Master of Science

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Anomaly Detection Using Data Mining Techniques

Margaret H. Dunham, Yu Meng, Donya Quick, Jie
Huang, Charlie Isaksson CSE Department Southern
Methodist University Dallas, Texas
75275 mhd_at_engr.smu.edu This material is based
upon work supported by the National Science
Foundation under Grant No. IIS-0208741
2
Objectives/Outline

• Develop modeling techniques which can
  learn/forget past behavior of spatiotemporal
  stream events. Apply to prediction of anomalous
  events.
• Introduction
• EMM Overview
• EMM Applications to Anomaly Detection
• EMM Applications to Nuclear Testing
• Future Work

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Outline

• Introduction
• Motivation
• What is an anomaly?
• Spatiotemporal Data
• Modeling Spatiotemporal Data
• EMM Overview
• EMM Applications to Anomaly Detection
• Emm Applications to Nuclear Testing
• Future Work

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Motivation

• A growing number of applications generate streams
  of data.
• Computer network monitoring data
• Call detail records in telecommunications
• Highway transportation traffic data
• Online web purchase log records
• Sensor network data
• Stock exchange, transactions in retail chains,
  ATM operations in banks, credit card
  transactions.
• Data mining techniques play a key role in
  modeling and analyzing this data.

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What is Anomaly?

• Event that is unusual
• Event that doesnt occur frequently
• Predefined event
• What is unusual?
• What is deviation?

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What is Anomaly in Stream Data?

• 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 an anomaly
• Snow in upstate New York in June is rare
• Rare events may change over time

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Statistical View of Anomaly

• Outlier
• Data item that is outside the normal distribution
  of the data
• Identify by Box Plot

Image from Data Mining, Introductory and Advanced
Topics, Prentice Hall, 2002.
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Statistical View of Anomaly

• Identify by looking at distribution
• THIS DOES NOT WORK with stream data

Image from www.wikipedia.org, Normal distribution.
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Data Mining View of Anomaly

• Classification Problem
• Build classifier from training data
• Problem is that training data shows what is NOT
  an anomaly
• Thus an anomaly is anything that is not viewed as
  normal by the classification technique
• MUST build dynamic classifier
• Identify anomalous behavior
• Signatures of what anomalous behavior looks like
• Input data is identified as anomaly if it is
  similar enough to one of these signatures
• Mixed Classification and Signature

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Visualizing Anomalies

• Temporal Heat Map (THM) is a visualization
  technique for streaming data derived from
  multiple sensors.
• Two dimensional structure similar to an infinite
  table.
• Each row of the table is associated with one
  sensor value.
• Each column of the table is associated with a
  point in time.
• Each cell within the THM is a color
  representation of the sensor value
• Colors normalized (in our examples)
• 0 While
• 0.5 Blue
• 1.0 - Red

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THM of VoIP Data

• VoIP traffic data was provided by Cisco Systems
  and represents logged VoIP traffic in their
  Richardson, Texas facility from Mon Sep 22
  121732 2003 to Mon Nov 17 112911 2003.

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Spatiotemporal Stream Data

• Records may arrive at a rapid rate
• High volume (possibly infinite) of continuous
  data
• Concept drifts Data distribution changes on the
  fly
• Data does not necessarily fit any distribution
  pattern
• Multidimensional
• Temporal
• Spatial
• Data are collected in discrete time intervals,
• Data are in structured format, lta1, a2, gt
• Data hold an approximation of the Markov
  property.

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Spatiotemporal Environment

• Events arriving in a stream
• At any time, t, we can view the state of the
  problem as represented by a vector of n numeric
  values
• Vt ltS1t, S2t, ..., Sntgt

Time
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Data Stream Modeling

• Single pass Each record is examined at most once
• Bounded storage Limited Memory for storing
  synopsis
• Real-time Per record processing time must be low
• Summarization (Synopsis )of data
• Use data NOT SAMPLE
• Temporal and Spatial
• Dynamic
• Continuous (infinite stream)
• Learn
• Forget
• Sublinear growth rate - Clustering

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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 ltNi,Njgt 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.
• Our solution
• Extensible Markov Model (EMM)
• Cluster real world events
• Allow Markov chain to grow and shrink dynamically

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Outline

• Introduction
• EMM Overview
• EMM Applications to Anomaly Detection
• EMM Applications to Nuclear Testing
• 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 AMM

• Our proposed EMM model is similar to AMM, but is
  more flexible
• EMM continues to learn during the application
  phase.
• 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.
• EMMIncrement algorithm, which updates MM at time
  t 1 given the MM at time t and classification
  measure result at time t 1.
• Additional algorithms may be added to modify the
  model or for applications.

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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
• Nearest Neighbhor O(n)
• BIRCH O(lg n)
• Requires second phase to recluster initial

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EMMIncrement
lt18,10,3,3,1,0,0gt lt17,10,2,3,1,0,0gt lt16,9,2,3,1,0,
0gt lt14,8,2,3,1,0,0gt lt14,8,2,3,0,0,0gt lt18,10,3,3,1,
1,0.gt
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EMMDecrement
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
Servent Data
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EMM Performance Growth Rate
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EMM Performance Growth Rate
Minnesota Traffic Data
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Outline

• Introduction
• EMM Overview
• EMM Applications to Anomaly Detection
• EMM Applications to Nuclear Testing
• Future Work

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Datasets/Anomalies

• MnDot Minnesota Department of Transportation
• Automobile Accident
• Ouse and Serwent River flow data from England
• Flood
• Drought
• KDD Cup99
• http//kdd.ics.uci.edu/databases/kddcup99/kddcup9
  9.html
• Intrusion
• Cisco VoIP VoIP traffic data obtained at Cisco
• Unusual Phone Call

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Rare Event Detection
Detected unusual weekend traffic pattern
Weekdays Weekend
Minnesota DOT Traffic Data
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Our Approach to Detect Anomalies

• 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 t1 is below
  this threshold
• The updated transition probability of the MC
  transition from node at time t to the node at t1
  is below the threshold

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EMM Labels for Anomaly Detection

• Label of Nodes (CF)
• Cluster feature ltCNi, LSigt
• CNi cardinality
• LSi first moment (Medoid or Centroid based)
  give defines here.
• Label of Links
• ltCLijgt

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Determining Rare

• Occurrence Frequency (OFc) of a node Nc
• OFc
• Normalized Transition Probability (NTPmn), from
  one state, Nm, to another, Nn
• NTPmn

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EMMRare

• Given
• Rule1 CNi lt thCN
• Rule2 CLij lt thCL
• Rule3 OFc lt thOF
• Rule4 NTPmn lt thNTP
• Input Gt EMM at time t
• i Current state at time t
• R R1, R2,,RN A set of rules
• Output At Boolean alarm at time t
• Algorithm
• At

1 ?Ri True 0 ?Ri False
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Rare Event in Cisco Data
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Risk assessment

• Problem Mitigate false alarm rate while
  maintaining a high detection rate.
• Methodology
• Historic feedbacks can be used as a free resource
  to take out some possibly safe anomalies
• Combine anomaly detection model and users
  feedbacks.
• Risk level index
• Evaluation metrics Detection rate, false alarm
  rate.
• Detection rate
• False alarm rate
• Operational Curve

Detection rate TP/(TPTN) False alarm rate
FP/(TPFP)
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Reducing False Alarms

• Calculate Risk using historical feedback
• Historical Feedback
• Count of true alarms

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Detection Rate Experiments
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False Alarm Rate
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Outline

• Introduction
• EMM Overview
• EMM Applications to Anomaly Detection
• EMM Applications to Nuclear Testing
• Future Work

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Research Objectives

• Apply proven spatiotemporal modeling technique to
  seismic data
• Construct EMM to model sensor data
• Local EMM at location or area
• Hierarchical EMM to summarize lower level models
• Represent all data in one vector of values
• EMM learns normal behavior
• Develop new similarity metrics to include all
  sensor data types (Fusion)
• Apply anomaly detection algorithms

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Input Data Representation

• Vector of sensor values (numeric) at precise time
  points or aggregated over time intervals.
• Need not come from same sensor types.
• Similarity/distance between vectors used to
  determine creation of new nodes in EMM.

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EMM with Seismic Data

• Input Wave arrivals (all or one per sensor)
• Identify states and changes of states in seismic
  data
• Wave form would first have to be converted into a
  series of vectors representing the activity at
  various points in time.
• Initial Testing with RDG data
• Use amplitude, period, and wave type

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New Distance Measure

• Data ltamplitude, period, wave typegt
• Different wave type 100 difference
• For events of same wave type
• 50 weight given to the difference in amplitude.
• 50 weight given to the difference in period.
• If the distance is greater than the threshold, a
  state change is required.
•  ?amplitude
• amplitudenew amplitudeaverage /
  amplitudeaverage
• ?period
• periodnew periodaverage /
  periodaverage

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EMM with Seismic Data
States 1, 2, and 3 correspond to Noise, Wave A,
and Wave B respectively.
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Preliminary Testing

• RDG data February 1, 1981 6 earthquakes
• Find transition times close to known earthquakes
• 9 total nodes
• 652 total transitions
• Found all quakes

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Outline

• Introduction
• EMM Overview
• EMM Applications to Anomaly Detection
• EMM Applications to Nuclear Testing
• Future Work

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Ongoing/Future Work

• Extend to Emerging Patterns
• Extend to Hierarchical/Distributed
• Yu Su
• Test with more data KDD Cup
• Compare to other approaches
• Charlie Isaksson
• Apply to nuclear testing

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Hierarchical EMM
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• Thanks!

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References

• Zhigang Li and Margaret H. Dunham, STIFF A
  Forecasting Framework for Spatio-Temporal Data,
  Proceedings of the First International Workshop
  on Knowledge Discovery in Multimedia and Complex
  Data, May 2002, pp 1-9.
• Zhigang Li, Liangang Liu, and Margaret H. Dunham,
  Considering Correlation Between Variables to
  Improve Spatiotemporal Forecasting, Proceedings
  of the PAKDD Conference, May 2003, pp 519-531.
• Jie Huang, Yu Meng, and Margaret H. Dunham,
  Extensible Markov Model, Proceedings IEEE ICDM
  Conference, November 2004, pp 371-374.
• Yu Meng and Margaret H. Dunham, Efficient
  Mining of Emerging Events in a Dynamic
  Spatiotemporal, Proceedings of the IEEE PAKDD
  Conference, April 2006, Singapore. (Also in
  Lecture Notes in Computer Science, Vol 3918,
  2006, Springer Berlin/Heidelberg, pp 750-754.)
• Yu Meng and Margaret H. Dunham, Mining
  Developing Trends of Dynamic Spatiotemporal Data
  Streams, Journal of Computers, Vol 1, No 3,
  June 2006, pp 43-50.
• Charlie Isaksson, Yu Meng, and Margaret H.
  Dunham, Risk Leveling of Network Traffic
  Anomalies, International Journal of Computer
  Science and Network Security, Vol 6, No 6, June
  2006, pp 258-265.
• Margaret H. Dunham and Vijay Kumar, Stream
  Hierarchy Data Mining for Sensor Data,
  Innovations and Real-Time Applications of
  Distributed Sensor Networks (DSN) Symposium,
  November 26, 2007, Shreveport Louisiana.