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. First, the dimensionality of the symbolic representation is the same as the original data, and virtually all data mining algorithms scale poorly with dimensionality. Second, 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 representation on various data mining tasks of clustering, classification, query by content, anomaly detection, motif discovery, and visualization.

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Experiencing SAX: a novel symbolic representation of time series

A review on time series data mining

Time-series clustering - A decade review

The steep rise in music downloading over CD sales has created a major shift in the music industry away from physical media formats and towards online products and services. Music is one of the most popular types of online information and there are now hundreds of music streaming and download services operating on the World-Wide Web. Some of the music collections available are approaching the scale of ten million tracks and this has posed a major challenge for searching, retrieving, and organizing music content. Research efforts in music information retrieval have involved experts from music perception, cognition, musicology, engineering, and computer science engaged in truly interdisciplinary activity that has resulted in many proposed algorithmic and methodological solutions to music search using content-based methods. This paper outlines the problems of content-based music information retrieval and explores the state-of-the-art methods using audio cues (e.g., query by humming, audio fingerprinting, content-based music retrieval) and other cues (e.g., music notation and symbolic representation), and identifies some of the major challenges for the coming years.

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Content-Based Music Information Retrieval: Current Directions and Future Challenges

Linear modal synthesis methods have often been used to generate sounds for rigid bodies. One of the key challenges in widely adopting such techniques is the lack of automatic determination of satisfactory material parameters that recreate realistic audio quality of sounding materials. We introduce a novel method using prerecorded audio clips to estimate material parameters that capture the inherent quality of recorded sounding materials. Our method extracts perceptually salient features from audio examples. Based on psychoacoustic principles, we design a parameter estimation algorithm using an optimization framework and these salient features to guide the search of the best material parameters for modal synthesis. We also present a method that compensates for the differences between the real-world recording and sound synthesized using solely linear modal synthesis models to create the final synthesized audio. The resulting audio generated from this sound synthesis pipeline well preserves the same sense of material as a recorded audio example. Moreover, both the estimated material parameters and the residual compensation naturally transfer to virtual objects of different sizes and shapes, while the synthesized sounds vary accordingly. A perceptual study shows the results of this system compare well with real-world recordings in terms of material perception.

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Example-guided physically based modal sound synthesis

Knowledge Discovery in time series usually requires symbolic time series. Many discretization methods that convert numeric time series to symbolic time series ignore the temporal order of values. This often leads to symbols that do not correspond to states of the process generating the time series and cannot be interpreted meaningfully. We propose a new method for meaningful unsupervised discretization of numeric time series called Persist. The algorithm is based on the Kullback-Leibler divergence between the marginal and the self-transition probability distributions of the discretization symbols. Its performance is evaluated on both artificial and real life data in comparison to the most common discretization methods. Persist achieves significantly higher accuracy than existing static methods and is robust against noise. It also outperforms Hidden Markov Models for all but very simple cases.

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Optimizing time series discretization for knowledge discovery

We present a new method for the understandable description of local temporal relationships in multivariate data, called Time Series Knowledge Mining (TSKM). We define the Time Series Knowledge Representation (TSKR) as a new language for expressing temporal knowledge in time interval data. The patterns have a hierarchical structure, with levels corresponding to the temporal concepts duration, coincidence, and partial order. The patterns are very compact, but offer details for each element on demand. In comparison with related approaches, the TSKR is shown to have advantages in robustness, expressivity, and comprehensibility. The search for coincidence and partial order in interval data can be formulated as instances of the well known frequent itemset problem. Efficient algorithms for the discovery of the patterns are adapted accordingly. A novel form of search space pruning effectively reduces the size of the mining result to ease interpretation and speed up the algorithms. Human interaction is used during the mining to analyze and validate partial results as early as possible and guide further processing steps. The efficacy of the methods is demonstrated using two real life data sets. In an application to sports medicine the results were recognized as valid and useful by an expert of the field.

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Efficient mining of understandable patterns from multivariate interval time series

Pattern mining based on data compression has been successfully applied in many data mining tasks. For itemset data, the Krimp algorithm based on the minimumdescription length MDL principle was shown to be very effective in solving the redundancy issue in descriptive pattern mining. However, for sequence data, the redundancy issue of the set of frequent sequential patterns is not fully addressed in the literature. In this article, we study MDL-based algorithms for mining non-redundant sets of sequential patterns from a sequence database. First, we propose an encoding scheme for compressing sequence data with sequential patterns. Second, we formulate the problem of mining the most compressing sequential patterns from a sequence database. We show that this problem is intractable and belongs to the class of inapproximable problems. Therefore, we propose two heuristic algorithms. The first of these uses a two-phase approach similar to Krimp for itemset data. To overcome performance issues in candidate generation, we also propose GoKrimp, an algorithm that directly mines compressing patterns by greedily extending a pattern until no additional compression benefit of adding the extension into the dictionary. Since checks for additional compression benefit of an extension are computationally expensive we propose a dependency test which only chooses related events for extending a given pattern. This technique improves the efficiency of the GoKrimp algorithm significantly while it still preserves the quality of the set of patterns. We conduct an empirical study on eight datasets to show the effectiveness of our approach in comparison to the state-of-the-art algorithms in terms of interpretability of the extracted patterns, run time, compression ratio, and classification accuracy using the discovered patterns as features for different classifiers. © 2013 Wiley Periodicals, Inc. Statistical Analysis and Data Mining, 2013

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Mining Compressing Sequential Patterns

We present a unifying view of temporal concepts and data models in order to categorize existing approaches for unsupervised pattern mining from symbolic temporal data. In particular we distinguish time point-based methods and interval-based methods as well as univariate and multivariate methods. The mining paradigms and the robustness of many proposed approaches are compared to aid the selection of the appropriate method for a given problem. For time points, sequential pattern mining algorithms can be used to express equality and order of time points with gaps in multivariate data. For univariate data and limited gaps suffix tree methods are more efficient. Recently, efficient algorithms have been proposed to mine the more general concept of partial order from time points. For time interval data with precise start and end points the relations of Allen can be used to formulate patterns. The recently proposed Time Series Knowledge Representation is more robust on noisy data and offers an alternative semantic that avoids ambiguity and is more expressive. For both pattern languages efficient mining algorithms have been proposed.

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Unsupervised pattern mining from symbolic temporal data

We present a new approach to mining patterns from symbolic interval data that extends previous approaches by allowing semi-intervals and partially ordered patterns The mining algorithm combines and adapts efficient algorithms from sequential pattern and itemset mining for discovery of the new semi-interval patterns The semi-interval patterns and semi-interval partial order patterns are more flexible than patterns over full intervals, and are empirically demonstrated to be more useful as features in classification settings We performed an extensive empirical evaluation on seven real life interval databases totalling over 146k intervals from more than 400 classes demonstrating the flexibility and usefulness of the patterns

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Fabian Mörchen

Papers

Optimizing time series discretization for knowledge discovery

Efficient mining of understandable patterns from multivariate interval time series

Mining Compressing Sequential Patterns

Unsupervised pattern mining from symbolic temporal data

Robust Mining of Time Intervals with Semi-interval Partial Order Patterns.