EMMBuild algorithm, which updates MM at time t + 1 given the MM at time t and classification measure result at time t + 1.

Additional algorithms are used to modify the model or for applications.

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EMMBuildInput: Vt = <S1, S2, …, Sn>: Observed values at n different locations at time t.

G: EMM with m states at time t-1.Nc:Current state at time t-1.

Output: G: EMM graph at time t.Nc:Current state at time t.

if G = empty then // Initialize G, first input vector is the first state N1 = Vt; CN1 = 0; Nc = N1;else // update G as new input comes in foreach Ni in G determine EMMSim(Vt, Ni); let Nn be node with largest similarity value, sim; if sim >= threshold then // update matching state information CNc = CNc + 1; if Lcn exists CLcn = CLcn + 1; else create new transition Lcn = <Nc,Nn>; CLcn = 1; Nc = Nn; else // create a new state Nm+1 represented by Vt create new node Nm+1; Nm+1 = Vt; CNm+1 = 0; create new transition Lc(m+1) = <Nc, Nm+1>; CLc(m+1) = 1; CNc = CNc + 1; Nc = Nm+1;

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EMMSim

Find closest node to incoming event. If none “close” create new node Labeling of cluster is centroid/medoid of

members in cluster Problem

O(n) BIRCH O(lg n)

• Requires second phase to recluster initial

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EMMBuild

<18,10,3,3,1,0,0><18,10,3,3,1,0,0>

<17,10,2,3,1,0,0><17,10,2,3,1,0,0>

<16,9,2,3,1,0,0><16,9,2,3,1,0,0>

<14,8,2,3,1,0,0><14,8,2,3,1,0,0>

<14,8,2,3,0,0,0><14,8,2,3,0,0,0>

<18,10,3,3,1,1,0.><18,10,3,3,1,1,0.>

1/3

N1

N2

2/3

N3

1/11/3

N1

N2

2/3

1/1

N3

1/1

1/2

1/3

N1

N2

2/31/2

1/2

N3

1/1

2/3

1/3

N1

N2

N1

2/21/1

N1

1

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EMMDecrement

•N2

•N1 •N3

•N5 •N6

•2/2

•1/3

•1/3

•1/3

•1/2

•N1 •N3

•N5 •N6

•1/6

•1/6

•1/6

•1/3

•1/3

•1/3

Delete N2

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EMM Advantages

Dynamic Adaptable Use of clustering Learns rare event Scalable:

Growth of EMM is not linear on size of data. Hierarchical feature of EMM

Creation/evaluation quasi-real time Distributed / Hierarchical extensions

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Growth of EMM

0

100

200

300

400

500

600

700

800

1 80 159

238

317

396

475

554

633

712

791

870

949

1028

1107

1186

1265

1344

1423

1502

number of input data (total 1574)

num

ber o

f st

ate

in m

ode

l

threshold 0.994

threshold 0.995

threshold 0.996

threshold 0.997

threshold 0.998

Servent Data

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EMM Performance – Growth Rate

Data Sim

Threshold

0.99 0.992 0.994 0.996 0.998

Serwent

Jaccrd 156 190 268 389 667

Dice 72 92 123 191 389

Cosine 11 14 19 31 61

Ovrlap 2 2 3 3 4

Ouse

Jaccrd 56 66 81 105 162

Dice 40 43 52 66 105

Cosine 6 8 10 13 24

Ovrlap 1 1 1 1 1

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EMM Performance – Growth Rate

Minnesota Traffic Data

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Error Rates

Normalized Absolute Ratio Error (NARE)

NARE =

Root Means Square (RMS)

RMS =

N

t

N

t

tO

tPtO

1

1

)(

|)()(|

N

tPtON

t

1

2))()((

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EMM Performance - Prediction

NARE RMSNo of States

RLF 0.321423 1.5389

EMMTh=0.95 0.068443 0.43774 20Th=0.99 0.046379 0.4496 56

Th=0.995 0.055184 0.57785 92

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EMM Water Level Prediction – Ouse Data

0

1

2

3

4

5

6

7

8

1

38

75

112

14

9

18

6

22

3

26

0

29

7

33

4

37

1

40

8

44

5

48

2

51

9

55

6

59

3

63

0

66

7

Input Time Series

Wa

ter

Le

ve

l (m

)

RLF Prediction EMM Prediction Observed

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Objectives/Outline

Develop modeling techniques which can “learn/forget” past behavior of spatiotemporal events. Apply to prediction of rare events.

Introduction EMM Overview

EMM Applications to Rare Event Detection

Future Work

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Rare Event

Rare - Anomalous – Surprising Out of the ordinary Not outlier detection

No knowledge of data distribution Data is not static Must take temporal and spatial values into account May be interested in sequence of events

Ex: Snow in upstate New York is not rare Snow in upstate New York in June is rare

Rare events may change over time

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Rare Event Examples

The amount of traffic through a site in a particular time interval as extremely high or low.

The type of traffic (i.e. source IP addresses or destination addresses) is unusual.

Current traffic behavior is unusual based on recent precious traffic behavior.

Unusual behavior at several sites.

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What is a Rare Event?

Not an outlier We don’t know anything about the distribution of

the data. Even if we did the data continues changing. A model created based on a static view may not fit tomorrow’s data.

We view a rare event as: Unusual state of the network (or subset thereof). Transition between network states which does

not frequently occur. Base rare event detection on determining events or

transitions between events that do not frequently occur.

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Rare Event Examples – VoIP Traffic

The amount of traffic through a site in a particular time interval as extremely high or low.

The type of traffic (i.e. source IP addresses or destination addresses) is unusual.

Current traffic behavior is unusual based on recent precious traffic behavior.

Unusual behavior at several sites.

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Rare Event Detection Applications

Intrusion Detection Fraud Flooding Unusual automobile/network traffic

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Rare Event Detection Techniques

Signature Based Created signatures for normal behavior Rule based Pattern Matching State Transition Analysis

Statistical Based Profiles of normal behavior

Data Mining Base Classification Clustering

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EMM Rare Event Prediction – VoIP Traffic

Predict rare events at a specific site (switch) representing an area of the network.

Use: Identify when rare transition occurs Identify rare event by creation of new node

Hierarchical EMM:

Collect rare event information at a higher level by constructing an EMM of more global events from several sites there.

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Our Approach

By learning what is normal, the model can predict what is not

Normal is based on likelihood of occurrence Use EMM to build model of behavior We view a rare event as:

Unusual event Transition between events states which does

not frequently occur. Base rare event detection on determining events

or transitions between events that do not frequently occur.

Continue learning

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EMMRare

EMMRare algorithm indicates if the current input event is rare. Using a threshold occurrence percentage, the input event is determined to be rare if either of the following occurs:

The frequency of the node at time t+1 is below this threshold

The updated transition probability of the MC transition from node at time t to the node at t+1 is below the threshold

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Determining Rare

Occurrence Frequency (OFc) of a node Nc as defined by:

OFc =

Likewise when determining what is meant by small for a transition probability, we should look at a normalized rather than actual value. We, thus, define the Normalized Transition Probability (NTPmn), from one state, Nm, to another, Nn, as:

NTPmn =

c ii

CN CN

mn ii

CL CN

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Ongoing/Future Work

Extend to Emerging Patterns Incorporate techniques to reduce False

Alarms Extend to Hierarchical/Distributed

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Conclusion

We welcome feedback