LNAI 2682 Model Independent Bounding of the Supports of Boolean Formulae in Binary Data 1st Edition by Artur Bykowski, Jouni Seppänen, Jaakko Hollmén ISBN 9783540224792 354022479X

Data mining algorithms such as the Apriori method for finding frequent sets in sparse binary data can be used for efficient computation of a large number of summaries from huge data sets. The collection of frequent sets gives a collection of marginal frequencies about the underlying data set. Sometimes, we would like to use a collection of such marginal frequencies instead of the entire data set (e.g. when the original data is inaccessible for confidentiality reasons) to compute other interesting summaries. Using combinatorial arguments, we may obtain tight upper and lower bounds on the values of inferred summaries. In this paper, we consider a class of summaries wider than frequent sets, namely that of frequencies of arbitrary Boolean formulae. Given frequencies of a number of any different Boolean formulae, we consider the problem of finding tight bounds on the frequency of another arbitrary formula. We give a general formulation of the problem of bounding formula frequencies given some background information, and show how the bounds can be obtained by solving a linear programming problem. We illustrate the accuracy of the bounds by giving empirical results on real data sets.

LNAI 2682 Model Independent Bounding of the Supports of Boolean Formulae in Binary Data 1st Edition Table of contents:

Chapter 1: Introduction to Boolean Formulae and Binary Data

• Understanding Boolean Formulae
• The Role of Binary Data in Data Mining
• The Importance of Support in Boolean Formulae
• Challenges in Mining Boolean Formulae from Binary Data

Chapter 2: Fundamentals of Support in Boolean Formulae

• What is Support in Data Mining?
• Support of Boolean Formulae: Definitions and Properties
• The Role of Support in Mining Association Rules and Frequent Patterns
• Modeling Binary Data with Boolean Formulae

Chapter 3: Bounding the Support of Boolean Formulae

• What Does Bounding Mean in the Context of Boolean Formulae?
• Methods for Estimating Support in Large Binary Datasets
• Exact vs. Approximate Bounding
• Challenges in Bounding Supports for Large-Scale Data

Chapter 4: Model-Independent Bounding Techniques

• Overview of Model-Independent Methods
• The Need for Model Independence in Bounding Support
• Algorithms for Model-Independent Bounding
• Theoretical Foundations of Bounding Techniques

Chapter 5: Optimizing the Bounding Process

• Efficiency in Bounding Algorithms
• Performance Considerations: Time Complexity and Accuracy
• Approaches to Improve Bounding Precision
• Trade-Offs Between Speed and Accuracy in Bounding Techniques

Chapter 6: Applications of Bounding Supports in Data Mining

• Using Support Bounds for Efficient Rule Mining
• Bounding in Frequent Itemset Mining
• Applications in Feature Selection and Data Preprocessing
• Real-World Use Cases: Market Basket Analysis, Bioinformatics, and More

Chapter 7: Advanced Techniques in Bounding Boolean Formulae

• Higher-Order Boolean Formulae and Complex Constraints
• Multi-dimensional Bounding of Supports
• Integrating Bounding Techniques with Other Data Mining Paradigms (e.g., Classification, Clustering)
• Recent Advances and Research Directions

Chapter 8: Case Studies and Practical Implementations

• Case Study 1: Mining Binary Data for Frequent Itemsets
• Case Study 2: Predictive Modeling with Boolean Formulae
• Case Study 3: Efficiency Gains from Bounding in Large-Scale Mining Applications
• Lessons Learned from Implementations

Chapter 9: Future Trends in Bounding Supports of Boolean Formulae

• Emerging Trends in Data Mining for Boolean Formulae
• The Future of Support Bounding in Big Data and Distributed Systems
• Integrating Machine Learning with Bounding Techniques
• Open Challenges and Research Opportunities

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