Dr. Hesam Izakian October 2014. 2 Spatial time series Problem formulation Anomaly detection in spatial time series- questions Overall scheme

Cluster-Centric Anomaly Detection and

Characterization in Spatial Time Series

Dr. Hesam Izakian

October 2014

2

Spatial time series Problem formulation Anomaly detection in spatial time series- questions Overall scheme of the proposed method

o Time series segmentationo Spatial time series clusteringo Assigning anomaly scores to clusterso Visualizing the propagation of anomalies

An outbreak detection scenario Application Conclusions

Outline

3

Structure of datao A set of spatial coordinateso One or more time series for

each point

Exampleso Daily average temperature in different climate stationso Stock market indexes in different countrieso Number of absent students in different schoolso Number emergency department visits in different hospitalso Measured signals in different parts of brain

Spatial time series

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There are N spatial time series

Objective: Find a spatial neighborhood of data

In a time interval

Containing a high level of unexpected changes

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Problem formulation

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Spatial neighborhood of datao Size of neighborhoodo Overlapping neighborhoods

Unexpected changes (anomalies)o What kind of changes are expected/not expectedo How to evaluate the level of unexpected changes

Anomaly visualization Anomaly characterization

o What was the source of anomalyo How the anomaly is propagated over time

Anomaly detection in spatial time series- questions

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Revealing the structure of data in various time intervals Comparing the revealed structures

Overall scheme of the proposed method

Sliding window

Spatial time series clustering

Spatial time series data

KUUU ,,, 21

Anomaly scores

Fuzzy relations

Ksss ,,, 21

KKRRR 1,-2,32,1 ,,,


KWWW ,,, 21

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Time series part segmentation

Sliding windowo Spatio-temporal subsequenceso Local view of time series part

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Sliding window



KWWW ,,, 21

KUUU ,,, 21

Anomaly scores

Fuzzy relations

Ksss ,,, 21

KKRRR 1,-2,32,1 ,,,

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Fuzzy C-Means clustering- visual illustration

1 1 1 1 1 0 0 0 0 00 0 0 0 0 1 1 1 1 1

BA

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Fuzzy C-Means clustering- visual illustration

0.91 0.96 1.00 0.95 0.70 0.30 0.05 0.00 0.04 0.090.09 0.04 0.00 0.05 0.30 0.70 0.95 1.00 0.96 0.91

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Fuzzy C-Means clustering…

Partitions N data Into clusters Result:

Objective function:

Minimization:

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12

Reveals available structure within datao In form of partition matrices

Challengeso Different sources: Spatial part vs. temporal parto Different dimensionality in each parto Different structure within each part


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In spatial time series, we define

Adopted FCM objective function

Characteristicso When λ=0: Only spatial part of data in clusteringo A higher value of λ : a higher impact of time series part in

clusteringo Optimal value of λ: Optimal impact of each part in clustering

Spatial time series clustering…

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Spatial-time series clustering- Optimal value of λ

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15



Sliding window



KWWW ,,, 21

KUUU ,,, 21

Anomaly scores

Fuzzy relations

Ksss ,,, 21

KKRRR 1,-2,32,1 ,,,

16

Assign an anomaly score to each single subsequence based on historical data

Aggregating anomaly scores inside revealed clusters

Assigning anomaly scores to clusters in different time windows

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17



Sliding window



KWWW ,,, 21

KUUU ,,, 21

Anomaly scores

Fuzzy relations

Ksss ,,, 21

KKRRR 1,-2,32,1 ,,,

18

Visualizing the propagation of anomalies- Fuzzy relations

Objective: quantifying relations between clusters

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19

Visualizing the propagation of anomalies…

Objective function to construct relation

Optimization

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Example

An outbreak o In southern part of Albertao Using NAADSM for 100 days

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Example…

A sliding window is usedo Length : 20o Movement: 10

Generated spatio-temporal subsequences:

22

23

Example…

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Example…

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Example…

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Example…

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Application Implemented for Agriculture and Rural Development

(Government of Alberta) Using KNIME (Konstanz Information Miner) Animal health surveillance in Alberta Anomaly detection Data visualization

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Conclusions

A framework for anomaly detection and characterization in spatial time series is developed

A sliding window to generate a set of spatio-temporal subsequences is considered

Clustering is used to discover the available structure within the spatio-temporal subsequences

An anomaly score assigned to each revealed spatio-temporal cluster

A fuzzy relation technique is proposed to quantify the relations between clusters in successive time steps

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Thank you

Documents

Dr. Hesam Izakian October 2014. 2 Spatial time series Problem formulation Anomaly detection in spatial time series- questions Overall scheme