Transcript Extending Spatial Hot Spot Detection Techniques to

Extending Spatial Hot Spot Detection
Techniques to Temporal Dimensions
Sungsoon Hwang
Department of Geography
State University of New York at Buffalo
DMGIS ’05
Outlines
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Introduction
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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
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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
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Conclusions
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”
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
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
– Knox’s test for space-time interaction (Knox 1964)
– Temporal extension to K function (Diggle et al. 1995)
Space K function
• K function
• Test for spatial clustering
I h (dij )
R
ˆ
K (h)  2 
n i j
wij
Kˆ (h)
ˆ
L(h) 
h
•
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• High positive value of L(h)
indicates spatial clustering
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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 < h, or is 0 otherwise,
wij is the adjustment factor of edge
effect.

• Peak at L(h) across h
indicates optimal scale
Time K function
• K function
It (dij )
L
ˆ
K (t )  2 
n i j
wij
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• Test for temporal clustering
Lˆ (t )  Kˆ (t )  2t
L: total duration
n: total number of observed events
t: time interval
dij: interval between i and j
I: 1 if dij < t , 0 otherwise
wij: adjustment factor of edge effect
Space-time K function
• Extension of space K function
R
Kˆ ij (h) 
ni n j
nj
ni

I h (dij )
wij
i 1 j 1
• Extension of time K function
L
Kˆ ij (t ) 
ni n j
nj
ni

I t (dij )
i 1 j 1
wij
• Spatio-temporal K function
LR
Kˆ (h, t ) 
ni n j
ni
nj

i 1 j 1
I h ,t ( d ij )
wij
Dˆ (h, t )  Kˆ (h, t )  Kˆ (h) Kˆ (t )
Study areas
Motor Vehicle Crash,
New York State ’96 – ‘01
Motor Vehicle Crash,
New York City ’96 – ‘01
N
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Source data: Fatality Analysis Reporting System (FARS), NHTSA
Space K function
New York State
New York State kernel density map for
total fatal crashes (r = 16 km)
New York City
New York City (King, Queens County) kernel
density map of total fatal crashes (r=0.18 km)
Time K function
New York State
New York City
Extension of space K function
New York State
New York State kernel density map for
fatal crashes in May (r=30km)
New York City
New York City kernel density map of
fatal crashes on November (r=0.36)
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.