Extending Spatial Hot Spot Detection Techniques to Temporal Dimensions

1
Extending Spatial Hot Spot Detection Techniques
to Temporal Dimensions

• Sungsoon Hwang
• Department of Geography
• State University of New York at Buffalo
• DMGIS 05

2
Outlines

• Introduction
• Approaches to hot spot detection
• Spatial statistical approach to hot spot
  detection (point pattern analysis)
• Review of point pattern analysis
• Time in point pattern analysis
• Extending K function to temporal dimensions
• Space K function
• Time K function
• Space-time K function
• Case studies detecting traffic accident hot
  spots
• Fatal motor vehicle crashes in New York State
  between 96 01
• Fatal motor vehicle crashes in New York City
  between 96 01
• Conclusions

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Approaches to detecting hot spots

• Non-spatial statistical approach
• Designed to derive homogenous groupings
• Not limited to 2-D geographic space (i.e.
  multidimensional)
• Space is not properly treated
• Spatial statistical approach
• Tests departures from complete spatial randomness
• Takes into account the nature of spatial behavior
• Also known as point pattern analysis

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Review of point pattern analysis

• Global statistics (intensity)
• Quadrat method events in a given spatial frame
  
• Kernel estimation smoothing based on probability
  distribution
• Local statistics (spatial dependence)
• Nearest neighbor detects the tendency for
  localized pattern at the smallest scales
• K function detects hot spots at varying scales

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Time in point pattern analysis

• Time provides important clues in spatial point
  pattern analysis
• For understanding causality (e.g. before/after)
• Intensity of spatial events varies by time
• Previous studies
• Knoxs test for space-time interaction (Knox
  1964)
• Temporal extension to K function (Diggle et al.
  1995)

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Space K function

• K function
• R is area of study area,
• n is the total number of observed events,
• h is the distance considered for local scale
  variation (or band size),
• dij is the distance between event i and event j,
• Ih is 1 if dij lt h, or is 0 otherwise,
• wij is the adjustment factor of edge effect.

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Time K function

• K function

• Test for temporal clustering

• L total duration
• n total number of observed events
• t time interval
• dij interval between i and j
• I 1 if dij lt t , 0 otherwise
• wij adjustment factor of edge effect

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Space-time K function

• Extension of space K function
• Extension of time K function
• Spatio-temporal K function

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Study areas
Motor Vehicle Crash, New York State 96 01
Motor Vehicle Crash, New York City 96 01
Source data Fatality Analysis Reporting System
(FARS), NHTSA
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Space K function
New York State
New York City
New York State kernel density map for total fatal
crashes (r 16 km)
New York City (King, Queens County) kernel
density map of total fatal crashes (r0.18 km)
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Time K function
New York State
New York City
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Extension of space K function
New York State
New York City
New York State kernel density map for fatal
crashes in May (r30km)
New York City kernel density map of fatal crashes
on November (r0.36)
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Conclusions

• Space K function detects spatial clusters
• Time K function detects temporal clusters
• Space-time K function detects
• Temporal extension of space K function detects
  spatial clusters of point events stratified by
  categorical temporal attributes
• Spatial extension of temporal K function detects
  temporal clusters of point events stratified by
  categorical spatial attributes
• Spatio-temporal K function detects space-time
  interaction
• Case studies demonstrate that temporal extension
  of space K function is useful in discovering
  pattern that would have been unnoticed if
  observed events were not disaggregated by
  temporal types and if the whole range of possible
  scales were not explored.