| Description |
1 online resource (x, 73 pages) |
| Series |
SpringerBriefs in computer science, 2191-5768 |
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SpringerBriefs in computer science.
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| Contents |
880-01 Introduction -- Theory behind the SAR Model -- Parallel Exact SAR Model Solutions -- Comparing Exact and Approximate SAR Model Solutions -- Parallel Implementations of Approximate SAR Model Solutions -- A New Approximation: Gauss-Lanczos Approximated SAR Model Solution -- Conclusions and Future Work -- Supplementary Materials |
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880-01/(S Machine generated contents note: 1. Introduction -- 1.1. Background Information -- 1.2. Spatial Data Mining -- 1.3. Related Work -- 1.4. Contributions -- 1.5. Outline and Scope -- 2. Theory behind the SAR Model -- 2.1. Example Neighborhood Matrix (W) on Regular (Uniform) Grid Space -- 2.2. Illustration of the Neighborhood Matrix Formation on a 4-by-4 Regular Grid Space -- 2.3. Constructing the Neighborhood Matrix W on Irregular Grid Space -- 2.4. Derivation of the ML (Concentrated Log-likelihood) Function -- 2.4.1. Effect of SAR Autoregression Parameter ρ -- 2.5. Types of Optimization -- 3. Parallel Exact SAR Model Solutions -- 3.1. Problem Statement -- 3.2. Serial Implementation -- 3.3. Proposed Parallel Formulation -- 3.3.1. Stage A: Computing Eigenvalues -- 3.3.2. Stage B: The Golden Section Search -- 3.3.3. Stage C: Least Squares -- 3.4. Algebraic Cost Model -- 3.5. Experimental Work and Discussion -- 3.5.1. Which load-balancing method provides the best speedup-- 3.5.2. How does problem size impact speedup-- 3.5.3. How does chunk size affect speedup-- 3.5.4. How does number of processors affect speedup-- 3.6. Summary -- 4. Comparing Exact and Approximate SAR Model Solutions -- 4.1. Problem Statement -- 4.2. Approximation by Taylor's Series Expansion -- 4.3. Why is Taylor's Series Approximation valid-- 4.4. Approximation by Chebyshev Polynomials -- 4.5. Why is Chebyshev Polynomial Approximation valid-- 4.6. Experiment Design -- 4.7. Experimental Results -- 4.8. Summary -- 5. Parallel Implementations of Approximate SAR Model Solutions -- 5.1. Problem Statement -- 5.2. Related Work -- 5.3. Operation Cost Analysis -- 5.4. Experimental Design -- 5.5. Experimental Results -- 5.6. Summary -- 6. New Approximation: Gauss-Lanczos Approximated SAR Model Solution -- 6.1. Problem Statement -- 6.2. New Approximation: Gauss-Lanczos Method -- 6.3. Algebraic Error Ranking -- 6.4. Experimental Design and System Setup -- 6.5. Summary -- 7. Conclusions and Future Work -- 8. Supplementary Materials -- 8.1. Moran's I Index: Quantifying the Auto-correlation in Datasets -- 8.2. Simple Overview of Log-likelihood Theory -- 8.3. Derivation of Log-likelihood Function for SARMA Model -- 8.4. Proof for Eigen-values of Markov Matrix which are bounded in [-1, +1] and occur in ± pairs -- 8.5. Basic Linear Algebra Facts -- 8.6. Proof of symmetry of (I -- ρW)T (I -- M) (I -- ρW) -- 8.7. Proof of (I -- ρW)T (I -- M)(I -- ρW) [≥] 0 -- 8.8. Single Variable Optimization: The Golden Section Search -- 8.9. Multi-variable Search |
| Summary |
Explosive growth in the size of spatial databases has highlighted the need for spatial data mining techniques to mine the interesting but implicit spatial patterns within these large databases. This book explores computational structure of the exact and approximate spatial autoregression (SAR) model solutions. Estimation of the parameters of the SAR model using Maximum Likelihood (ML) theory is computationally very expensive because of the need to compute the logarithm of the determinant (log-det) of a large matrix in the log-likelihood function. The second part of the book introduces theory on SAR model solutions. The third part of the book applies parallel processing techniques to the exact SAR model solutions. Parallel formulations of the SAR model parameter estimation procedure based on ML theory are probed using data parallelism with load-balancing techniques. Although this parallel implementation showed scalability up to eight processors, the exact SAR model solution still suffers from high computational complexity and memory requirements. These limitations have led the book to investigate serial and parallel approximate solutions for SAR model parameter estimation. In the fourth and fifth parts of the book, two candidate approximate-semi-sparse solutions of the SAR model based on Taylor's Series expansion and Chebyshev Polynomials are presented. Experiments show that the differences between exact and approximate SAR parameter estimates have no significant effect on the prediction accuracy. In the last part of the book, we developed a new ML based approximate SAR model solution and its variants in the next part of the thesis. The new approximate SAR model solution is called the Gauss-Lanczos approximated SAR model solution. We algebraically rank the error of the Chebyshev Polynomial approximation, Taylor's Series approximation and the Gauss-Lanczos approximation to the solution of the SAR model and its variants. In other words, we established a novel relationship between the error in the log-det term, which is the approximated term in the concentrated log-likelihood function and the error in estimating the SAR parameter for all of the approximate SAR model solutions |
| Analysis |
Computer science |
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Database management |
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Information storage and retrieval systems |
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Artificial intelligence |
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Information Storage and Retrieval |
| Bibliography |
Includes bibliographical references |
| Notes |
English |
| Subject |
Data mining.
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Spatial analysis (Statistics)
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Spatial data infrastructures.
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Autoregression (Statistics)
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Information Storage and Retrieval
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Data Mining
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spatial analysis.
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COMPUTERS -- General.
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Informatique.
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Autoregression (Statistics)
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Data mining
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Spatial analysis (Statistics)
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Spatial data infrastructures
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| Form |
Electronic book
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| Author |
Celik, Mete
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| ISBN |
9781461418429 |
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1461418429 |
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1461418410 |
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9781461418412 |
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9781461418436 |
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1461418437 |
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