442
ing technologies continuously monitor the land surface of the earth and collect
valuable data about water bodies, agricultural fields, and so on. For groundwater observation, the U.S. Geological Survey is creating a national network of
gauge stations to develop a water census for both quality and quantity.
Over the last several decades, the spatial, spectral, and temporal resolutions
of FEW datasets have improved greatly through the deployment of improved
remote sensing and ground sensing systems. These improvements have led to
the collection of synoptic scale data and enabled a variety of new FEW applications. However, these improvements also pose novel computing questions
and challenges due to the unique nature of spatial and spatiotemporal data
(Shekhar et al. 2011a; Shekhar et al. 2015a; Shekhar et al. 2011b). Spatial and
spatiotemporal FEW data have unique characteristics that can be summarized
as follows:
Spatiotemporal autocorrelation: Per the first law of geography (Tobler
1970), everything is related to everything else, but nearby things are more
related than distant things. What this law tells us is that spatial data are not
independently distributed, and autocorrelation exists (Shekhar et al. 2015b). For
spatiotemporal data, temporal autocorrelation exists in addition to spatial autocorrelation. For example, in remote sensing images, nearby pixels are often in
the same thematic class (e.g., forest or water), and consecutive snapshots of
the same locations are often very similar.
Spatial heterogeneity: Spatial heterogeneity describes the fact that samples
often do not follow an identical distribution in the entire space due to varying
geographic features. Thus, a global model for the entire space fails to capture the
varying relationships between features and the target variable in different regions.
For example, the spectral characteristics of remote sensing images on surface
water in tropical areas probably look different from those in temperate areas.
Non-Euclidean space, anisotropy: Current spatiotemporal modeling techniques often assume Euclidean space with isotropic and symmetric spatial
neighborhoods. However, in many real-world applications, data are collected
in a network space (e.g., river networks, road networks) (Isaak et al. 2014;
Oliver et al. 2014a; 2014b). One of the main challenges of spatiotemporal data
modeling in a network space is to account for the unique network structure
(e.g., one-ways, connectivity, left-turns). Such network structure often violates
the common assumption that spatial dependency is isotropic in Euclidean
space, and thus requires asymmetric neighborhoods with directionality.
Recently, some new research has been conducted in spatial network statistics
and computer/data science methods, e.g., network K-function and network
spatial autocorrelation, network point cluster analysis and clumping method,
network point density estimation, network spatial interpolation (Kriging).
Nevertheless, most techniques apply only to Euclidean space. Future research
is needed in this area.
Temporal non-stationarity: The statistical distribution of FEW data is not
stationary, as assumed by many traditional models; it changes over time. The
stationarity assumption means that the model created in the training phase of
E. Eftelioglu and S. Shekhar
ing technologies continuously monitor the land surface of the earth and collect
valuable data about water bodies, agricultural fields, and so on. For groundwater observation, the U.S. Geological Survey is creating a national network of
gauge stations to develop a water census for both quality and quantity.
Over the last several decades, the spatial, spectral, and temporal resolutions
of FEW datasets have improved greatly through the deployment of improved
remote sensing and ground sensing systems. These improvements have led to
the collection of synoptic scale data and enabled a variety of new FEW applications. However, these improvements also pose novel computing questions
and challenges due to the unique nature of spatial and spatiotemporal data
(Shekhar et al. 2011a; Shekhar et al. 2015a; Shekhar et al. 2011b). Spatial and
spatiotemporal FEW data have unique characteristics that can be summarized
as follows:
Spatiotemporal autocorrelation: Per the first law of geography (Tobler
1970), everything is related to everything else, but nearby things are more
related than distant things. What this law tells us is that spatial data are not
independently distributed, and autocorrelation exists (Shekhar et al. 2015b). For
spatiotemporal data, temporal autocorrelation exists in addition to spatial autocorrelation. For example, in remote sensing images, nearby pixels are often in
the same thematic class (e.g., forest or water), and consecutive snapshots of
the same locations are often very similar.
Spatial heterogeneity: Spatial heterogeneity describes the fact that samples
often do not follow an identical distribution in the entire space due to varying
geographic features. Thus, a global model for the entire space fails to capture the
varying relationships between features and the target variable in different regions.
For example, the spectral characteristics of remote sensing images on surface
water in tropical areas probably look different from those in temperate areas.
Non-Euclidean space, anisotropy: Current spatiotemporal modeling techniques often assume Euclidean space with isotropic and symmetric spatial
neighborhoods. However, in many real-world applications, data are collected
in a network space (e.g., river networks, road networks) (Isaak et al. 2014;
Oliver et al. 2014a; 2014b). One of the main challenges of spatiotemporal data
modeling in a network space is to account for the unique network structure
(e.g., one-ways, connectivity, left-turns). Such network structure often violates
the common assumption that spatial dependency is isotropic in Euclidean
space, and thus requires asymmetric neighborhoods with directionality.
Recently, some new research has been conducted in spatial network statistics
and computer/data science methods, e.g., network K-function and network
spatial autocorrelation, network point cluster analysis and clumping method,
network point density estimation, network spatial interpolation (Kriging).
Nevertheless, most techniques apply only to Euclidean space. Future research
is needed in this area.
Temporal non-stationarity: The statistical distribution of FEW data is not
stationary, as assumed by many traditional models; it changes over time. The
stationarity assumption means that the model created in the training phase of
E. Eftelioglu and S. Shekhar