Absract. This paper is concerned with the evaluation of methods for scattered data interpolation and some of the results of the tests when applied to a number of methods. The process involves evaluation of the methods in terms of timing, storage, accuracy, visual pleasantness of the surface, and ease of implementation. To indicate the flavor of the type of results obtained, we give a summary table and representative perspective plots of several surfaces.

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Scattered data interpolation: tests of some methods

This paper surveys locally weighted learning, a form of lazy learning and memory-based learning, and focuses on locally weighted linear regression. The survey discusses distance functions, smoothing parameters, weighting functions, local model structures, regularization of the estimates and bias, assessing predictions, handling noisy data and outliers, improving the quality of predictions by tuning fit parameters, interference between old and new data, implementing locally weighted learning efficiently, and applications of locally weighted learning. A companion paper surveys how locally weighted learning can be used in robot learning and control.

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Locally Weighted Learning

Preface Readership Acknowledgements Introduction Part I. The Context for Spatial Data Analysis: 1. Spatial data analysis: scientific and policy context 2. The nature of spatial data Part II. Spatial Data: Obtaining Data And Quality Issues: 3. Obtaining spatial data through sampling 4. Data quality: implications for spatial data analysis Part III. The Exploratory Analysis of Spatial Data: 5. Exploratory analysis of spatial data 6. Exploratory spatial data analysis: visualisation methods 7. Exploratory spatial data analysis: numerical methods Part IV. Hypothesis Testing in the Presence of Spatial Autocorrelation: 8. Hypothesis testing in the presence of spatial dependence Part V. Modeling Spatial Data: 9. Models for the statistical analysis of spatial data 10. Statistical modeling of spatial variation: descriptive modeling 11. Statistical modeling of spatial variation: explanatory modeling Appendices References Index.

/pdf/spatial-data-analysis-theory-and-practice-94s5yre4u5.pdf

Spatial Data Analysis: Theory and Practice

A variety of numerical methods for fitting a function to data given at a set of points scattered throughout a domain in the plane are surveyed. Four classes of methods are discussed: (1) global interpolation; (2) local interpolation; (3) global approximation; and (4) local approximation. Also, two-stage methods and contouring are discussed. The surfaces constructed include polynomials, spline functions, and rational functions, among others.

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Fitting surfaces to scattered data

Large variability and correlations among the coefficients obtained from the method of geographically weighted regression (GWR) have been identified in previous research. This is an issue that poses a serious challenge for the utility of the method as a tool to investigate multivariate relationships. The objectives of this paper are to assess: (1) the ability of GWR to discriminate between a spatially constant processes and one with spatially varying relationships; and (2) to accurately retrieve spatially varying relationships. Extensive numerical experiments are used to investigate situations where the underlying process is stationary and nonstationary, and to assess the degree to which spurious intercoefficient correlations are introduced. Two different implementations of GWR and cross-validation approaches are assessed. Results suggest that judicious application of GWR can be used to discern whether the underlying process is nonstationary. Furthermore, evidence of spurious correlations indicates that ca...

A Simulation-Based Study of Geographically Weighted Regression as a Method for Investigating Spatially Varying Relationships

Machine contouring of irregularly spaced observations can be performed in three basic steps: (1) In large areas with no data points, control values are interpolated by a specified mathematical rule. These values keep the next step “well behaved.” (2) A regional polynomial surface is fitted by least squares to the original and interpolated points. (3) The surface of step (2) is deformed smoothly to pass through the original observations. The final product is similar in appearance to hand‐drawn maps. The complete mathematical theory is developed in an appendix.

Chester R. Pelto

Papers

Automatic Contouring of Irregularly Spaced Data