A Polynomial Time Metric for Attributed Trees 1st edition by Andrea Torsello, Dzena Hidovic, Marcello Pelillo ISBN 3540219811 9783540219811

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Product details:

ISBN 10:       3540219811
ISBN 13: 978-3540219811
Author:        Andrea Torsello, Džena Hidović, Marcello Pelillo 
 

A Polynomial-Time Metric for Attributed Trees 1st Table of contents:

1. Introduction

   • 1.1 Motivation for Attributed Tree Metrics
   • 1.2 Applications of Tree Matching and Comparison
   • 1.3 Challenges in Defining and Computing Metrics for Attributed Trees
   • 1.4 Contributions of the Paper
   • 1.5 Structure of the Paper

2. Related Work

   • 2.1 Tree Metrics and Tree Edit Distances
   • 2.2 Attributed Tree Matching Techniques
   • 2.3 Algorithms for Computing Tree Metrics
   • 2.4 Metrics in Graph Theory and Their Applications
   • 2.5 Limitations of Existing Tree Metrics and Their Computation

3. Preliminaries

   • 3.1 Definition of Attributed Trees
   • 3.2 Attributes and Their Role in Tree Comparison
   • 3.3 Existing Metrics for Trees and Graphs
   • 3.4 The Concept of Metric Spaces in Tree Matching
   • 3.5 Polynomial-Time Algorithms: Overview and Significance

4. Problem Definition

   • 4.1 Formalizing the Problem of Attributed Tree Comparison
   • 4.2 Properties of a Metric for Attributed Trees
   • 4.3 Distances Between Attributed Nodes and Edges
   • 4.4 Structure of the Attributed Tree Space
   • 4.5 Assumptions and Constraints of the Proposed Metric

5. A Polynomial-Time Metric for Attributed Trees

   • 5.1 Overview of the Proposed Metric
   • 5.2 Computation of Node and Edge Similarity
   • 5.3 Definition of the Distance Between Attributed Trees
   • 5.4 Algorithm for Computing the Metric
   • 5.5 Time Complexity Analysis: Proof of Polynomial-Time Computation
   • 5.6 Theoretical Properties and Guarantees of the Metric

6. Algorithm Design

   • 6.1 Step-by-Step Algorithm for Computing the Tree Metric
   • 6.2 Data Structures and Techniques for Efficient Calculation
   • 6.3 Optimization Strategies for Large Trees
   • 6.4 Handling Different Types of Attributes (e.g., Continuous, Categorical)
   • 6.5 Parallelization or Approximation Techniques for Scalability

7. Experimental Setup and Evaluation

   • 7.1 Datasets for Attributed Tree Comparison
   • 7.2 Evaluation Metrics for Tree Similarity
   • 7.3 Comparison with Existing Tree Metrics
   • 7.4 Experimental Protocols and Scenarios
   • 7.5 Performance Analysis of the Polynomial-Time Metric

8. Results and Discussion

   • 8.1 Quantitative Results of Metric Computation
   • 8.2 Qualitative Analysis: Visualizing Tree Distances
   • 8.3 Efficiency and Scalability of the Proposed Metric
   • 8.4 Comparison with Non-Polynomial Time Approaches
   • 8.5 Applicability to Real-World Datasets and Problems
   • 8.6 Limitations and Challenges

9. Applications

   • 9.1 Hierarchical Data Analysis
   • 9.2 Taxonomy and Ontology Comparison
   • 9.3 Bioinformatics: Phylogenetic Tree Comparison
   • 9.4 Natural Language Processing: Syntactic Tree Matching
   • 9.5 Machine Learning: Tree-based Models and Their Similarity

10. Challenges and Future Directions

• 10.1 Handling Complex Trees with High-Dimensional Attributes
• 10.2 Extending the Metric to Dynamic or Evolving Trees
• 10.3 Improving Algorithmic Efficiency for Large-Scale Applications
• 10.4 Integrating Deep Learning for Learning-Based Tree Metrics
• 10.5 Future Research in Attributed Tree Comparison

11. Conclusion

• 11.1 Summary of Contributions and Key Findings
• 11.2 Practical Implications and Impact of the Proposed Metric
• 11.3 Future Work and Open Questions
• 11.4 Final Remarks

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