Our world is filled with both beautiful and brainy people, but how often does a Nobel Prize winner also wins a beauty pageant? Let us assume that someone who is both very beautiful and very smart is more rare than what we would expect from the combination of the number of beautiful and brainy people. Of course there will still always be some individuals that defy this stereotype; these beautiful brainy people are exactly the class of anomaly we focus on in this paper. They do not posses intrinsically rare qualities, it is the unexpected combination of factors that makes them stand out.In this paper we define the above described class of anomaly and propose a method to quickly identify them in transaction data. Further, as we take a pattern set based approach, our method readily explains why a transaction is anomalous. The effectiveness of our method is thoroughly verified with a wide range of experiments on both real world and synthetic data.
When a seismologist analyses a new seismogram it is often useful to have access to a set of similar seismograms. For example if she tries to determine the event, if any, that caused the particular readings on her seismogram. So, the question is: when are two seismograms similar?To define such a notion of similarity, we first preprocess the seismogram by a wavelet decomposition, followed by a discretisation of the wavelet coefficients. Next we introduce a new type of patterns on the resulting set of aligned symbolic time series. These patterns, called block patterns, satisfy an Apriori property and can thus be found with a levelwise search. Next we use MDL to define when a set of such patterns is characteristic for the data. We introduce the MuLTi-Krimp algorithm to find such code sets.In experiments we show that these code sets are both good at distinguishing between dissimilar seismograms and good at recognising similar seismograms. Moreover, we show how such a code set can be used to generate a synthetic seismogram that shows what all seismograms in a cluster have in common.
We study how to obtain concise descriptions of discrete multivariate sequential data. In particular, how to do so in terms of rich multivariate sequential patterns that can capture potentially highly interesting (cor)relations between sequences. To this end we allow our pattern language to span over the domains (alphabets) of all sequences, allow patterns to overlap temporally, as well as allow for gaps in their occurrences.We formalise our goal by the Minimum Description Length principle, by which our objective is to discover the set of patterns that provides the most succinct description of the data. To discover highquality pattern sets directly from data, we introduce DITTO, a highly efficient algorithm that approximates the ideal result very well.Experiments show that DITTO correctly discovers the patterns planted in synthetic data. Moreover, it scales favourably with the length of the data, the number of attributes, the alphabet sizes. On real data, ranging from sensor networks to annotated text, DITTO discovers easily interpretable summaries that provide clear insight in both the univariate and multivariate structure.
We study how to obtain concise descriptions of discrete multivariate sequential data. In particular, how to do so in terms of rich multivariate sequential patterns that can capture potentially highly interesting (cor)relations between sequences. To this end we allow our pattern language to span over the domains (alphabets) of all sequences, allow patterns to overlap temporally, as well as allow for gaps in their occurrences.We formalise our goal by the Minimum Description Length principle, by which our objective is to discover the set of patterns that provides the most succinct description of the data. To discover highquality pattern sets directly from data, we introduce DITTO, a highly efficient algorithm that approximates the ideal result very well.Experiments show that DITTO correctly discovers the patterns planted in synthetic data. Moreover, it scales favourably with the length of the data, the number of attributes, the alphabet sizes. On real data, ranging from sensor networks to annotated text, DITTO discovers easily interpretable summaries that provide clear insight in both the univariate and multivariate structure.
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