Mining frequent itemsets in a stream

Calders, Toon; Dexters, Nele; Gillis, Joris J. M.; Goethals, Bart

doi:10.1016/j.is.2012.01.005

Cited by 58 publications

(24 citation statements)

References 22 publications

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“…Luckily, Calders et al [11] demonstrated that we can use the classic PAVA algorithm by Ayer et al [5] to solve this problem for every value of j in total O(n) time.…”

Section: Linear Approximation Algorithmmentioning

confidence: 99%

Density-Friendly Graph Decomposition

Tatti

2019

ACM Trans. Knowl. Discov. Data

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Decomposing a graph into a hierarchical structure via k-core analysis is a standard operation in any modern graph-mining toolkit. k-core decomposition is a simple and efficient method that allows to analyze a graph beyond its mere degree distribution. More specifically, it is used to identify areas in the graph of increasing centrality and connectedness, and it allows to reveal the structural organization of the graph.Despite the fact that k-core analysis relies on vertex degrees, k-cores do not satisfy a certain, rather natural, density property. Simply put, the most central k-core is not necessarily the densest subgraph. This inconsistency between k-cores and graph density provides the basis of our study.We start by defining what it means for a subgraph to be locally-dense, and we show that our definition entails a nested chain decomposition of the graph, similar to the one given by k-cores, but in this case the components are arranged in order of increasing density. We show that such a locally-dense decomposition for a graph G = (V , E) can be computed in polynomial time. The running time of the exact decomposition algorithm is O |V | 2 |E| but is significantly faster in practice. In addition, we develop a linear-time algorithm that provides a factor-2 approximation to the optimal locally-dense decomposition. Furthermore, we show that the k-core decomposition is also a factor-2 approximation, however, as demonstrated by our experimental evaluation, in practice k-cores have different structure than locally-dense subgraphs, and as predicted by the theory, k-cores are not always well-aligned with graph density. of the human brain [19], graph visualization [3], as well as influence analysis [22,33] and team formation [9].The fact that the k-core decomposition of a graph gives a chain of subgraphs where vertex degrees are higher in the inner cores, suggests that we should expect that the inner cores are, in certain sense, more dense or more connected than the outer cores. As we will show shortly, this statement is not true. Furthermore, in this paper we show how to obtain a graph decomposition for which the statement is true, namely, the inner subgraphs of the decomposition are denser than the outer ones. To quantify density, we adopt a classic notion used in the densest-subgraph problem [13,17], where density is defined as the ratio between the edges and the vertices of a subgraph. This density definition can be also viewed as the average degree divided by 2.Our motivating observation is that k-cores are not ordered according to this density definition. The next example demonstrates that the most inner core is not necessarily the densest subgraph, and in fact, we can increase the density by either adding or removing vertices.

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“…Luckily, Calders et al [11] demonstrated that we can use the classic PAVA algorithm by Ayer et al [5] to solve this problem for every value of j in total O(n) time.…”

Section: Linear Approximation Algorithmmentioning

confidence: 99%

Density-Friendly Graph Decomposition

Tatti

2019

ACM Trans. Knowl. Discov. Data

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“…Both supervised and unsupervised techniques have been employed to automatically adapt and construct event patterns. A widely used unsupervised learning technique is the frequency-based analysis of sequences of events (e.g., Yu et al [2004], Lee and Lee [2005], Vautier et al [2007], Álvarez et al [2010], and Calders et al [2014]). Frequency-based analysis is a promising approach for discovering unknown events in databases or logs, but it is limited to propositional learning.…”

Section: Distributed Event Recognitionmentioning

confidence: 99%

Event Recognition Challenges and Techniques

Artikis

Gal

Kalogeraki

et al. 2014

ACM Trans. Internet Technol.

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“…Further interestingness measures for episodes, either statistically motivated or aimed at removing bias toward smaller episodes, were made by Garriga [22], Gwadera et al [23,24], Calders et al [25], and Tatti [9]. All these methods, however, were limited to finding interesting episodes, and stopped short of discovering association rules between them.…”

Section: Related Workmentioning

confidence: 99%

MARBLES: Mining Association Rules Buried in Long Event Sequences

Čule

Tatti

Goethals

2012

Proceedings of the 2012 SIAM International Conference on Data Mining

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Sequential pattern discovery is a well-studied field in data mining. Episodes are sequential patterns that describe events that often occur in the vicinity of each other. Episodes can impose restrictions on the order of the events, which makes them a versatile technique for describing complex patterns in the sequence. Most of the research on episodes deals with special cases such as serial and parallel episodes, while discovering general episodes is surprisingly understudied. This is particularly true when it comes to discovering association rules between them.In this paper we propose an algorithm that mines association rules between two general episodes. On top of the traditional definitions of frequency and confidence, we introduce two novel confidence measures for the rules. The major challenge in mining these association rules is pattern explosion. To limit the output, we aim to eliminate all redundant rules. We define the class of closed association rules, and show that this class contains all non-redundant output. To make the algorithm efficient, we use further pruning steps along the way. First of all, we generate only free and closed frequent episodes from which we create candidate rules, we speed up the evaluation of the rules, and finally prune the remaining non-closed rules from the output.

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Mining frequent itemsets in a stream

Cited by 58 publications

References 22 publications

Density-Friendly Graph Decomposition

Density-Friendly Graph Decomposition

Event Recognition Challenges and Techniques

MARBLES: Mining Association Rules Buried in Long Event Sequences

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