Mining Frequent Itemsets over Uncertain Databases (1208.0292v1)

Abstract: In recent years, due to the wide applications of uncertain data, mining frequent itemsets over uncertain databases has attracted much attention. In uncertain databases, the support of an itemset is a random variable instead of a fixed occurrence counting of this itemset. Thus, unlike the corresponding problem in deterministic databases where the frequent itemset has a unique definition, the frequent itemset under uncertain environments has two different definitions so far. The first definition, referred as the expected support-based frequent itemset, employs the expectation of the support of an itemset to measure whether this itemset is frequent. The second definition, referred as the probabilistic frequent itemset, uses the probability of the support of an itemset to measure its frequency. Thus, existing work on mining frequent itemsets over uncertain databases is divided into two different groups and no study is conducted to comprehensively compare the two different definitions. In addition, since no uniform experimental platform exists, current solutions for the same definition even generate inconsistent results. In this paper, we firstly aim to clarify the relationship between the two different definitions. Through extensive experiments, we verify that the two definitions have a tight connection and can be unified together when the size of data is large enough. Secondly, we provide baseline implementations of eight existing representative algorithms and test their performances with uniform measures fairly. Finally, according to the fair tests over many different benchmark data sets, we clarify several existing inconsistent conclusions and discuss some new findings.

• The paper defines and relates two frequent itemset types for uncertain databases (expected support and probabilistic), demonstrating their convergence on large datasets.
• The study compares eight algorithms for mining uncertain databases and evaluates approximation techniques, showing Normal distribution methods are efficient for large datasets.
• Experiments show algorithm performance varies by data density (UApriori for dense, UH-Mine for sparse) and exact methods incur higher computation costs than approximations.

Mining Frequent Itemsets over Uncertain Databases: A Technical Analysis

This paper addresses the critical challenge of mining frequent itemsets within uncertain databases, a problem that diverges fundamentally from its counterpart in deterministic databases due to the random nature of itemset support. In uncertain databases, the itemset support is not a fixed count but a random variable, which necessitates a bifurcated approach to define what constitutes a frequent itemset. The paper delineates two prevalent definitions: the expected support-based frequent itemset and the probabilistic frequent itemset, providing insights into their interoperability and unified applicability when data volume increases substantially.

Key Findings and Contributions:

1. Unified Definition and Relationship Examination:
   • The authors demonstrate a mathematical correlation between expected support-based frequent itemsets and probabilistic frequent itemsets. The paper establishes that these definitions converge under large data sets, where the expected value and variance of itemset support allow the computation of frequent probabilities through statistical distributions such as Poisson Binomial and Normal distributions, following the Lyapunov Central Limit Theorem.
2. Consistency in Algorithm Performance:
   • Baseline implementations of eight representative algorithms are presented, facilitating a fair comparison across dense and sparse datasets with varying probability distributions. The inclusion of uniform experimental measures eliminates discrepancies stemming from disparate experimental setups in prior research, thus resolving past contradictory conclusions.
3. Approximation Techniques and Their Efficacy:
   • The paper explores approximation approaches leveraging statistical distributions for efficient computation, notably through Poisson and Normal distributions. The Normal distribution-based approximation proves particularly effective in large datasets, significantly reducing computational complexity and resource allocation compared to exact methods.

Experimental Insights:

• Algorithmic Performance:
  • The research shows a nuanced comparison of algorithm efficiency conditioned by dataset density and support thresholds. Under dense conditions and higher thresholds, breadth-first algorithms like UApriori outperform, whereas depth-first algorithms like UH-Mine excel in sparse settings and lower thresholds.
• Memory and Computational Trade-offs:
  • Exact methods provide precise results but at the cost of increased computational overheads and memory usage, while approximation methods offer substantial computational reduction, maintaining high accuracy levels in extensive datasets.

Implications for Future Research:

• The exploration of uncertain databases remains ripe for refinement, with hybrid models potentially enhancing frequent itemset discovery. The convergence of definitions as data scales open pathways for integrating deterministic approaches in uncertain environments, ensuring algorithmic resilience across varied dataset configurations.
• This paper sets a foundational platform for future investigations into the probabilistic analysis of uncertain data and the potential for machine learning applications in pattern recognition and data synthesis.

Conclusion:

This research makes substantial strides in elevating the understanding and efficiency of frequent itemset mining in uncertain databases. By harmonizing definitions and offering robust comparative analysis, it paves the way for enhanced data processing methodologies that respond dynamically to the inherent uncertainties of modern data landscapes.