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1 Introduction
1.1 The Background and Applications
1.2 The Evolution and Development
1.3 The Challenges and Issues
1.4 Content and Organization of the Book
2 Maximal Prevalent Co-location Patterns
2.1 Introduction
2.2 Why the MCHT Method Is Proposed for Mining MPCPs
2.3 Formal Problem Statement and Appropriate Mining Framework
2.3.1 Co-Location Patterns
2.3.2 Related Work
2.3.3 Contributions and Novelties
2.4 The Novel Mining Solution
2.4.1 The Overall Mining Framework
2.4.2 Bit-String-Based Maximal Clique Enumeration
2.4.3 Constructing the Participating Instance Hash Table
2.4.4 Calculating Participation Indexes and Filtering MPCPs
2.4.5 The Analysis of Time and Space Complexities
2.5 Experiments
2.5.1 Data Sets
2.5.2 Experimental Objectives
2.5.3 Experimental Results and Analysis
2.6 Chapter Summary
3 Maximal Sub-prevalent Co-location Patterns
3.1 Introduction
3.2 Basic Concepts and Properties
3.3 A Prefix-Tree-Based Algorithm (PTBA)
3.3.1 Basic Idea
3.3.2 Algorithm
3.3.3 Analysis and Pruning
3.4 A Partition-Based Algorithm (PBA)
3.4.1 Basic Idea
3.4.2 Algorithm
3.4.3 Analysis of Computational Complexity
3.5 Comparison of PBA and PTBA
3.6 Experimental Evaluation
3.6.1 Synthetic Data Generation
3.6.2 Comparison of Computational Complexity Factors
3.6.3 Comparison of Expected Costs Involved in Identifying Candidates
3.6.4 Comparison of Candidate Pruning Ratio
3.6.5 Effects of the Parameter Clumpy
3.6.6 Scalability Tests
3.6.7 Evaluation with Real Data Sets
3.7 Related Work
3.8 Chapter Summary
4 SPI-Closed Prevalent Co-location Patterns
4.1 Introduction
4.2 Why SPI-Closed Prevalent Co-locations Improve Mining
4.3 The Concept of SPI-Closed and Its Properties
4.3.1 Classic Co-location Pattern Mining
4.3.2 The Concept of SPI-Closed
4.3.3 The Properties of SPI-Closed
4.4 SPI-Closed Miner
4.4.1 Preprocessing and Candidate Generation
4.4.2 Computing Co-location Instances and Their PI Values
4.4.3 The SPI-Closed Miner
4.5 Qualitative Analysis of the SPI-Closed Miner
4.5.1 Discovering the Correct SPI-Closed Co-location Set Ω
4.5.2 The Running Time of SPI-Closed Miner
4.6 Experimental Evaluation
4.6.1 Experiments on Real-life Data Sets
4.6.2 Experiments with Synthetic Data Sets
4.7 Related Work
4.8 Chapter Summary
5 Top-k Probabilistically Prevalent Co-location Patterns
5.1 Introduction
5.2 Why Mining Top-k Probabilistically Prevalent Co-location Patterns (Top-k PPCPs)
5.3 Definitions
5.3.1 Spatially Uncertain Data
5.3.2 Prevalent Co-locations
5.3.3 Prevalence Probability
5.3.4 Min_PI-Prevalence Probabilities
5.3.5 Top-k PPCPs
5.4 A Framework of Mining Top-k PPCPs
5.4.1 Basic Algorithm
5.4.2 Analysis and Pruning of Algorithm 5.
5.5 Improved Computation of P(c, min_PI)
5.5.1 0-1-Optimization
5.5.2 The Matrix Method
5.5.3 Polynomial Matrices
5.6 Approximate Computation of P(c, min_PI)
5.7 Experimental Evaluations
5.7.1 Evaluation on Synthetic Data Sets
5.7.2 Evaluation on Real Data Sets
5.8 Chapter Summary
6 Non-redundant Prevalent Co-location Patterns
6.1 Introduction
6.2 Why We Need to Explore Non-redundant Prevalent Co-locations
6.3 Problem Definition
6.3.1 Semantic Distance
6.3.2 δ-Covered
6.3.3 The Problem Definition and Analysis
6.4 The RRclosed Method
6.5 The RRnull Method
6.5.1 The Method
6.5.2 The Algorithm
6.5.3 The Correctness Analysis
6.5.4 The Time Complexity Analysis
6.5.5 Comparative Analysis
6.6 Experimental Results
6.6.1 On the Three Real Data Sets
6.6.2 On the Synthetic Data Sets
6.7 Related Work
6.8 Chapter Summ