scholarly journals Ising Model for Interpolation of Spatial Data on Regular Grids

Entropy ◽  
2021 ◽  
Vol 23 (10) ◽  
pp. 1270
Author(s):  
Milan Žukovič ◽  
Dionissios T. Hristopulos
Keyword(s):  
Ising Model ◽  
Spatial Data ◽  
Nearest Neighbor ◽  
Correlated Data ◽  
Continuous Variables ◽  
Regression Problem ◽  
Spatially Correlated ◽  
Regular Grids ◽  
Non Gaussian ◽  
Gaussian Data

We apply the Ising model with nearest-neighbor correlations (INNC) in the problem of interpolation of spatially correlated data on regular grids. The correlations are captured by short-range interactions between “Ising spins”. The INNC algorithm can be used with label data (classification) as well as discrete and continuous real-valued data (regression). In the regression problem, INNC approximates continuous variables by means of a user-specified number of classes. INNC predicts the class identity at unmeasured points by using the Monte Carlo simulation conditioned on the observed data (partial sample). The algorithm locally respects the sample values and globally aims to minimize the deviation between an energy measure of the partial sample and that of the entire grid. INNC is non-parametric and, thus, is suitable for non-Gaussian data. The method is found to be very competitive with respect to interpolation accuracy and computational efficiency compared to some standard methods. Thus, this method provides a useful tool for filling gaps in gridded data such as satellite images.

Bayesian residual analysis for spatially correlated data

2019 ◽  
Vol 20 (2) ◽  
pp. 171-194 ◽  
Author(s):  
Viviana GR Lobo ◽  
Thaís CO Fonseca
Keyword(s):  
Spatial Data ◽  
Density Ratio ◽  
Spatial Models ◽  
Residual Analysis ◽  
Correlated Data ◽  
Point Of View ◽  
Spatially Correlated ◽  
Wind Speeds ◽  
Standardized Residuals ◽  
Outlying Observation

This work considers residual analysis and predictive techniques for the identification of individual and multiple outliers in geostatistical data. The standardized Bayesian spatial residual is proposed and computed for three competing models: the Gaussian, Student-t and Gaussian-log-Gaussian spatial processes. In this context, the spatial models are investigated regarding their plausibility for datasets contaminated with outliers. The posterior probability of an outlying observation is computed based on the standardized residuals and different thresholds for outlier discrimination are tested. From a predictive point of view, methods such as the conditional predictive ordinate, the predictive concordance and the Savage–Dickey density ratio for hypothesis testing are investigated for identification of outliers in the spatial setting. For illustration, contaminated datasets are considered to assess the performance of the three spatial models for identification of outliers in spatial data. Furthermore, an application to wind speed modelling is presented to illustrate the usefulness of the proposed tools to detect regions with large wind speeds.

Quadratic Discriminant Analysis of Spatially Correlated Data

2001 ◽  
Vol 6 (2) ◽  
pp. 15-28 ◽  
Author(s):  
K. Dučinskas ◽  
J. Šaltytė
Keyword(s):  
Discriminant Function ◽  
Error Rate ◽  
Gaussian Random Field ◽  
Correlated Data ◽  
Covariance Matrices ◽  
Classification Rule ◽  
Spatial Correlations ◽  
Linear Quadratic ◽  
Spatial Correlation Function ◽  
Spatially Correlated

The problem of classification of the realisation of the stationary univariate Gaussian random field into one of two populations with different means and different factorised covariance matrices is considered. In such a case optimal classification rule in the sense of minimum probability of misclassification is associated with non-linear (quadratic) discriminant function. Unknown means and the covariance matrices of the feature vector components are estimated from spatially correlated training samples using the maximum likelihood approach and assuming spatial correlations to be known. Explicit formula of Bayes error rate and the first-order asymptotic expansion of the expected error rate associated with quadratic plug-in discriminant function are presented. A set of numerical calculations for the spherical spatial correlation function is performed and two different spatial sampling designs are compared.

Temporal and Spatial Pattern of a Privet (Ligustrum vulgare) Invasion

2013 ◽  
Vol 6 (2) ◽  
pp. 310-319 ◽  
Author(s):  
Wanying Zhao ◽  
Charles Goebel ◽  
John Cardina
Keyword(s):  
Spatial Pattern ◽  
Spatial Data ◽  
Nearest Neighbor ◽  
Management Strategies ◽  
Age Distribution ◽  
Lag Phase ◽  
Suitable Habitat ◽  
Second Phase ◽  
Invasion History ◽  
Cumulative Number

AbstractPrivet has escaped from cultivation and is invading natural areas throughout eastern North America. Understanding the pattern of invasion over time could help us develop more efficient management strategies. We studied the invasion history and spatial distribution pattern of privet by mapping age and spatial data for established patches in a 132-ha (326 ac) forested natural area in northeast Ohio. We determined the age of 331 geo-referenced patches by counting annual rings, and mapped them with corresponding land habitat. Age distribution and cumulative number of privet patches over about 40 yr showed three phases of invasion. The initial 19-yr lag phase was characterized as a dispersed spatial pattern (based on nearest neighbor analysis), with patches located mostly at edges of different habitats and open places. In a second phase of about 15 yr, an average of 19 patches were initiated yearly, in a pattern that trended towards clustered. The final phase began around 2007, as the rate of new patch establishment declined, possibly because of saturation of the suitable habitat. Establishment of new patches was not associated with specific habitats. Aggregation of patches with similar ages increased after 1998 and became significantly clustered. Mapping of clusters of old and young patches identified invasion hot spots and barriers. Results affirmed that the best time for invasive control is during the lag phase. By monitoring edge habitats associated with early establishment, managers might detect and control early invaders and delay the onset of the expansion phase.

scholarly journals Semantics of Voids within Data: Ignorance-Aware Machine Learning

2021 ◽  
Vol 10 (4) ◽  
pp. 246
Author(s):  
Vagan Terziyan ◽  
Anton Nikulin
Keyword(s):  
Spatial Data ◽  
Information Science ◽  
Nearest Neighbor ◽  
Geographical Information ◽  
Two Dimensional ◽  
Prototype Selection ◽  
Data Space ◽  
Important Concern ◽  
Traditional Classification ◽  
Nearest Neighbor Classifiers

Operating with ignorance is an important concern of geographical information science when the objective is to discover knowledge from the imperfect spatial data. Data mining (driven by knowledge discovery tools) is about processing available (observed, known, and understood) samples of data aiming to build a model (e.g., a classifier) to handle data samples that are not yet observed, known, or understood. These tools traditionally take semantically labeled samples of the available data (known facts) as an input for learning. We want to challenge the indispensability of this approach, and we suggest considering the things the other way around. What if the task would be as follows: how to build a model based on the semantics of our ignorance, i.e., by processing the shape of “voids” within the available data space? Can we improve traditional classification by also modeling the ignorance? In this paper, we provide some algorithms for the discovery and visualization of the ignorance zones in two-dimensional data spaces and design two ignorance-aware smart prototype selection techniques (incremental and adversarial) to improve the performance of the nearest neighbor classifiers. We present experiments with artificial and real datasets to test the concept of the usefulness of ignorance semantics discovery.

Kriging and univariate modeling of a spatially correlated data

1988 ◽  
Vol 1 (2) ◽  
pp. 133-147 ◽  
Author(s):  
M.H. Alemi ◽  
A.S. Azari ◽  
D.R. Nielsen
Keyword(s):  
Correlated Data ◽  
Spatially Correlated ◽  
Spatially Correlated Data
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