Properties of the spatial unilateral first-order ARMA model

1993 ◽  
Vol 25 (3) ◽  
pp. 631-648 ◽  
Author(s):  
Sabyasachi Basu ◽  
Gregory C. Reinsel
Keyword(s):  
Spatial Data ◽  
Likelihood Function ◽  
Moving Average ◽  
Spatial Models ◽  
Arma Model ◽  
Substantial Effect ◽  
Two Dimensional ◽  
Estimation Of Parameters ◽  
First Order ◽  
Spatial Lattice Data

For two-dimensional spatial data, a spatial unilateral autoregressive moving average (ARMA) model of first order is defined and its properties studied. The spatial correlation properties for these models are explicitly obtained, as well as simple conditions for stationarity and conditional expectation (interpolation) properties of the model. The multiplicative or linear-by-linear first-order spatial models are seen to be a special case which have proved to be of practical use in modeling of two-dimensional spatial lattice data, and hence the more general models should prove to be useful in applications. These unilateral models possess a convenient computational form for the exact likelihood function, which gives proper treatment to the border cell values in the lattice that have a substantial effect in estimation of parameters. Some simulation results to examine properties of the maximum likelihood estimator and a numerical example to illustrate the methods are briefly presented.

Properties of the spatial unilateral first-order ARMA model

1993 ◽  
Vol 25 (03) ◽  
pp. 631-648 ◽  
Author(s):  
Sabyasachi Basu ◽  
Gregory C. Reinsel
Keyword(s):  
Spatial Data ◽  
Likelihood Function ◽  
Moving Average ◽  
Spatial Models ◽  
Arma Model ◽  
Substantial Effect ◽  
Two Dimensional ◽  
Estimation Of Parameters ◽  
First Order ◽  
Spatial Lattice Data

For two-dimensional spatial data, a spatial unilateral autoregressive moving average (ARMA) model of first order is defined and its properties studied. The spatial correlation properties for these models are explicitly obtained, as well as simple conditions for stationarity and conditional expectation (interpolation) properties of the model. The multiplicative or linear-by-linear first-order spatial models are seen to be a special case which have proved to be of practical use in modeling of two-dimensional spatial lattice data, and hence the more general models should prove to be useful in applications. These unilateral models possess a convenient computational form for the exact likelihood function, which gives proper treatment to the border cell values in the lattice that have a substantial effect in estimation of parameters. Some simulation results to examine properties of the maximum likelihood estimator and a numerical example to illustrate the methods are briefly presented.

ADAPTIVE, FREQUENCY DOMAIN, 2-D MODELING USING SPATIOTEMPORAL SIGNALS

1996 ◽  
Vol 06 (04) ◽  
pp. 351-358
Author(s):  
WASFY B. MIKHAEL ◽  
HAOPING YU
Keyword(s):  
Frequency Domain ◽  
Moving Average ◽  
System Modeling ◽  
Arma Model ◽  
Model Parameters ◽  
Two Dimensional ◽  
Convergence Factor ◽  
Arma Process ◽  
Auto Regressive ◽  
Unknown System

In this paper, an adaptive, frequency domain, steepest descent algorithm for two-dimensional (2-D) system modeling is presented. Based on the equation error model, the algorithm, which characterizes the 2-D spatially linear and invariant unknown system by a 2-D auto-regressive, moving-average (ARMA) process, is derived and implemented in the 3-D spatiotemporal domain. At each iteration, corresponding to a given pair of input and output 2-D signals, the algorithm is formulated to minimize the error-function’s energy in the frequency domain by adjusting the 2-D ARMA model parameters. A signal dependent, optimal convergence factor, referred to as the homogeneous convergence factor, is developed. It is the same for all the coefficients but is updated once per iteration. The resulting algorithm is called the Two-Dimensional, Frequency Domain, with Homogeneous µ*, Adaptive Algorithm (2D-FD-HAA). In addition, the algorithm is implemented using the 2-D Fast Fourier Transform (FFT) to enhance the computational efficiency. Computer simulations demonstrate the algorithm’s excellent adaptation accuracy and convergence speed. For illustration, the proposed algorithm is successfully applied to modeling a time varying 2-D system.

scholarly journals Three-Dimensional Thematic Map Imaging of the Yacht Port on the Example of the Polish National Sailing Centre Marina in Gdańsk

2021 ◽  
Vol 11 (15) ◽  
pp. 7016
Author(s):  
Pawel S. Dabrowski ◽  
Cezary Specht ◽  
Mariusz Specht ◽  
Artur Makar
Keyword(s):  
Spatial Data ◽  
Convex Surface ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Future Research ◽  
Two Dimensional ◽  
Thematic Maps ◽  
Research Directions ◽  
Future Research Directions ◽  
The Many

The theory of cartographic projections is a tool which can present the convex surface of the Earth on the plane. Of the many types of maps, thematic maps perform an important function due to the wide possibilities of adapting their content to current needs. The limitation of classic maps is their two-dimensional nature. In the era of rapidly growing methods of mass acquisition of spatial data, the use of flat images is often not enough to reveal the level of complexity of certain objects. In this case, it is necessary to use visualization in three-dimensional space. The motivation to conduct the study was the use of cartographic projections methods, spatial transformations, and the possibilities offered by thematic maps to create thematic three-dimensional map imaging (T3DMI). The authors presented a practical verification of the adopted methodology to create a T3DMI visualization of the marina of the National Sailing Centre of the Gdańsk University of Physical Education and Sport (Poland). The profiled characteristics of the object were used to emphasize the key elements of its function. The results confirmed the increase in the interpretative capabilities of the T3DMI method, relative to classic two-dimensional maps. Additionally, the study suggested future research directions of the presented solution.

scholarly journals An ABC-optimized fuzzy ELECTRE approach for assessing petroleum potential at the petroleum system level

2020 ◽  
Vol 12 (1) ◽  
pp. 580-597
Author(s):  
Mohamad Hamzeh ◽  
Farid Karimipour
Keyword(s):  
Spatial Data ◽  
Spatial Models ◽  
Model Performance ◽  
Essential Elements ◽  
Petroleum System ◽  
Petroleum Exploration ◽  
System Level ◽  
Data Sets ◽  
Petroleum Potential ◽  
Spatial Data Sets

AbstractAn inevitable aspect of modern petroleum exploration is the simultaneous consideration of large, complex, and disparate spatial data sets. In this context, the present article proposes the optimized fuzzy ELECTRE (OFE) approach based on combining the artificial bee colony (ABC) optimization algorithm, fuzzy logic, and an outranking method to assess petroleum potential at the petroleum system level in a spatial framework using experts’ knowledge and the information available in the discovered petroleum accumulations simultaneously. It uses the characteristics of the essential elements of a petroleum system as key criteria. To demonstrate the approach, a case study was conducted on the Red River petroleum system of the Williston Basin. Having completed the assorted preprocessing steps, eight spatial data sets associated with the criteria were integrated using the OFE to produce a map that makes it possible to delineate the areas with the highest petroleum potential and the lowest risk for further exploratory investigations. The success and prediction rate curves were used to measure the performance of the model. Both success and prediction accuracies lie in the range of 80–90%, indicating an excellent model performance. Considering the five-class petroleum potential, the proposed approach outperforms the spatial models used in the previous studies. In addition, comparing the results of the FE and OFE indicated that the optimization of the weights by the ABC algorithm has improved accuracy by approximately 15%, namely, a relatively higher success rate and lower risk in petroleum exploration.

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.

scholarly journals Spatial analysis for political scientists

2021 ◽  
pp. 1-17
Author(s):  
Jessica Di Salvatore ◽  
Andrea Ruggeri
Keyword(s):  
Comparative Politics ◽  
Spatial Data ◽  
Spatial Clustering ◽  
Statistical Tests ◽  
Spatial Regression ◽  
Spatial Models ◽  
Building Blocks ◽  
Spatial Relationships ◽  
Electoral Studies ◽  
Data Points

Abstract How does space matter in our analyses? How can we evaluate diffusion of phenomena or interdependence among units? How biased can our analysis be if we do not consider spatial relationships? All the above questions are critical theoretical and empirical issues for political scientists belonging to several subfields from Electoral Studies to Comparative Politics, and also for International Relations. In this special issue on methods, our paper introduces political scientists to conceptualizing interdependence between units and how to empirically model these interdependencies using spatial regression. First, the paper presents the building blocks of any feature of spatial data (points, polygons, and raster) and the task of georeferencing. Second, the paper discusses what a spatial matrix (W) is, its varieties and the assumptions we make when choosing one. Third, the paper introduces how to investigate spatial clustering through visualizations (e.g. maps) as well as statistical tests (e.g. Moran's index). Fourth and finally, the paper explains how to model spatial relationships that are of substantive interest to some of our research questions. We conclude by inviting researchers to carefully consider space in their analysis and to reflect on the need, or the lack thereof, to use spatial models.

scholarly journals Solving puzzles in deformed JT gravity: phase transitions and non-perturbative effects

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Clifford V. Johnson ◽  
Felipe Rosso
Keyword(s):  
Phase Structure ◽  
Scalar Potential ◽  
String Equation ◽  
Two Dimensional ◽  
Leading Order ◽  
Classical Analysis ◽  
First Order ◽  
First Order Phase Transition ◽  
Definition Of ◽  
First Order Phase

Abstract Recent work has shown that certain deformations of the scalar potential in Jackiw-Teitelboim gravity can be written as double-scaled matrix models. However, some of the deformations exhibit an apparent breakdown of unitarity in the form of a negative spectral density at disc order. We show here that the source of the problem is the presence of a multi-valued solution of the leading order matrix model string equation. While for a class of deformations we fix the problem by identifying a first order phase transition, for others we show that the theory is both perturbatively and non-perturbatively inconsistent. Aspects of the phase structure of the deformations are mapped out, using methods known to supply a non-perturbative definition of undeformed JT gravity. Some features are in qualitative agreement with a semi-classical analysis of the phase structure of two-dimensional black holes in these deformed theories.

Spatial clustering analysis of green economy based on knowledge graph

2021 ◽  
pp. 1-10
Author(s):  
Shiyuan Zhou ◽  
Xiaoqin Yang ◽  
Qianli Chang
Keyword(s):  
Spatial Data ◽  
Clustering Analysis ◽  
Spatial Clustering ◽  
Evaluation Model ◽  
Principal Component ◽  
Green Economy ◽  
Membership Degree ◽  
Two Dimensional ◽  
Dimensional Graph ◽  
Improved Algorithm

By organically combining principal component analysis, spatial autocorrelation algorithm and two-dimensional graph theory clustering algorithm, the comprehensive evaluation model of regional green economy is explored and established. Based on the evaluation index system of regional green economy, this paper evaluates the development of regional green economy comprehensively by using principal component analysis, and evaluates the competitive advantage of green economy and analyzes the spatial autocorrelation based on the evaluation results. Finally, the green economy and local index score as observed values, by using the method of two-dimensional graph clustering analysis of spatial clustering. In view of the fuzzy k –modes cluster membership degree measure method without considering the defects of the spatial distribution of object, double the distance and density measurement of measure method is introduced into the fuzzy algorithm of k –modes, thus in a more reasonable way to update the membership degree of the object. Vote, MUSH-ROOM and ZOO data sets in UCI machine learning library were used for testing, and the F value of the improved algorithm was better than that of the previous one, indicating that the improved algorithm had good clustering effect. Finally, the improved algorithm is applied to the spatial data collected from Baidu Map to cluster, and a good clustering result is obtained, which shows the feasibility and effectiveness of the algorithm applied to spatial data. Results show that the development of green economy using the analysis method of combining quantitative analysis and qualitative analysis, explores the connotation of green economy with space evaluation model is feasible, small make up for the qualitative analysis of the green economy in the past, can objective system to reflect the regional green economic development level, will help policy makers scientific formulating regional economic development strategy, green integrated development of regional green economy from the macroscopic Angle, the development of network system.

Sign in / Sign up

Export Citation Format

Share Document