Mining probabilistic representative frequent patterns from uncertain data

Copyright © SIAM. Probabilistic frequent pattern mining over uncertain data has received a great deal of attention recently due to the wide applications of uncertain data. Similar to its counterpart in deterministic databases, however, probabilistic frequent pattern mining suffers from the same problem of generating an exponential number of result patterns. The large number of discovered patterns hinders further evaluation and analysis, and calls for the need to find a small number of representative patterns to approximate all other patterns. This paper formally defines the problem of probabilistic representative frequent pattern (P-RFP) mining, which aims to find the minimal set of patterns with sufficiently high probability to represent all other patterns. The problem's bottleneck turns out to be checking whether a pattern can probabilistically represent another, which involves the computation of a joint probability of supports of two patterns. To address the problem, we propose a novel and efficient dynamic programming-based approach. Moreover, we have devised a set of effective optimization strategies to further improve the computation efficiency. Our experimental results demonstrate that the proposed P-RFP mining effectively reduces the size of probabilistic frequent patterns. Our proposed approach not only discovers the set of P-RFPs efficiently, but also restores the frequency probability information of patterns with an error guarantee

Summarizing data with representative patterns

University of Technology Sydney. Faculty of Engineering and Information Technology.The advance of technology makes data acquisition and storage become unprecedentedly convenient. It contributes to the rapid growth of not only the volume but also the veracity and variety of data in recent years, which poses new challenges to the data mining area. For example, uncertain data mining emerges due to its capability to model the inherent veracity of data; spatial data mining attracts much research attention as the widespread of location-based services and wearable devices. As a fundamental topic of data mining, how to effectively and efficiently summarize data in this situation still remains to be explored. This thesis studied the problem of summarizing data with representative patterns. The objective is to find a set of patterns, which is much more concise but still contains rich information of the original data, and may provide valuable insights for further analysis of data. In the light of this idea, we formally formulate the problem and provide effective and efficient solutions in various scenarios. We study the problem of summarizing probabilistic frequent patterns over uncertain data. Probabilistic frequent pattern mining over uncertain data has received much research attention due to the wide applicabilities of uncertain data. It suffers from the problem of generating an exponential number of result patterns, which hinders the analysis of patterns and calls for the need to find a small number of representative patterns to approximate all other patterns. We formally formulate the problem of probabilistic representative frequent pattern (P-RFP) mining, which aims to find the minimal set of patterns with sufficiently high probability to represent all other patterns. The bottleneck turns out to be checking whether a pattern can probabilistically represent another, which involves the computation of a joint probability of the supports of two patterns. We propose a novel dynamic programming-based approach to address the problem and devise effective optimization strategies to improve the computation efficiency. To enhance the practicability of P-RFP mining, we introduce a novel approximation of the joint probability with both theoretical and empirical proofs. Based on the approximation, we propose an Approximate P-RFP Mining (APM) algorithm, which effectively and efficiently compresses the probabilistic frequent pattern set. The error rate of APM is guaranteed to be very small when the database contains hundreds of transactions, which further affirms that APM is a practical solution for summarizing probabilistic frequent patterns. We address the problem of directly summarizing uncertain transaction database by formulating the problem as Minimal Probabilistic Tile Cover Mining, which aims to find a high-quality probabilistic tile set covering an uncertain database with minimal cost. We define the concept of Probabilistic Price and Probabilistic Price Order to evaluate and compare the quality of tiles, and propose a framework to discover the minimal probabilistic tile cover. The bottleneck is to check whether a tile is better than another according to the Probabilistic Price Order, which involves the computation of a joint probability. We prove that it can be decomposed into independent terms and calculated efficiently. Several optimization techniques are devised to further improve the performance. We analyze the problem of summarizing co-locations mined from spatial databases. Co-location pattern mining finds patterns of spatial features whose instances tend to locate together in geographic space. However, the traditional framework of co-location pattern mining produces an exponential number of patterns because of the downward closure property, which makes it difficult for users to understand, assess or apply the huge number of resulted patterns. To address this issue, we study the problem of mining representative co-location patterns (RCP). We first define a covering relationship between two co-location patterns then formally formulate the problem of Representative Co-location Pattern mining. To solve the problem of RCP mining, we propose the RCPFast algorithm adopting the post-mining framework and the RCPMS algorithm pushing pattern summarization into the co-location mining process

Interpretable multiclass classification by MDL-based rule lists

Interpretable classifiers have recently witnessed an increase in attention from the data mining community because they are inherently easier to understand and explain than their more complex counterparts. Examples of interpretable classification models include decision trees, rule sets, and rule lists. Learning such models often involves optimizing hyperparameters, which typically requires substantial amounts of data and may result in relatively large models. In this paper, we consider the problem of learning compact yet accurate probabilistic rule lists for multiclass classification. Specifically, we propose a novel formalization based on probabilistic rule lists and the minimum description length (MDL) principle. This results in virtually parameter-free model selection that naturally allows to trade-off model complexity with goodness of fit, by which overfitting and the need for hyperparameter tuning are effectively avoided. Finally, we introduce the Classy algorithm, which greedily finds rule lists according to the proposed criterion. We empirically demonstrate that Classy selects small probabilistic rule lists that outperform state-of-the-art classifiers when it comes to the combination of predictive performance and interpretability. We show that Classy is insensitive to its only parameter, i.e., the candidate set, and that compression on the training set correlates with classification performance, validating our MDL-based selection criterion

Mining Frequent Itemsets over Uncertain Databases

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.Comment: VLDB201

Efficient mining of frequent item sets on large uncertain databases

The data handled in emerging applications like location-based services, sensor monitoring systems, and data integration, are often inexact in nature. In this paper, we study the important problem of extracting frequent item sets from a large uncertain database, interpreted under the Possible World Semantics (PWS). This issue is technically challenging, since an uncertain database contains an exponential number of possible worlds. By observing that the mining process can be modeled as a Poisson binomial distribution, we develop an approximate algorithm, which can efficiently and accurately discover frequent item sets in a large uncertain database. We also study the important issue of maintaining the mining result for a database that is evolving (e.g., by inserting a tuple). Specifically, we propose incremental mining algorithms, which enable Probabilistic Frequent Item set (PFI) results to be refreshed. This reduces the need of re-executing the whole mining algorithm on the new database, which is often more expensive and unnecessary. We examine how an existing algorithm that extracts exact item sets, as well as our approximate algorithm, can support incremental mining. All our approaches support both tuple and attribute uncertainty, which are two common uncertain database models. We also perform extensive evaluation on real and synthetic data sets to validate our approaches. © 1989-2012 IEEE.published_or_final_versio

Model-based probabilistic frequent itemset mining

Data uncertainty is inherent in emerging applications such as location-based services, sensor monitoring systems, and data integration. To handle a large amount of imprecise information, uncertain databases have been recently developed. In this paper, we study how to efficiently discover frequent itemsets from large uncertain databases, interpreted under the Possible World Semantics. This is technically challenging, since an uncertain database induces an exponential number of possible worlds. To tackle this problem, we propose a novel methods to capture the itemset mining process as a probability distribution function taking two models into account: the Poisson distribution and the normal distribution. These model-based approaches extract frequent itemsets with a high degree of accuracy and support large databases. We apply our techniques to improve the performance of the algorithms for (1) finding itemsets whose frequentness probabilities are larger than some threshold and (2) mining itemsets with the {Mathematical expression} highest frequentness probabilities. Our approaches support both tuple and attribute uncertainty models, which are commonly used to represent uncertain databases. Extensive evaluation on real and synthetic datasets shows that our methods are highly accurate and four orders of magnitudes faster than previous approaches. In further theoretical and experimental studies, we give an intuition which model-based approach fits best to different types of data sets. © 2012 The Author(s).published_or_final_versio