Emerging Spatial Hotspots Detection

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Emerging Spatial Hotspots Detection

• Antony Philip (Group 7)
• http//webpages.charter.net/antonyp/csci8715.htm
• Date 05/01/2006

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Motivation - Applications

• Disease outbreak
• SARS, Bird Flu
• Mumps cases in IA, MN
• Traffic Incident Control
• Crime prevention
• Computer intrusion detection
• Severe Weather detection/prediction

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Definitions

• Spatial Outlier
• Inconsistent value of a spatial location based on
  the neighborhood statistics of that value at a
  particular time
• Emerging spatial outlier hotspots
• Spatial outliers which show significant and
  consistent change in the outlierness as time
  increases

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Problem Statement

• Given
• Time sequenced data values for the N spatial
  locations, F(T,N) f(t,n), tT-W1..T, n1..N.
  T is the present time and we have W frames of
  data, one per each time instance
• Output
• Set of identified spatial outliers in each of the
  spatial frames of data
• Subset of outliers identified at time t-L1 which
  are continue to be marked as spatial outliers in
  all the frames t-L1, t and now in t can be
  marked as potential hotspots.

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Procedural Steps

• Model Building
• Spatial Neighborhood Statistics
• Temporal Neighborhood Variation Statistics
• Test (Outliers and Hotspots)
• Spatial Local Outliers
• Spatial Local Outlier Hotspots
• Continuous Model Building/Learning

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Spatial Neighborhood Statistics

• Objective
• Find mean and std. dev of spatial neighborhood
  statistics S(x, t)
• Given
• Time sequenced data values for the N spatial
  locations, F(T,N) f(t,n), tT-W1..T, n1..N
• Connectivity information for the spatial data
  locations
• Assumption
• All the frames/data are without outliers
• Steps
• Compute S(x,t) as the difference of f(x,t) from
  average f(x,t) value in its neighborhood
• Compute the mean and std. dev by keeping the sum,
  sum squared values and count values of the S(x,t)
  samples

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Temporal Neighborhood Variation Statistics

• Objective
• Find mean and std. dev of temporal variation of
  spatial statistics S(x, t)
• Given
• Spatial Statistics S(x,t), S(x,t-1),..for all the
  locations in each of the time instances
• Assumption
• All the frames/data used for S(x,t) computation
  are without outliers
• Steps
• Compute U(x,t) S(x,t) S(x,t-1 for all t and
  x
• Compute the mean and std. dev of U(x,t) by
  keeping the sum, sum squared and count values of
  the samples added.

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Spatial Local Outliers

• Objective
• Find the list of outliers at time t for all
  locations x based on S(x,t)
• Given
• Spatial Statistics S(x,t) for locations x in time
  t
• Spatial Outlier Threshold (P)
• Mean (Ms) and Std. dev (SDs) of spatial
  statistics
• Steps
• Compute O(x,t) S(x,t) Ms/ SDs for all x
• Outlier condition abs(O(x,t)) gt P

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Spatial Local Outlier Hotspots

• Objective
• Find the list of hotspots at time t based on
  S(x,t) values of outliers at tt-L1
• Given
• Frame length L to find outliers
• S(x,t) values for outliers in time tt-L1
• Hotspots Threshold (Q)
• Mean (Mt) and Std. dev (SDt) of temporal
  variation statistics
• Steps
• Compute U(x,t) S(x,t) S(x,t-1 for all the
  outliers in tt-L1
• Check if all the U(x,t) values are of the same
  sign
• Compute HT(x,t) S(x,t) s(x, t-L1) Mt/
  SDt for all outliers x
• Hotspot condition abs(HT(x,t)) gt Q

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Continuous Model Building

• Mean and Std. Dev for the spatial and temporal
  variation statistics are calculated on demand
• Non outlier samples are continuously added to the
  model keeping sum, sum squared and count values
  to compute statistics.

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Example

• User specified
• Temporal Frame Length, L3
• Outlier threshold P 3
• Hotspots threshold Q 3
• Model (Learned)
• Spatial Statistics
• Mean Ms 0, SDs 1
• Temporal Variation Statistics
• Mean Mt 0, SDt 1

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Example
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Limitations

• An outlier must be present in at-least L
  consecutive frames and exceed the threshold to be
  marked as hotspot.
• Additional storage requirements to store
• Identified outliers in the past L frames and
  their S(x,t) values
• Spatial statistics S(x, t) and S(x, t-1) for the
  present and past spatio-temporal frame
• Not applicable in conditions where the outliers
  spread to neighbors quickly thereby causing the
  spatial neighborhood to be more uniform forming
  outlier clusters.

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Conclusions and Future work

• A method proposed to identify emerging outlier
  hotspots
• Proposed method is an extension of techniques
  defined for spatial outlier detection.
• Validation using real dataset and experimental
  data need to be done
• Clustering around spatial outliers to identify
  hotspot regions

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• Thank you