Application of Lasso to the Eigenvector Selection Problem in Eigenvector Based Spatial Filtering PDF Download
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Author: Hajime Seya
Publisher:
ISBN:
Category :
Languages : en
Pages : 27
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Book Description
Eigenvector based spatial filtering is one of the well-used approaches to model spatial autocorrelation among the observations or errors in a regression model. In this approach, subset of eigenvectors extracted from a modified spatial weight matrix is added to the model as explanatory variables. The subset is typically specified via the forward stepwise model selection procedure, but it is disappointingly slow when the number of observations n takes a large number. Hence as a complement or alternative, the present paper proposes the use of the LASSO (L1-penalized regression) to select the eigenvectors. The LASSO model selection procedure is applied to the well-known Boston housing dataset and simulation dataset, and its performance is compared with that of the stepwise procedure. The obtained results suggest that the LASSO is fairly fast compared the stepwise procedure, and can select eigenvectors effectively even if dataset is relatively large (n = 10000), to which the forward stepwise procedure is uneasy to apply.
Author: Hajime Seya
Publisher:
ISBN:
Category :
Languages : en
Pages : 27
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Book Description
Eigenvector based spatial filtering is one of the well-used approaches to model spatial autocorrelation among the observations or errors in a regression model. In this approach, subset of eigenvectors extracted from a modified spatial weight matrix is added to the model as explanatory variables. The subset is typically specified via the forward stepwise model selection procedure, but it is disappointingly slow when the number of observations n takes a large number. Hence as a complement or alternative, the present paper proposes the use of the LASSO (L1-penalized regression) to select the eigenvectors. The LASSO model selection procedure is applied to the well-known Boston housing dataset and simulation dataset, and its performance is compared with that of the stepwise procedure. The obtained results suggest that the LASSO is fairly fast compared the stepwise procedure, and can select eigenvectors effectively even if dataset is relatively large (n = 10000), to which the forward stepwise procedure is uneasy to apply.
Author: Rowan Cherodian
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
Author: Griffith, Daniel A.
Publisher: Edward Elgar Publishing
ISBN: 1800372825
Category : Social Science
Languages : en
Pages : 125
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Book Description
This Advanced Introduction provides a critical review and discussion of research concerning spatial statistics, differentiating between it and spatial econometrics, to answer a set of core questions covering the geographic-tagging-of-data origins of the concept and its theoretical underpinnings, conceptual advances, and challenges for future scholarly work. It offers a vital tool for understanding spatial statistics and surveys how concerns about violating the independent observations assumption of statistical analysis developed into this discipline.
Author: Daniel Griffith
Publisher: Academic Press
ISBN: 0128156929
Category : Business & Economics
Languages : en
Pages : 286
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Book Description
Spatial Regression Analysis Using Eigenvector Spatial Filtering provides theoretical foundations and guides practical implementation of the Moran eigenvector spatial filtering (MESF) technique. MESF is a novel and powerful spatial statistical methodology that allows spatial scientists to account for spatial autocorrelation in their georeferenced data analyses. Its appeal is in its simplicity, yet its implementation drawbacks include serious complexities associated with constructing an eigenvector spatial filter. This book discusses MESF specifications for various intermediate-level topics, including spatially varying coefficients models, (non) linear mixed models, local spatial autocorrelation, space-time models, and spatial interaction models. Spatial Regression Analysis Using Eigenvector Spatial Filtering is accompanied by sample R codes and a Windows application with illustrative datasets so that readers can replicate the examples in the book and apply the methodology to their own application projects. It also includes a Foreword by Pierre Legendre. Reviews the uses of ESF across linear regression, generalized linear regression, spatial autocorrelation measurement, and spatially varying coefficient models Includes computer code and template datasets for further modeling Provides comprehensive coverage of related concepts in spatial data analysis and spatial statistics
Author: A. Stewart Fotheringham
Publisher: John Wiley & Sons
ISBN: 0470855258
Category : Science
Languages : en
Pages : 282
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Book Description
Geographical Weighted Regression (GWR) is a new local modelling technique for analysing spatial analysis. This technique allows local as opposed to global models of relationships to be measured and mapped. This is the first and only book on this technique, offering comprehensive coverage on this new 'hot' topic in spatial analysis. * Provides step-by-step examples of how to use the GWR model using data sets and examples on issues such as house price determinants, educational attainment levels and school performance statistics * Contains a broad discussion of and basic concepts on GWR through to ideas on statistical inference for GWR models * uniquely features accompanying author-written software that allows users to undertake sophisticated and complex forms of GWR within a user-friendly, Windows-based, front-end (see book for details).
Author: Daniel A. Griffith
Publisher: Springer Science & Business Media
ISBN: 3540248064
Category : Science
Languages : en
Pages : 261
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Book Description
Scientific visualization may be defined as the transformation of numerical scientific data into informative graphical displays. The text introduces a nonverbal model to subdisciplines that until now has mostly employed mathematical or verbal-conceptual models. The focus is on how scientific visualization can help revolutionize the manner in which the tendencies for (dis)similar numerical values to cluster together in location on a map are explored and analyzed. In doing so, the concept known as spatial autocorrelation - which characterizes these tendencies - is further demystified.
Author: Shashi Shekhar
Publisher: Springer Science & Business Media
ISBN: 038730858X
Category : Computers
Languages : en
Pages : 1392
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Book Description
The Encyclopedia of GIS provides a comprehensive and authoritative guide, contributed by experts and peer-reviewed for accuracy, and alphabetically arranged for convenient access. The entries explain key software and processes used by geographers and computational scientists. Major overviews are provided for nearly 200 topics: Geoinformatics, Spatial Cognition, and Location-Based Services and more. Shorter entries define specific terms and concepts. The reference will be published as a print volume with abundant black and white art, and simultaneously as an XML online reference with hyperlinked citations, cross-references, four-color art, links to web-based maps, and other interactive features.
Author: Mohsen Pourahmadi
Publisher: John Wiley & Sons
ISBN: 1118034295
Category : Mathematics
Languages : en
Pages : 204
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Book Description
Methods for estimating sparse and large covariance matrices Covariance and correlation matrices play fundamental roles in every aspect of the analysis of multivariate data collected from a variety of fields including business and economics, health care, engineering, and environmental and physical sciences. High-Dimensional Covariance Estimation provides accessible and comprehensive coverage of the classical and modern approaches for estimating covariance matrices as well as their applications to the rapidly developing areas lying at the intersection of statistics and machine learning. Recently, the classical sample covariance methodologies have been modified and improved upon to meet the needs of statisticians and researchers dealing with large correlated datasets. High-Dimensional Covariance Estimation focuses on the methodologies based on shrinkage, thresholding, and penalized likelihood with applications to Gaussian graphical models, prediction, and mean-variance portfolio management. The book relies heavily on regression-based ideas and interpretations to connect and unify many existing methods and algorithms for the task. High-Dimensional Covariance Estimation features chapters on: Data, Sparsity, and Regularization Regularizing the Eigenstructure Banding, Tapering, and Thresholding Covariance Matrices Sparse Gaussian Graphical Models Multivariate Regression The book is an ideal resource for researchers in statistics, mathematics, business and economics, computer sciences, and engineering, as well as a useful text or supplement for graduate-level courses in multivariate analysis, covariance estimation, statistical learning, and high-dimensional data analysis.
Author: Max Kuhn
Publisher: Springer Science & Business Media
ISBN: 1461468493
Category : Medical
Languages : en
Pages : 595
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Book Description
Applied Predictive Modeling covers the overall predictive modeling process, beginning with the crucial steps of data preprocessing, data splitting and foundations of model tuning. The text then provides intuitive explanations of numerous common and modern regression and classification techniques, always with an emphasis on illustrating and solving real data problems. The text illustrates all parts of the modeling process through many hands-on, real-life examples, and every chapter contains extensive R code for each step of the process. This multi-purpose text can be used as an introduction to predictive models and the overall modeling process, a practitioner’s reference handbook, or as a text for advanced undergraduate or graduate level predictive modeling courses. To that end, each chapter contains problem sets to help solidify the covered concepts and uses data available in the book’s R package. This text is intended for a broad audience as both an introduction to predictive models as well as a guide to applying them. Non-mathematical readers will appreciate the intuitive explanations of the techniques while an emphasis on problem-solving with real data across a wide variety of applications will aid practitioners who wish to extend their expertise. Readers should have knowledge of basic statistical ideas, such as correlation and linear regression analysis. While the text is biased against complex equations, a mathematical background is needed for advanced topics.
Author: Roger S. Bivand
Publisher: Springer Science & Business Media
ISBN: 1461476186
Category : Medical
Languages : en
Pages : 414
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Book Description
Applied Spatial Data Analysis with R, second edition, is divided into two basic parts, the first presenting R packages, functions, classes and methods for handling spatial data. This part is of interest to users who need to access and visualise spatial data. Data import and export for many file formats for spatial data are covered in detail, as is the interface between R and the open source GRASS GIS and the handling of spatio-temporal data. The second part showcases more specialised kinds of spatial data analysis, including spatial point pattern analysis, interpolation and geostatistics, areal data analysis and disease mapping. The coverage of methods of spatial data analysis ranges from standard techniques to new developments, and the examples used are largely taken from the spatial statistics literature. All the examples can be run using R contributed packages available from the CRAN website, with code and additional data sets from the book's own website. Compared to the first edition, the second edition covers the more systematic approach towards handling spatial data in R, as well as a number of important and widely used CRAN packages that have appeared since the first edition. This book will be of interest to researchers who intend to use R to handle, visualise, and analyse spatial data. It will also be of interest to spatial data analysts who do not use R, but who are interested in practical aspects of implementing software for spatial data analysis. It is a suitable companion book for introductory spatial statistics courses and for applied methods courses in a wide range of subjects using spatial data, including human and physical geography, geographical information science and geoinformatics, the environmental sciences, ecology, public health and disease control, economics, public administration and political science. The book has a website where complete code examples, data sets, and other support material may be found: http://www.asdar-book.org. The authors have taken part in writing and maintaining software for spatial data handling and analysis with R in concert since 2003.
