scholarly journals A Markov Chain Monte Carlo Algorithm for Spatial Segmentation

Information ◽  
2021 ◽  
Vol 12 (2) ◽  
pp. 58
Author(s):  
Nishanthi Raveendran ◽  
Georgy Sofronov
Keyword(s):  
Spatial Data ◽  
Surface Profile ◽  
Real Data ◽  
Monte Carlo Algorithm ◽  
Spatial Data Analysis ◽  
Data Sets ◽  
Regular Lattice ◽  
Clustering Problem ◽  
Spatial Segmentation ◽  
Homogeneous Regions

Spatial data are very often heterogeneous, which indicates that there may not be a unique simple statistical model describing the data. To overcome this issue, the data can be segmented into a number of homogeneous regions (or domains). Identifying these domains is one of the important problems in spatial data analysis. Spatial segmentation is used in many different fields including epidemiology, criminology, ecology, and economics. To solve this clustering problem, we propose to use the change-point methodology. In this paper, we develop a new spatial segmentation algorithm within the framework of the generalized Gibbs sampler. We estimate the average surface profile of binary spatial data observed over a two-dimensional regular lattice. We illustrate the performance of the proposed algorithm with examples using artificially generated and real data sets.

An Introduction to Spatial Data Analysis

2020 ◽  
Author(s):  
Martin Wegmann ◽  
Jakob Schwalb-Willmann ◽  
Stefan Dech
Keyword(s):  
Remote Sensing ◽  
Data Analysis ◽  
Open Source ◽  
Spatial Data ◽  
Remote Sensing Data ◽  
Spatial Data Analysis ◽  
Data Sets ◽  
Data Handling ◽  
Book Covers

This is a book about how ecologists can integrate remote sensing and GIS in their research. It will allow readers to get started with the application of remote sensing and to understand its potential and limitations. Using practical examples, the book covers all necessary steps from planning field campaigns to deriving ecologically relevant information through remote sensing and modelling of species distributions. An Introduction to Spatial Data Analysis introduces spatial data handling using the open source software Quantum GIS (QGIS). In addition, readers will be guided through their first steps in the R programming language. The authors explain the fundamentals of spatial data handling and analysis, empowering the reader to turn data acquired in the field into actual spatial data. Readers will learn to process and analyse spatial data of different types and interpret the data and results. After finishing this book, readers will be able to address questions such as “What is the distance to the border of the protected area?”, “Which points are located close to a road?”, “Which fraction of land cover types exist in my study area?” using different software and techniques. This book is for novice spatial data users and does not assume any prior knowledge of spatial data itself or practical experience working with such data sets. Readers will likely include student and professional ecologists, geographers and any environmental scientists or practitioners who need to collect, visualize and analyse spatial data. The software used is the widely applied open source scientific programs QGIS and R. All scripts and data sets used in the book will be provided online at book.ecosens.org. This book covers specific methods including: what to consider before collecting in situ data how to work with spatial data collected in situ the difference between raster and vector data how to acquire further vector and raster data how to create relevant environmental information how to combine and analyse in situ and remote sensing data how to create useful maps for field work and presentations how to use QGIS and R for spatial analysis how to develop analysis scripts

scholarly journals A Three-Level Optimization Model for Nonlinearly Separable Clustering

2020 ◽  
Vol 34 (04) ◽  
pp. 3211-3218
Author(s):  
Liang Bai ◽  
Jiye Liang
Keyword(s):  
Optimization Model ◽  
Clustering Algorithms ◽  
Complex Structure ◽  
Computational Cost ◽  
Real Data ◽  
Data Sets ◽  
Real World Data ◽  
Clustering Problem ◽  
Efficiency And Effectiveness ◽  
Clustering Problems

Due to the complex structure of the real-world data, nonlinearly separable clustering is one of popular and widely studied clustering problems. Currently, various types of algorithms, such as kernel k-means, spectral clustering and density clustering, have been developed to solve this problem. However, it is difficult for them to balance the efficiency and effectiveness of clustering, which limits their real applications. To get rid of the deficiency, we propose a three-level optimization model for nonlinearly separable clustering which divides the clustering problem into three sub-problems: a linearly separable clustering on the object set, a nonlinearly separable clustering on the cluster set and an ensemble clustering on the partition set. An iterative algorithm is proposed to solve the optimization problem. The proposed algorithm can use low computational cost to effectively recognize nonlinearly separable clusters. The performance of this algorithm has been studied on synthetical and real data sets. Comparisons with other nonlinearly separable clustering algorithms illustrate the efficiency and effectiveness of the proposed algorithm.

scholarly journals Descriptive Clustering: ILP and CP Formulations with Applications

2018 ◽  
Author(s):  
Thi-Bich-Hanh Dao ◽  
Chia-Tung Kuo ◽  
S. S. Ravi ◽  
Christel Vrain ◽  
Ian Davidson
Keyword(s):  
Real Data ◽  
Pareto Optimal ◽  
Data Sets ◽  
Complex Data ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Conceptual Clustering ◽  
Clustering Problem ◽  
Health Care Records ◽  
Single Objective

In many settings just finding a good clustering is insufficient and an explanation of the clustering is required. If the features used to perform the clustering are interpretable then methods such as conceptual clustering can be used. However, in many applications this is not the case particularly for image, graph and other complex data. Here we explore the setting where a set of interpretable discrete tags for each instance is available. We formulate the descriptive clustering problem as a bi-objective optimization to simultaneously find compact clusters using the features and to describe them using the tags. We present our formulation in a declarative platform and show it can be integrated into a standard iterative algorithm to find all Pareto optimal solutions to the two objectives. Preliminary results demonstrate the utility of our approach on real data sets for images and electronic health care records and that it outperforms single objective and multi-view clustering baselines.

scholarly journals Superpixel Weighted Low-rank and Sparse Approximation for Hyperspectral Unmixing

2022 ◽  
Author(s):  
Taner Ince ◽  
Tugcan Dundar ◽  
Seydi Kacmaz ◽  
Hasari Karci
Keyword(s):  
Spatial Structure ◽  
Hyperspectral Image ◽  
Real Data ◽  
Approximation Problem ◽  
Sparse Approximation ◽  
Hyperspectral Data ◽  
Low Rank ◽  
Data Sets ◽  
Spatial Weight ◽  
Homogeneous Regions

We propose a superpixel weighted low-rank and sparse unmixing (SWLRSU) method for sparse unmixing. The proposed method consists of two steps. In the first step, we segment hyperspectral image into superpixels which are defined as the homogeneous regions with different shape and sizes according to the spatial structure. Then, an efficient method is proposed to obtain a spatial weight term using superpixels to capture the spatial structure of hyperspectral data. In the second step, we solve a superpixel guided low-rank and spatially weighted sparse approximation problem in which spatial weight term obtained in the first step is used as a weight term in sparsity promoting norm. This formulation exploits the spatial correlation of the pixels in the hyperspectral image efficiently, which yields satisfactory unmixing results. The experiments are conducted on simulated and real data sets to show the effectiveness of the proposed method.

scholarly journals Mathematical aspects of the kriging applied on landslide in Halenkovice (Czech Republic)

2016 ◽  
Vol 8 (1) ◽  
Author(s):  
Robert Zůvala ◽  
Eva Fišerová ◽  
Lukáš Marek
Keyword(s):  
Czech Republic ◽  
Data Analysis ◽  
Statistical Methods ◽  
Spatial Data ◽  
Spatial Data Analysis ◽  
Data Sets ◽  
Natural Phenomena ◽  
Digital Elevation ◽  
Geostatistical Techniques ◽  
Landslide Modelling

AbstractKriging is one of the geostatistical techniques for spatial data analysis that is usually used for a modelling of natural phenomena or a creation of digital elevation models. In this paper, we introduce kriging methods in the context of a landslide modelling in time. The proposed procedure, as well as most of the statistical methods, is designed for complete data sets,

scholarly journals Spatial prediction of a scalar variable based on data of a functional random field

2017 ◽  
Vol 10 (2) ◽  
pp. 315-344 ◽  
Author(s):  
Ramón Giraldo ◽  
Pedro Delicado ◽  
Jorge Mateu
Keyword(s):  
Data Analysis ◽  
Spatial Data ◽  
Auxiliary Information ◽  
Real Data ◽  
Spatial Prediction ◽  
Spatial Data Analysis ◽  
Sampling Location ◽  
Linear Model Of Coregionalization ◽  
Geostatistical Methods ◽  
Functional Context

Kriging and cokriging and their several related versions are techniques widely known and used in spatial data analysis. However, when the spatial data are functions a bridge between functional data analysis and geostatistics has to be built. I give an overview to cokriging analysis and multivariable spatial prediction to the case where the observations at each sampling location consist of samples of random functions. I extend multivariable geostatistical methods to the functional context. Our cokriging method predicts one variable at a time as in a classical multivariable sense, but considering as auxiliary information curves instead of vectors. I also give an extension of multivariable kriging to the functional context where is defined a predictor of a whole curve based on samples of curves located at a neighborhood of the prediction site. In both cases a non-parametric approach based on basis function expansion is used to estimate the parameters, and I prove that both proposals coincide when using such an approach. A linear model of coregionalization is used to define the spatial dependence among the coefficients of the basis functions, and therefore for estimating the functional parameters. As an illustration the methodological proposals are applied to analyze two real data sets corresponding to average daily temperatures measured at 35 weather stations located in the Canadian Maritime Provinces, and penetration resistance data collected at 32 sampling sites of an experimental plot.

scholarly journals Superpixel Weighted Low-rank and Sparse Approximation for Hyperspectral Unmixing

2022 ◽  
Author(s):  
Taner Ince ◽  
Tugcan Dundar ◽  
Seydi Kacmaz ◽  
Hasari Karci
Keyword(s):  
Spatial Structure ◽  
Hyperspectral Image ◽  
Real Data ◽  
Approximation Problem ◽  
Sparse Approximation ◽  
Hyperspectral Data ◽  
Low Rank ◽  
Data Sets ◽  
Spatial Weight ◽  
Homogeneous Regions

We propose a superpixel weighted low-rank and sparse unmixing (SWLRSU) method for sparse unmixing. The proposed method consists of two steps. In the first step, we segment hyperspectral image into superpixels which are defined as the homogeneous regions with different shape and sizes according to the spatial structure. Then, an efficient method is proposed to obtain a spatial weight term using superpixels to capture the spatial structure of hyperspectral data. In the second step, we solve a superpixel guided low-rank and spatially weighted sparse approximation problem in which spatial weight term obtained in the first step is used as a weight term in sparsity promoting norm. This formulation exploits the spatial correlation of the pixels in the hyperspectral image efficiently, which yields satisfactory unmixing results. The experiments are conducted on simulated and real data sets to show the effectiveness of the proposed method.

Results of testing, research and analysis of the basic clustering algorithms of numerical data sets

2019 ◽  
Vol 24 (1-2) ◽  
pp. 101-107
Author(s):  
Trokhymchuk R.M. ◽  
Keyword(s):  
Comparative Analysis ◽  
Multidimensional Scaling ◽  
Clustering Algorithms ◽  
Numerical Data ◽  
Real Data ◽  
Data Sets ◽  
Test Results ◽  
Clustering Problem

This work is devoted to the testing, research and comparative analysis of the most well-known and widely used methods and algorithms for clustering numerical data sets. Multidimensional scaling was applied to evaluate the results of solving the clustering problem by visualizing datasets at all stages of the implementation of the studied algorithms. All algorithms were tested for artificial and real data sets. As a result, for each of the investigated algorithms, the main characteristics were formulated in the form of their relative strengths and weaknesses. Based on the test results, conclusions and recommendations for using these algorithms are formulated.

scholarly journals Modeling Categorical Random Fields via Linear Bayesian Updating

2016 ◽  
Author(s):  
Xiang Huang ◽  
Zhizhong Wang
Keyword(s):  
Random Field ◽  
Spatial Data ◽  
Transition Probabilities ◽  
Prediction Method ◽  
Bayesian Updating ◽  
Spatial Data Analysis ◽  
Categorical Variables ◽  
Data Sets ◽  
Expert Opinions ◽  
Categorical Response

Categorical variables are common in spatial data analysis. Traditional analytical methods for deriving probabilities of class occurrence, such as kriging-family algorithms, have been hindered by the discrete characteristics of categorical fields. This study introduces the theoretical backgrounds of linear Bayesian updating (LBU) approach for spatial classification through expert system. Transition probabilities are interpreted as expert opinions for updating the prior marginal probabilities of categorical response variables. The main objective of this paper is to present the solid theoretical foundations of LBU and provide a categorical random field prediction method which yields relatively higher classification accuracy compared with conventional Markov chain random field (MCRF) approach. A real-world case study has also been carried out to demonstrate the superiority of our method. Since the LBU idea is originated from aggregating expert opinions and not restricted to conditional independent assumption (CIA), it may prove to be reasonably adequate for analyzing complex geospatial data sets, like remote sensing images or area-class maps.

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