Several important time series data mining problems reduce to the core task of finding approximately repeated subsequences in a longer time series. In an earlier work, we formalized the idea of approximately repeated subsequences by introducing the notion of time series motifs. Two limitations of this work were the poor scalability of the motif discovery algorithm, and the inability to discover motifs in the presence of noise. Here we address these limitations by introducing a novel algorithm inspired by recent advances in the problem of pattern discovery in biosequences. Our algorithm is probabilistic in nature, but as we show empirically and theoretically, it can find time series motifs with very high probability even in the presence of noise or “don’t care ” symbols. Not only is the algorithm fast, but it is an anytime algorithm, producing likely candidate motifs almost immediately, and gradually improving the quality of results over time.

The problem of finding a specified pattern in a time series database (i.e. query by content) has received much attention and is now a relatively mature field. In contrast, the important problem of enumerating all surprising or interesting patterns has received far less attention. This problem requires a meaningful definition of "surprise", and an efficient search technique. All previous attempts at finding surprising patterns in time series use a very limited notion of surprise, and/or do not scale to massive datasets. To overcome these lim- itations we introduce a novel technique that defines a pattern surprising if the frequency of its occurrence differs substantially from that expected by chance, given some previously seen data. This notion has the advantage of not requiring an explicit definition of surprise, which may be impossible to elicit from a domain expert. Instead the user simply gives the algorithm a collection of previously observed normal data. Our algorithm uses a suffix tree to efficiently encode the frequency of all observed patterns and allows a Markov model to predict the expected frequency of previously unobserved patterns. Once the suffix tree has been constructed, a measure of surprise for all the patterns in a new database can be determined in time and space linear in the size of the database. We demonstrate the utility of our approach with an extensive experimental evaluation.

Time series data is perhaps the most frequently encountered type of data examined by the data mining community. Clustering is perhaps the most frequently used data mining algorithm, being useful in it’s own right as an exploratory technique, and also as a subroutine in more complex data mining algorithms such as rule discovery, indexing, summarization, anomaly detection, and classification. Given these two facts, it is hardly surprising that time series clustering has attracted much attention. The data to be clustered can be in one of two formats: many individual time series, or a single time series, from which individual time series are extracted with a sliding window. Given the recent explosion of interest in streaming data and online algorithms, the latter case has received much attention. In this work we make a surprising claim. Clustering of streaming time series is completely meaningless. More concretely, clusters extracted from streaming time series are forced to obey a certain constraint that is pathologically unlikely to be satisfied by any dataset, and because of this, the clusters extracted by any clustering algorithm are essentially random. While this constraint can be intuitively demonstrated with a simple illustration and is simple to prove, it has never appeared in the literature. We can justify calling our claim surprising, since it invalidates the contribution of dozens of previously published papers. We will justify our claim with a theorem, illustrative examples, and a comprehensive set of experiments on reimplementations of previous work. Although the primary contribution of our work is to draw attention to the fact that an apparent solution to an important problem is incorrect and should no longer be used, we also introduce a novel method which, based on the concept of time series motifs, is able to meaningfully cluster some streaming time series datasets.

The problem of efficiently locating previously known patterns in a time series database (i.e., query by content) has received much attention and may now largely be regarded as a solved problem. However, from a knowledge discovery viewpoint, a more interesting problem is the enumeration of previously unknown, frequently occurring patterns. We call such patterns "motifs," because of their close analogy to their discrete counterparts in computation biology. An efficient motif discovery algorithm for time series would be useful as a tool for summarizing and visualizing massive time series databases. In addition, it could be used as a subroutine in various other data mining tasks, including the discovery of association rules, clustering and classification. In this work we carefully motivate, then introduce, a non-trivial definition of time series motifs. We propose an efficient algorithm to discover them, and we demonstrate the utility and efficiency of our approach on several real world datasets.

Moments before the launch of every space vehicle, engineering discipline specialists must make a critical go/no-go decision. The cost of a false positive, allowing a launch in spite of a fault, or a false negative, stopping a potentially successful launch, can be measured in the tens of millions of dollars, not including the cost in morale and other more intangible detriments. The Aerospace Corporation is responsible for providing engineering assessments critical to the go/no-go decision for every Department of Defense space vehicle. These assessments are made by constantly monitoring streaming telemetry data in the hours before launch. We will introduce VizTree, a novel time-series visualization tool to aid the Aerospace analysts who must make these engineering assessments. VizTree was developed at the University of California, Riverside and is unique in that the same tool is used for mining archival data and monitoring incoming live telemetry. The use of a single tool for both aspects of the task allows a natural and intuitive transfer of mined knowledge to the monitoring task. Our visualization approach works by transforming the time series into a symbolic representation, and encoding the data in a modified suffix tree in which the frequency and other properties of patterns are mapped onto colors and other visual properties. We demonstrate the utility of our system by comparing it with state-of-the-art batch algorithms on several real and synthetic datasets.

The problem of characterizing and detecting recurrent sequence patterns such as substrings or motifs and related associations or rules is variously pursued in order to compress data, unveil structure, infer succinct descriptions, extract and classify features, etc. In Molecular Biology, exceptionally frequent or rare words in bio-sequences have been implicated in various facets of biological function and structure. The discovery, particularly on a massive scale, of such patterns poses interesting methodological and algorithmic problems, and often exposes scenarios in which tables and synopses grow faster and bigger than the raw sequences they are meant to encapsulate. In previous study, the ability to succinctly compute, store, and display unusual substrings has been linked to a subtle interplay between the combinatorics of the subword of a word and local monotonicities of some scores used to measure the departure from expectation.

The problem of efficiently locating previously known patterns in a time series database (i.e., query by content) has received much attention and may now largely be regarded as a solved problem. However, from a knowledge discovery viewpoint, a more interesting problem is the enumeration of previously unknown, frequently occurring patterns. We call such patterns "motifs", because of their close analogy to their discrete counterparts in computation biology. An efficient motif discovery algorithm for time series would be useful as a tool for summarizing and visualizing massive time series databases. In addition it could be used as a subroutine in various other data mining tasks, including the discovery of association rules, clustering and classification.

Many high level representations of time series have been proposed for data mining, including Fourier transforms, wavelets, eigenwaves, piecewise polynomial models etc. Many researchers have also considered symbolic representations of time series, noting that such representations would potentiality allow researchers to avail of the wealth of data structures and algorithms from the text processing and bioinformatics communities. While many symbolic representations of time series have been introduced over the past decades, they all suffer from two fatal flaws. Firstly, the dimensionality of the symbolic representation is the same as the original data, and virtually all data mining algorithms scale poorly with dimensionality. Secondly, although distance measures can be defined on the symbolic approaches, these distance measures have little correlation with distance measures defined on the original time series. In this work we formulate a new symbolic representation of time series. Our representation is unique in that it allows dimensionality/numerosity reduction, and it also allows distance measures to be defined on the symbolic approach that lower bound corresponding distance measures defined on the original series. As we shall demonstrate, this latter feature is particularly exciting because it allows one to run certain data mining algorithms on the efficiently manipulated symbolic representation, while producing identical results to the algorithms that operate on the original data. In particular, we will demonstrate the utility of our

GenRGenS is a software tool dedicated to randomly generating genomic sequences and structures. It handles several classes of models useful for sequence analysis, such as Markov chains, Hidden Markov models, weighted context-free grammars, regular expressions and PROSITE expressions. GenRGenS is the only program that can handle weighted context-free grammars, thus allowing the user to model and generate structured objects (such as RNA secondary structures) of any given desired size. GenRGenS also allows the user to combine several of these different models at the same time. Availability: Source and executable files of GenRGenS (in Java) and the complete user’s manual are freely available at dev.GenRGenS@lri.fr

Assessing statistical significance of overrepresentation of exceptional words is becoming an important task in computational biology.