Novel method for measuring spatial dependencies turns less data into
more data

Date:
October 21, 2020
Source:
NYU Tandon School of Engineering
Summary:
Researcher makes 'little data' act big through, the application
of mathematical techniques normally used for time-series, to
spatial processes.



FULL STORY ==========================================================================
The identification of human migration driven by climate change, the
spread of COVID-19, agricultural trends, and socioeconomic problems
in neighboring regions depends on data -- the more complex the model,
the more data is required to understand such spatially distributed
phenomena. However, reliable data is often expensive and difficult to
obtain, or too sparse to allow for accurate predictions.


========================================================================== Maurizio Porfiri, Institute Professor of mechanical and aerospace,
biomedical, and civil and urban engineering and a member of the Center for Urban Science and Progress (CUSP) at the NYU Tandon School of Engineering, devised a novel solution based on network and information theory that
makes "little data" act big through, the application of mathematical
techniques normally used for time- series, to spatial processes.

The study, "An information-theoretic approach to study spatial
dependencies in small datasets," featured on the cover of Proceedings
of the Royal Society A: Mathematical, Physical and Engineering Sciences, describes how, from a small sample of attributes in a limited number of locations, observers can make robust inferences of influences, including interpolations to intermediate areas or even distant regions that share
similar key attributes.

"Most of the time the data sets are poor," Porfiri explained. "Therefore,
we took a very basic approach, applying information theory to explore
whether influence in the temporal sense could be extended to space,
which allows us to work with a very small data set, between 25 and
50 observations," he said. "We are taking one snapshot of the data
and drawing connections -- not based on cause-and-effect, but on
interaction between the individual points -- to see if there is some
form of underlying, collective response in the system." The method,
developed by Porfiri and collaborator Manuel Ruiz Mari'n of the Department
of Quantitative Methods, Law and Modern Languages, Technical University
of Cartagena, Spain, involved:
* Consolidating a given data set into a small range of admissible
symbols,
similar to the way a machine learning system can identify a face
with limited pixel data: a chin, cheekbones, forehead, etc.

* Applying an information-theory principle to create a test that
is non-
parametric (one that assumes no underlying model for the interaction
between locations) to draw associations between events and to
discover whether uncertainty at a particular location is reduced
if one has knowledge about the uncertainty in another location.

Porfiri explained that since a non-parametric approach posits no
underlying structure for the influences between nodes, it confers
flexibility in how nodes can be associated, or even how the concept of
a neighbor is defined.

"Because we abstract this concept of a neighbor, we can define
it in the context of any quality that you like, for example,
ideology. Ideologically, California can be a neighbor of New York, though
they are not geographically co-located. They may share similar values."
The team validated the system against two case studies: population
migrations in Bangladesh due to sea level rise and motor vehicle deaths
in the U.S., to derive a statistically principled insight into the
mechanisms of important socioeconomic problems.

"In the first case, we wanted to see if migration between locations could
be predicted by geographic distance or the severity of the inundation
of that particular district -- whether knowledge of which district is
close to another district or knowledge of the level of flooding will
help predict the size of migration," said Ruiz Mari'n .

For the second case, they looked at the spatial distribution of
alcohol-related automobile accidents in 1980, 1994, and 2009, comparing
states with a high degree of such accidents to adjacent states and to
states with similar legislative ideologies about drinking and driving.

"We discovered a stronger relationship between states sharing borders
than between states sharing legislative ideologies pertaining to alcohol consumption and driving." Next, Porfiri and Ruiz Mari'n are planning to
extend their method to the analysis of spatio-temporal processes, such
as gun violence in the U.S. -- a major research project recently funded
by the National Science Foundation's LEAP HI program -- or epileptic
seizures in the brain. Their work could help understand when and where
gun violence can happen or seizures may initiate.


========================================================================== Story Source: Materials provided by
NYU_Tandon_School_of_Engineering. Note: Content may be edited for style
and length.


========================================================================== Journal Reference:
1. Maurizio Porfiri, Manuel Ruiz Mari'n. An information-theoretic
approach
to study spatial dependencies in small datasets. Proceedings of the
Royal Society A: Mathematical, Physical and Engineering Sciences,
2020; 476 (2242): 20200113 DOI: 10.1098/rspa.2020.0113 ==========================================================================

Link to news story: https://www.sciencedaily.com/releases/2020/10/201021140908.htm

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