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Rotation-invariant similarity in time series using bag-of-patterns representation
- J INTELL INF SYST
, 2012
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L.: Time-series classification through histograms of symbolic polynomials. arXiv preprint arXiv:1307.6365 (2013) Hubness-aware classification, instance selection and feature construction 27
"... Abstract—Time-series classification has attracted considerable research attention due to the various domains where time-series data are observed, ranging from medicine to econometrics. Traditionally, the focus of time-series classification has been on short time-series data composed of a unique patt ..."
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Cited by 2 (1 self)
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Abstract—Time-series classification has attracted considerable research attention due to the various domains where time-series data are observed, ranging from medicine to econometrics. Traditionally, the focus of time-series classification has been on short time-series data composed of a unique pattern with intra-class pattern distortions and variations, while recently there have been attempts to focus on longer series composed of various local patterns. This study presents a novel method which can detect local patterns in long time-series via fitting local polynomial functions of arbitrary degrees. The coefficients of the polyno-mial functions are converted to symbolic words via equivolume discretizations of the coefficients ’ distributions. The symbolic polynomial words enable the detection of similar local patterns by assigning the same words to similar polynomials. Moreover, a histogram of the frequencies of the words is constructed from each time-series ’ bag of words. Each row of the histogram enables a new representation for the series and symbolize the existence of local patterns and their frequencies. Experimental evidence demonstrates outstanding results of our method compared to the state-of-art baselines, by exhibiting the best classification accuracies in all the datasets and having statistically significant improvements in the absolute majority of experiments. I.
U.S. Army Corps of Engineers
"... Spatial trajectory analysis is crucial to uncovering insights into the motives and nature of human behavior. In this work, we study the problem of discovering motifs in trajectories based on symbolically transformed representations and context free grammars. We propose a fast and robust grammar indu ..."
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Spatial trajectory analysis is crucial to uncovering insights into the motives and nature of human behavior. In this work, we study the problem of discovering motifs in trajectories based on symbolically transformed representations and context free grammars. We propose a fast and robust grammar induction algorithm called mSEQUITUR to infer a grammar rule set from a trajectory for motif generation. Second, we designed the Symbolic Trajectory Analysis and VIsualization System (STAVIS), the first of its kind trajectory analytical system that applies grammar inference to derive trajectory signatures and enable mining tasks on the signatures. Third, an empirical evaluation is performed to demonstrate the efficiency and effectiveness of mSEQUITUR for generating trajectory signatures and discovering motifs.
Mining for Patterns in Financial Time Series
"... There is a widespread belief that certain patterns of stock prices over time portend specific future types of movement of those prices. We consider various criteria for identifying these types of patterns, and briefly look at some historical price data. We then look at various specific types of brea ..."
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There is a widespread belief that certain patterns of stock prices over time portend specific future types of movement of those prices. We consider various criteria for identifying these types of patterns, and briefly look at some historical price data. We then look at various specific types of breakout movements, and discuss ways to determine bags of patterns that may tend to precede these breakouts. Key Words: clustering of time series subsequences, streaming data, rule discovery 1.
1Scalable Classification of Repetitive Time Series Through Frequencies of Local Polynomials
"... Abstract—Time-series classification has attracted considerable re-search attention due to the various domains where time-series data are observed, ranging from medicine to econometrics. Traditionally, the focus of time-series classification has been on short time-series data composed of a unique pat ..."
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Abstract—Time-series classification has attracted considerable re-search attention due to the various domains where time-series data are observed, ranging from medicine to econometrics. Traditionally, the focus of time-series classification has been on short time-series data composed of a unique pattern with intra-class pattern distortions and variations, while recently there have been attempts to focus on longer, repetitive series composed of repeating local patterns. The primary contribution of this study relies on presenting a novel method which can detect local patterns in repetitive time-series via fitting local polynomial functions of arbitrary degrees. We express the repetitiveness degrees of time-series datasets via a novel measure. Furthermore, our method approximates local polynomials in linear time and ensures an overall linear running time complexity. The coefficients of the polynomial functions are converted to symbolic words via equivolume discretizations of the coefficients ’ distributions. The symbolic polynomial words enable the detection of similar local patterns by assigning the same words to similar polynomials. Moreover, a histogram of the frequencies of the words is constructed from each time-series ’ bag of words. Each row of the histogram enables a new representation for the series and symbolizes the occurrence of local patterns and their frequencies. In an experimental comparison against state of the art baselines on repetitive datasets, our method exhibits significant improvements in terms of prediction accuracy. 1
Invariant Factorization of Time Series
"... Time-series classification is an important domain of machine learn-ing and a plethora of methods have been developed for the task. In comparison to existing approaches, this study presents a novel method which decomposes a time-series dataset into latent patterns and membership weights of local segm ..."
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Time-series classification is an important domain of machine learn-ing and a plethora of methods have been developed for the task. In comparison to existing approaches, this study presents a novel method which decomposes a time-series dataset into latent patterns and membership weights of local segments to those patterns. The process is formalized as a constrained objective function and a tai-lored stochastic coordinate descent optimization is applied. The time-series are projected to a new feature representation consisting of the sums of the membership weights, which captures frequen-cies of local patterns. Features from various sliding window sizes are concatenated in order to encapsulate the interaction of patterns from different sizes. Finally, a large-scale experimental comparison against 6 state of the art baselines and 43 real life datasets is con-ducted. The proposed method outperforms all the baselines with statistically significant margins in terms of prediction accuracy. 1
An Information Theoretic Criterion for Empirical Validation of Time Series Models
, 2015
"... Simulated models suffer intrinsically from validation and comparison problems. The choice of a suitable indicator quantifying the distance between the model and the data is pivotal to model selection. However, how to validate and discriminate between alternative models is still an open problem calli ..."
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Simulated models suffer intrinsically from validation and comparison problems. The choice of a suitable indicator quantifying the distance between the model and the data is pivotal to model selection. However, how to validate and discriminate between alternative models is still an open problem calling for further investigation, especially in light of the increasing use of simulations in social sciences. In this paper, we present an information theoretic cri-terion to measure how close models ’ synthetic output replicates the properties of observable time series without the need to resort to any likelihood function or to impose stationarity requirements. The indicator is sufficiently general to be applied to any kind of model able to simulate or predict time series data, from simple univariate models such as Auto Re-gressive Moving Average (ARMA) and Markov processes to more complex objects including agent-based or dynamic stochastic general equilibrium models. More specifically, we use a simple function of the L-divergence computed at different block lengths in order to select the model that is better able to reproduce the distributions of time changes in the data. To evaluate the L-divergence, probabilities are estimated across frequencies including a correc-
