Dear Heitor, have you heard of process mining? Process mining is a discipline for discovering and analyzing temporal patterns based on time-stamped data. The analysis techniques go well beyond sequence mining and can discover more elaborate patterns. Have a look here: http://www.processmining.org/

Your idea of temporal association rules has not been solved yet in process mining but would be possible: first discover A,B,C ->D (with certain threshold/confidence parameters), then use classification techniques to discover the time window.

A technique you might be interested in is: https://westergaard.eu/2013/10/declare-mining-for-dummies/

Nice tools to explore process mining further are: http://www.fluxicon.com/disco/ and http://www.promtools.org/prom6/

Thanks Mr. Fahland, I will have a closer look at process mining.

I am not quit sure about process mining but have worked with sequences a bit. I think, There are three different kinds of features useful in majority of sequence mining task (namely classification, clustering and association). 1) Staring symbol of the seq. 2) Ending symbol of Seq. 3) some symbol seen at some position in the seq. (also called observation) 5) some symbol occurring after some other symbol (also called transition uni-gram, b'coz we are relating with only one previous symbol . it could be extended to bi-gram, tri-gram or N-gram in general depending on the complexity.

I have used Probabilistic Models, like Hidden Markov Models and linear chain CRF (conditional random fields) that can create a (probabilistic) model from the data by extracting above said feature. These models can be used to answer any query of type A1^A2....An-->'?' (i.e. having observed the seq. A1,A2,....An what is the most likely next symbol). Such a query are basic building blocks of classification and association mining(pattern association you just describe). However using above algorithms for sequence clustering (unsupervised learning where sequences are not labeled) is still limited and research is still going on in this direction, I my self working on hierarchical clustering of sequences using HMM in unsupervised set up.

HMM and CRF are widely used in sequence prediction and modelling in NLP and Bioinformatics. (which i think are quite a complex and largest sequence data we have till date)

hope u find it useful.

Thanks for your answer Mr. Mukesh. I am not familiar with HMM and CRF, therefore could you please advise if these probabilistic models are able to incorporate information related to time distances between events? For example, assuming we are mining the data below, is there a way to parametrize any of these probabilistic methods, such that they can uncover patterns such as 'A occurs before B in about a month' based on entries #1 (A occurs before B [~32 days]) and #4 (A occurs before B [~28 days]).

#1 A (2012-02-20) B (2012-03-23) C (2013-01-20)

#2 B (2003-04-30) D (2004-03-20)

#3 B (2010-09-10) A (2010-10-01) C (2010-10-02)

#4 A (2010-01-10) B (2010-02-07)

Best Regards,

Heitor

For data sets, you might want to explore the datasets at kaggle.com. For example, the accelerometer data set (http://www.kaggle.com/c/accelerometer-biometric-competition) was timestamped.

The IEEE TaskForce on process mining provides 5 event longs with time-stamped data. The data may not be as large as in bioinformatics, but the temporal patterns are challenging. For each of the logs extensive information is available. The data has also been used in contests, allowing for comparing analysis results.

http://www.win.tue.nl/ieeetfpm/doku.php?id=shared:process_mining_logs

You may see the following papers. But I could not find any standard database for this.

1. Finding locally and periodically frequent sets and periodic association rules; Lecture Notes in Computer Science (LNCS), Vol 3776,(Proceedings of PReMI05 (International Conference on Pattern Recognition and Machine Intelligence), India)2005, 576-582;

Well,

in terms of symbolic temporal pattern mining, or episode mining, which is what you talk about, there's a bunch of different ways to approach mining, and a bunch of different constraints that can be used to constrain the patterns.

Generally speaking, as in the case of non-temporal pattern mining, the co-occurrence patterns, such as the A-B-C-D you give as a first example, form the basis for forming eventual rules of the form A,B,C -> D for instance. So mining episodes and mining rules is basically the same.

W.r.t. to the third pattern you ask for, you'd need the pattern A-B-C, with A, B in any order - this type of pattern is typically called a "generalized" episode. The second temporal constraint could be addressed by a maximum gap constraint, see for instance " Discovering Unbounded Episodes in Sequential Data", Casas-Garriga 2003. I am not sure about the first temporal constraint because I don't exactly know whether you want to constraint the temporal gap between A and B (maybe by a minimum gap constraint) or whether you just want to allow time windows of a relatively large size. In both cases this can be addressed by existing episode mining techniques from the late 90s, early 2000s.

So far for your concrete question. For the second one - for episode mining, there's precious little data available. I've proposed a data generator and evaluated some of the existing techniques in "Understanding episode mining techniques: Benchmarking on diverse, realistic, artificial data" (to appear autumn 2014), so if you're interested, maybe have a look at the preprint (https://lirias.kuleuven.be/bitstream/123456789/394451/1/lirias-version.pdf) - this will also give you an overview about existing techniques.

The situation is better for numerical temporal pattern mining, for which Eamonn Keogh has collected a lot of benchmarking data (http://www.cs.ucr.edu/~eamonn/time_series_data/).

I hope that some of this helps, A

The data set you describe really corresponds to the problem of sequential pattern mining (either from static or streaming data). The case you describe (patterns where events occur within a time window or separated by a gap) is know as "time constraints" in the world of sequential patterns. The first paper on this topic is GSP ( http://dl.acm.org/citation.cfm?id=650382 ) where the authors introduce the notions of sliding window, min-gap and max-gap.

You might also be interested in hybrid patterns, where data can be stamped with either a period or a specific time.

Here is a survey you migh find interesting on sequential pattern mining:

https://www.researchgate.net/publication/235246737_Sequential_Pattern_Mining_Approaches_and_Algorithms

Article Sequential Pattern Mining: Approaches and Algorithms

A bit late to the game, but in case anyone stumbles upon this post: recently I have worked on a method that extends sequential pattern mining to more complex, non-sequential, pattern, e.g. loops, concurrency, choices (inclusive or exclusive), etc. This positions the approach in-between sequential pattern mining and process mining, as it has the locality of sequential pattern mining and support the large set of process constructs typically seen in process mining.

http://www.sciencedirect.com/science/article/pii/S2352664516300232

Thanks to Venkatesh-Prasad Ranganath and Dirk Fahland for providing information on data sets. I was looking for data sets since long back.