Spatiotemporal Change Pattern Mining: A Multi-disciplinary Perspective - Space-Time Integration in Geography and GIScience - page 315

17.5.3 Change Interval Discovery

The change interval discovery problem was proposed to model an enduring change
of value that takes place during a time period or within a spatial path. Such change
patterns may be found in precipitation time series where a multi-decadal drought
occurs, or on a spatial path across different ecological zones where vegetation cover
shifts quickly from forest to desert. An algebraic interest measure named “sameness
degree” was proposed based on the differences between neighboring values

AV G f x g

Sameness Degree D

AV G ™ f x g

(Zhou et al. 2011 ). An interval with sameness degree exceeding a threshold is
considered as an interval of change. The authors also provided a computational
approach for enumerating and filtering sub-intervals.

17.5.4 Spatial Wombling Techniques

Spatial wombling origins from ecology where boundaries between ecological zones
are investigated (Womble 1951 ). Statistical approaches have been designed to find
statistically significant borders
Between different regions or contour maps. In a hierarchical Bayesian approach
(Lu and Carlin 2005 ), value differences between neighboring locations or areas that
exceed a threshold are selected as candidates, and a boundary likelihood value
(BLV) is estimated using Markov Chain Monte Carlo (MCMC) simulations to
find statistically significant boundaries. Other approaches have been proposed on
geostatistical (Liang 2009 ), areal (Lu and Carlin 2005 ), and point process (Liang
et al. 2009 ) data models.

17.5.5 Spatial/ST Scan Statistics and Emerging Cluster

Detection

Spatial scan statistics (Kulldorff and Nagarwalla 1995 ) employs a hypothesis
testing, where the null hypothesis H 0 is: the probability of disease inside any region
is the same as that outside the region, and the alternative hypothesis H 1 is that in a
certain region Z, there is a higher probability ( q in ) of each disease inside than out-
side ( q out ). A likelihood ratio score is then maximized among all the possible spatial
regions to find the most likely cluster of disease. The original scan statistic assumes
that the events follow a Bernoulli or a Poisson model. Later extensions on the same
ideas explored assumptions of normal (Kulldorff et al. 2009 ), exponential (Huang
et al. 2007 ), ordinal (Jung et al 2007 ), and non-parametric models (Kulldorff et al.