The effects of spatial autoregressive dependencies on inference in ordinary least squares: a geometric approach

There is a common belief that the presence of residual spatial autocorrelation in ordinary least squares (OLS) regression leads to inflated significance levels in beta coefficients and, in particular, inflated levels relative to the more efficient spatial error model (SEM). However, our simulations show that this is not always the case. Hence, the purpose of this paper is to examine this question from a geometric viewpoint. The key idea is to characterize the OLS test statistic in terms of angle cosines and examine the geometric implications of this characterization. Our first result is to show that if the explanatory variables in the regression exhibit no spatial autocorrelation, then the distribution of test statistics for individual beta coefficients in OLS is independent of any spatial autocorrelation in the error term. Hence, inferences about betas exhibit all the optimality properties of the classic uncorrelated error case. However, a second more important series of results show that if spatial autocorrelation is present in both the dependent and explanatory variables, then the conventional wisdom is correct. In particular, even when an explanatory variable is statistically independent of the dependent variable, such joint spatial dependencies tend to produce “spurious correlation” that results in over-rejection of the null hypothesis. The underlying geometric nature of this problem is clarified by illustrative examples. The paper concludes with a brief discussion of some possible remedies for this problem.     

Artificial Neural Network (ANN) Based Inversion of Benthic Substrate Bottom Type and Bathymetry in Optically Shallow Waters - Initial Model Results

Ocean-colour remote sensing in optically shallow waters is influenced by contribution from the water column depth as well as by the substrate type. Therefore, it is required to include the contribution from the water column and substrate bottom type for bathymetry estimation. In this report we demonstrate the use of Artificial Neural Network (ANN) based approach to spectrally distinguish various benthic bottom types and estimate depth of substrate bottom simultaneously in optically shallow waters. We have used in-water radiative transfer simulation modeling to generate simulated top-of-the-water column reflectance the four major benthic bottom types viz. sea grass, coral sand, green algae and red algae using Hydrolight simulation model. The simulated remote sensing reflectance, for the four benthic bottom types having benthic bottom depth up to 30 m were generated for moderately clear waters. A multi-layer perceptron (MLP) type neural network was trained using the simulated data. ANN based approach was used for classification of the benthic bottom type and simultaneous inversion of bathymetry. Simulated data was inverted to yield benthic bottom type classification with an accuracy of ~98% for the four benthic substrate types and the substrate depth were estimated with an error of 0% for sea grass, 1% for coral sand and 1–3% for green and red algae up to 25 m, whereas for substrate bottom deeper than 25 m depth the classification errors increased by 2–5% for three substrate bottom types except sea grass bottom type. The initial results are promising which needs validation using the in-situ measured remote sensing reflectance spectra for implementing further on satellite data.     

Water Harvesting Structure Positioning by Using Geo-Visualization Concept and Prioritization of Mini-Watersheds Through Morphometric Analysis in the Lower Tapi Basin

Geo-visualization concept has been used for positioning water harvesting structures in Varekhadi watershed consisting of 26 mini watersheds, falling in Lower Tapi Basin (LTB), Surat district, Gujarat state. For prioritization of the mini watersheds, morphometric analysis was utilized by using the linear parameters such as bifurcation ratio (R_b), drainage density (D_d), stream frequency (F_u), texture ratio (T), length of overland flow (L_o) and the shape parameter such as form factor (R_f), shape factor (B_s), elongation ratio (R_e), compactness constant (C_c) and circularity ratio (R_c). The different prioritization ranks were assigned after evaluation of the compound factor. 3 Dimensional (3D) Elevation Model (DEM) from Shuttle Radar Topography Mission (SRTM) and DEM from topo contour were analyzed in ArcScene 9.1 and the fly tool was utilized for the Geo-visualization of Varekhadi mini watersheds as per the priority ranks. Combining this with soil map and slope map, the best feasibility of positioning check dams in mini-watershed no. 1, 5 and 24 has been proposed, after validation of the sites.     

A Hierarchical Hybrid SVM Method for Classification of Remotely Sensed Data

The focus of this work is on developing a new hierarchical hybrid Support Vector Machine (SVM) method to address the problems of classification of multi or hyper spectral remotely sensed images and provide a working technique that increases the classification accuracy while lowering the computational cost and complexity of the process. The paper presents issues in analyzing large multi/hyper spectral image data sets for dimensionality reduction, coping with intra pixel spectral variations, and selection of a flexible classifier with robust learning process. Experiments conducted revealed that a computationally cheap algorithm that uses Hamming distance between the pixel vectors of different bands to eliminate redundant bands was quite effective in helping reduce the dimensionality. The paper also presents the concept of extended mathematical morphological profiles for segregating the input pixel vectors into pure or mixed categories which will enable further computational cost reductions. The proposed method’s overall classification accuracy is tested with IRS data sets and the Airborne Visible Infrared Imaging Spectroradiometer Indian Pines hyperspectral benchmark data set and presented.     

Spectral and Spatial Quality Analysis in Pan Sharpening Process

Image fusion is a process to obtain new images containing more information by combining images obtained same or different sensors. With most of the earth observation satellites, high spatial resolution panchromatic images and low spatial resolution multispectral images are obtained. As an example of image fusion ??pan sharpening?? is a process of combining of high spatial resolution panchromatic images and low spatial resolution multispectral images. At the end of the fusion process both high spatial and spectral resolution new images are obtained. In this study, panchromatic and multispectral images gathered from Ikonos were used. Panchromatic and multispectral images belonging to the same sensor were combined by using different image fusion methods. As pan sharpening methods Brovey transform, Modified IHS, Principal Component Analysis (PCA), Wavelet PC transform and Wavelet A Trous transformation methods were used. Quality of fused products was evaluated from the point of view of both visual and statistical criteria. While wavelet based methods are succesfull in terms of protection of spectral quality of original multispectral images, the colorbased and statistical methods are giving better results within the improvement of spatial content.     

Recent advances in accessibility research: Representation,methodology and applications

 In this article we examine recent advances in accessibility research and their implications for future studies. We base our discussion on three intersecting dimensions that are useful for evaluating the contribution of recent studies: representation, methodology and applications. Various examples are selected to show that research concerned with representation and methodological problem solving is often applied to issues of broad concern in policy and planning. It is, however, not clear that the simultaneous treatment of representation, methodological and application issues has ever been fully worked out. The questions raised in this article may serve as a foundation for addressing issues pertinent to accurate representation, improved model building, and more rigorous applications in accessibility research. Received: 9 December 2002 / Accepted: 10 February 2003     

Groebner-basis solution of the three-dimensional resection problem (P4P)

The three-dimensional (3-D) resection problem is usually solved by first obtaining the distances connecting the unknown point P{X,Y,Z} to the known points P_i{X_i,Y_i,Z_i}i=1,2,3 through the solution of the three nonlinear Grunert equations and then using the obtained distances to determine the position {X,Y,Z} and the 3-D orientation parameters {,, }. Starting from the work of the German J. A. Grunert (1841), the Grunert equations have been solved in several substitutional steps and the desire as evidenced by several publications has been to reduce these number of steps. Similarly, the 3-D ranging step for position determination which follows the distance determination step involves the solution of three nonlinear ranging (`Bogenschnitt') equations solved in several substitution steps. It is illustrated how the algebraic technique of Groebner basis solves explicitly the nonlinear Grunert distance equations and the nonlinear 3-D ranging (`Bogenschnitt') equations in a single step once the equations have been converted into algebraic (polynomial) form. In particular, the algebraic tool of the Groebner basis provides symbolic solutions to the problem of 3-D resection. The various forward and backward substitution steps inherent in the classical closed-form solutions of the problem are avoided. Similar to the Gauss elimination technique in linear systems of equations, the Groebner basis eliminates several variables in a multivariate system of nonlinear equations in such a manner that the end product normally consists of a univariate polynomial whose roots can be determined by existing programs e.g. by using the roots command in Matlab.Acknowledgments.The first author wishes to acknowledge the support of JSPS (Japan Society of Promotion of Science) for the financial support that enabled the completion of the write-up of the paper at Kyoto University, Japan. The author is further grateful for the warm welcome and the good working atmosphere provided by his hosts Professors S. Takemoto and Y. Fukuda of the Department of Geophysics, Graduate School of Science, Kyoto University, Japan.