what is the definition of a probabilistic database?

The authors define an SLU probabilistic database Dp to be an ordered list 〈r1, . . . , rn〉 of records of the form (eid , e,W) where eid is an event-id, e is an event and W is a probability distribution over S; the list is ordered by eid.

What are the parameters that the authors consider in their experiments?

The authors consider following three parameters in their experiments: number of sources D, average number of events per source C, and support threshold θ.

What is the definition of a frequent 2-sequence?

It is argued that any of the frequent 2-sequences must begin with a frequent 1-sequence and therefore, the complete set of sequential patterns can be partitioned into as many subsets as the number of frequent 1-sequences where each 1-sequence is taken as a prefix.

What is the corresponding sequence of s?

For a sequence s = 〈s1, . . . , sq〉 and source i, when scanning Bi,s up-to the first non-zero entry e` which means sq ⊆ e`, for every item x in e` that is not in sq and is lexicographically greater than all items in sq, update F ′[x] as follows:F ′[x] := (1− c`) ∗ F ′[x] +

What is the probability of a possible world?

As a possible world is a deterministic instance of a given probabilistic database,concepts like the support of a sequence in a possible world do apply.

What is the probability of a possible world in a probabilistic database?

The expected support of a sequence s in Dp is computed as follows:ES(s,Dp) = ∑D∗∈PW (Dp)Pr[D∗] ∗ Sup(s,D∗), (1)The problem the authors consider is:Given an SLU probabilistic database Dp, determine all sequences s such that ES(s,Dp) ≥ θm, for some user-specified threshold θ, 0 < θ ≤ 1.

what is the recurrence of the p-sequence?

(4)Lemma 1. Given a p-sequence Dpi and a sequence s, by applying Eq. 4 repeatedly, the authors correctly compute Pr[s Dpi ].fast L1 computation.

Open AccessBook Chapter10.1007/978-3-642-20847-8_18

Mining sequential patterns from probabilistic databases

Q: What have the authors contributed in "Mining sequential patterns from probabilistic databases by pattern-growth" ?

The authors propose a pattern-growth approach for mining sequential patterns from probabilistic databases. The authors also noted the difficulties in generalizing PrefixSpan to the probabilistic case ( PrefixSpan is a pattern-growth algorithm, considered to be the best performer for deterministic sequential pattern mining ). The authors overcome these difficulties in this note and adapt PrefixSpan to work under probabilistic settings. The authors then report on an experimental evaluation of the candidate generateand-test approaches against the pattern-growth approach.

Q: What is the key contribution of this work?

The key contributions of this work are to formulate the analogue of a projected database in probabilistic settings, and to identify the appropriate L1 computation to perform on the projected database.

Q: How is the subset of sequential patterns mined?

The subset of sequential patterns is mined by constructing the set of projected databases based on frequent 1-sequences and mining each recursively.

Q: What is the objective of the definition of probabilistic database?

The objective is to find all sequences s such that Sup(s,D) ≥ θm for some user-defined threshold 0 < θ ≤ 1.Probabilistic Databases.

Muhammad Muzammal, +1 more

- 24 May 2011

- pp 210-221

TL;DR: In this article, the authors consider sequential pattern mining in situations where there is uncertainty about which source an event is associated with and use dynamic programming (DP) to compute the probability that a source supports a sequence.

Abstract: We consider sequential pattern mining in situations where there is uncertainty about which source an event is associated with. We model this in the probabilistic database framework and consider the problem of enumerating all sequences whose expected support is sufficiently large. Unlike frequent itemset mining in probabilistic databases [C. Aggarwal et al. KDD'09; Chui et al., PAKDD'07; Chui and Kao, PAKDD'08], we use dynamic programming (DP) to compute the probability that a source supports a sequence, and show that this suffices to compute the expected support of a sequential pattern. Next, we embed this DP algorithm into candidate generate-and-test approaches, and explore the pattern lattice both in a breadth-first (similar to GSP) and a depth-first (similar to SPAM) manner. We propose optimizations for efficiently computing the frequent 1-sequences, for re-using previously-computed results through incremental support computation, and for elmiminating candidate sequences without computing their support via probabilistic pruning. Preliminary experiments show that our optimizations are effective in improving the CPU cost.

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Most frequently asked questions

1. What have the authors contributed in "Mining sequential patterns from probabilistic databases by pattern-growth" ?

The authors propose a pattern-growth approach for mining sequential patterns from probabilistic databases.. The authors also noted the difficulties in generalizing PrefixSpan to the probabilistic case ( PrefixSpan is a pattern-growth algorithm, considered to be the best performer for deterministic sequential pattern mining ).. The authors overcome these difficulties in this note and adapt PrefixSpan to work under probabilistic settings.. The authors then report on an experimental evaluation of the candidate generateand-test approaches against the pattern-growth approach.

2. What is the key contribution of this work?

The key contributions of this work are to formulate the analogue of a projected database in probabilistic settings, and to identify the appropriate L1 computation to perform on the projected database.

3. How is the subset of sequential patterns mined?

The subset of sequential patterns is mined by constructing the set of projected databases based on frequent 1-sequences and mining each recursively.

4. What is the objective of the definition of probabilistic database?

The objective is to find all sequences s such that Sup(s,D) ≥ θm for some user-defined threshold 0 < θ ≤ 1.Probabilistic Databases.

Table 1. An SLU event database (L) transformed to p-sequences (R). Note that the events like e1 (marked with † on (R)) can only be associated with one of the sources X,Y and Z in any possible world.

Table 2. An example of computing the ES of all S-extensions of s = (a) for source X in the sample database of Table 1. The gray row is the BX,s array. In the bottom half, the cells that changed in F ′ after processing the corresponding event are marked as gray. After processing source X, values in the final column are updated to G′.

Fig. 1. Scalability of the three algorithms for decreasing values of θ, for synthetic dataset (C10D10K) (L) and for real dataset Gazelle (R).

Fig. 2. Scalability for increasing number of sources D, with average number of events per source C = 10 and ES = 1% (L), and for increasing number of events per sources C with number of sources D = 10K and ES = 25% (R).

Table 3. Number of DP computations (in millions) performed by each algorithm, for the set of experiments in Fig. 1 (L) and in Fig. 2 (R).

Citations

•Journal Article•10.1145/3314107

A Survey of Parallel Sequential Pattern Mining

Wensheng Gan, +4 more

- 07 Jun 2019

- ACM Transactions on Knowledge Discovery ...

TL;DR: An in-depth survey of the current status of parallel SPM (PSPM) is investigated and provided, including detailed categorization of traditional serial SPM approaches, and state-of-the art PSPM.

...read moreread less

290

Journal Article•10.1016/J.ESWA.2013.07.094

Sliding window based weighted maximal frequent pattern mining over data streams

Gangin Lee, +2 more

- 01 Feb 2014

- Expert Systems With Applications

TL;DR: A novel algorithm, weighted maximal frequent pattern mining over data streams based on sliding window model (WMFP-SW), which outperforms previous algorithms in terms of runtime, memory usage, and scalability.

...read moreread less

100

Proceedings Article•10.1109/CVPR.2016.289

Mining 3D Key-Pose-Motifs for Action Recognition

Chunyu Wang, +2 more

- 27 Jun 2016

TL;DR: This work proposes an efficient algorithm to mine key-pose-motifs taking into account probabilities of an action from a sequence of 3D skeletal poses, and obtains state-of-the-art performance on two benchmark datasets.

...read moreread less

Journal Article•10.1109/TKDE.2015.2454515

Mining Temporal Patterns in Time Interval-Based Data

Yi-Cheng Chen, +2 more

- 01 Dec 2015

- IEEE Transactions on Knowledge and Data ...

TL;DR: Two novel representations, endpoint representation and endtime representation, are proposed to simplify the processing of complex relationships among event intervals and develop two novel algorithms, Temporal Pattern Miner and Probabilistic Temporal pattern Miner, to discover three types of interval-based sequential patterns.

...read moreread less

Journal Article•10.1016/J.KNOSYS.2013.10.011

Mining maximal frequent patterns by considering weight conditions over data streams

Unil Yun, +2 more

- 01 Jan 2014

- Knowledge Based Systems

TL;DR: A novel method for mining Weighted Maximal Frequent Patterns over data streams, called MWS (Maximal frequent pattern mining with Weight conditions over data Streams), which guarantees efficient mining performance in the data stream environment by scanning stream databases only once, and prevents overheads of pattern extractions with an abbreviated notation.

...read moreread less

...

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References

Lecture Notes in Computer Science 2382

Petrus Bollen

- 01 Jan 2002

36.7K

•Book

Data Mining: Concepts and Techniques

Jiawei Han, +2 more

- 08 Sep 2000

TL;DR: This book presents dozens of algorithms and implementation examples, all in pseudo-code and suitable for use in real-world, large-scale data mining projects, and provides a comprehensive, practical look at the concepts and techniques you need to get the most out of real business data.

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29.9K

Proceedings Article•10.1145/170035.170072

Mining association rules between sets of items in large databases

Rakesh Agrawal, +2 more

- 01 Jun 1993

TL;DR: An efficient algorithm is presented that generates all significant association rules between items in the database of customer transactions and incorporates buffer management and novel estimation and pruning techniques.

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17K

Reducibility Among Combinatorial Problems.

Richard M. Karp

- 01 Jan 1972

TL;DR: Throughout the 1960s I worked on combinatorial optimization problems including logic circuit design with Paul Roth and assembly line balancing and the traveling salesman problem with Mike Held, which made me aware of the importance of distinction between polynomial-time and superpolynomial-time solvability.

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Introduction to Information Retrieval

Christopher D. Manning, +2 more

- 01 Jan 2008

TL;DR: In this article, the authors present an up-to-date treatment of all aspects of the design and implementation of systems for gathering, indexing, and searching documents; methods for evaluating systems; and an introduction to the use of machine learning methods on text collections.

...read moreread less

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Mining sequential patterns from probabilistic databases

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Most frequently asked questions

1. What have the authors contributed in "Mining sequential patterns from probabilistic databases by pattern-growth" ?

2. What is the key contribution of this work?

3. How is the subset of sequential patterns mined?

4. What is the objective of the definition of probabilistic database?

5. what is the definition of a probabilistic database?

6. What are the parameters that the authors consider in their experiments?

7. What is the definition of a frequent 2-sequence?

8. What is the corresponding sequence of s?

9. What is the probability of a possible world?

10. What is the probability of a possible world in a probabilistic database?

11. what is the recurrence of the p-sequence?

Figures

Citations

A Survey of Parallel Sequential Pattern Mining

Sliding window based weighted maximal frequent pattern mining over data streams

Mining 3D Key-Pose-Motifs for Action Recognition

Mining Temporal Patterns in Time Interval-Based Data

Mining maximal frequent patterns by considering weight conditions over data streams

References

Lecture Notes in Computer Science 2382

Data Mining: Concepts and Techniques

Mining association rules between sets of items in large databases

Reducibility Among Combinatorial Problems.

Introduction to Information Retrieval

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