Searching and Mining Trillions of Time Series Subsequences under Dynamic Time Warping
Most time series data mining algorithms use similarity search as a core subroutine, and thus the time taken for similarity search is the bottleneck for virtually all time series data mining algorithms. The difficulty of scaling search to large datasets largely explains why most academic work on time series data mining has plateaued at considering a few millions of time series objects, while much of industry and science sits on billions of time series objects waiting to be explored. In this work we show that by using a combination of four novel ideas we can search and mine truly massive time series for the first time. We demonstrate the following extremely unintuitive fact; in large datasets we can exactly search under DTW much more quickly than the current state-of-the-art Euclidean distance search algorithms. We demonstrate our work on the largest set of time series experiments ever attempted. In particular, the largest dataset we consider is larger than the combined size of all of the time series datasets considered in all data mining papers ever published. We show that our ideas allow us to solve higher-level time series data mining problem such as motif discovery and clustering at scales that would otherwise be untenable. In addition to mining massive datasets, we will show that our ideas also have implications for real-time monitoring of data streams, allowing us to handle much faster arrival rates and/or use cheaper and lower powered devices than are currently possible.
Characteristic-Based Clustering for Time Series Data
AbstractWith the growing importance of time series clustering research, particularly for similarity searches amongst long time series such as those arising in medicine or finance, it is critical for us to find a way to resolve the outstanding problems that make most clustering methods impractical under certain circumstances. When the time series is very long, some clustering algorithms may fail because the very notation of similarity is dubious in high dimension space; many methods cannot handle missing data when the clustering is based on a distance metric.This paper proposes a method for clustering of time series based on their structural characteristics. Unlike other alternatives, this method does not cluster point values using a distance metric, rather it clusters based on global features extracted from the time series. The feature measures are obtained from each individual series and can be fed into arbitrary clustering algorithms, including an unsupervised neural network algorithm, self-organizing map, or hierarchal clustering algorithm.Global measures describing the time series are obtained by applying statistical operations that best capture the underlying characteristics: trend, seasonality, periodicity, serial correlation, skewness, kurtosis, chaos, nonlinearity, and self-similarity. Since the method clusters using extracted global measures, it reduces the dimensionality of the time series and is much less sensitive to missing or noisy data. We further provide a search mechanism to find the best selection from the feature set that should be used as the clustering inputs.The proposed technique has been tested using benchmark time series datasets previously reported for time series clustering and a set of time series datasets with known characteristics. The empirical results show that our approach is able to yield meaningful clusters. The resulting clusters are similar to those produced by other methods, but with some promising and interesting variations that can be intuitively explained with knowledge of the global characteristics of the time series.
Addressing Big Data Time Series: Mining Trillions of Time Series Subsequences Under Dynamic Time Warping
Most time series data mining algorithms use similarity search as a core subroutine, and thus the time taken for similarity search is the bottleneck for virtually all time series data mining algorithms, including classification, clustering, motif discovery, anomaly detection, and so on. The difficulty of scaling a search to large datasets explains to a great extent why most academic work on time series data mining has plateaued at considering a few millions of time series objects, while much of industry and science sits on billions of time series objects waiting to be explored. In this work we show that by using a combination of four novel ideas we can search and mine massive time series for the first time. We demonstrate the following unintuitive fact: in large datasets we can exactly search under Dynamic Time Warping (DTW) much more quickly than the current state-of-the-art Euclidean distance search algorithms. We demonstrate our work on the largest set of time series experiments ever attempted. In particular, the largest dataset we consider is larger than the combined size of all of the time series datasets considered in all data mining papers ever published. We explain how our ideas allow us to solve higher-level time series data mining problems such as motif discovery and clustering at scales that would otherwise be untenable. Moreover, we show how our ideas allow us to efficiently support the uniform scaling distance measure, a measure whose utility seems to be underappreciated, but which we demonstrate here. In addition to mining massive datasets with up to one trillion datapoints, we will show that our ideas also have implications for real-time monitoring of data streams, allowing us to handle much faster arrival rates and/or use cheaper and lower powered devices than are currently possible.
Multivariate Time Series Imputation with Generative Adversarial Networks
Multivariate time series usually contain a large number of missing values, which hinders the application of advanced analysis methods on multivariate time series data. Conventional approaches to addressing the challenge of missing values, including mean/zero imputation, case deletion, and matrix factorization-based imputation, are all incapable of modeling the temporal dependencies and the nature of complex distribution in multivariate time series. In this paper, we treat the problem of missing value imputation as data generation. Inspired by the success of Generative Adversarial Networks (GAN) in image generation, we propose to learn the overall distribution of a multivariate time series dataset with GAN, which is further used to generate the missing values for each sample. Different from the image data, the time series data are usually incomplete due to the nature of data recording process. A modified Gate Recurrent Unit is employed in GAN to model the temporal irregularity of the incomplete time series. Experiments on two multivariate time series datasets show that the proposed model outperformed the baselines in terms of accuracy of imputation. Experimental results also showed that a simple model on the imputed data can achieve state-of-the-art results on the prediction tasks, demonstrating the benefits of our model in downstream applications.
A survey on forecasting of time series data
Time series analysis and forecasting future values has been a major research focus since years ago. Time series analysis and forecasting in time series data finds it significance in many applications such as business, stock market and exchange, weather, electricity demand, cost and usage of products such as fuels, electricity, etc. and in any kind of place that has specific seasonal or trendy changes with time. The forecasting of time series data provides the organization with useful information that is necessary for making important decisions. In this paper, a detailed survey of the various techniques applied for forecasting different types of time series dataset is provided. This survey covers the overall forecasting models, the algorithms used within the model and other optimization techniques used for better performance and accuracy. The various performance evaluation parameters used for evaluating the forecasting models are also discussed in this paper. This study gives the reader an idea about the various researches that take place within forecasting using the time series data.
neural network sensor network machine learning artificial neural network support vector machine deep learning time series data mining support vector vector machine wavelet transform data analysi deep neural network neural network model hidden markov model regression model deep neural anomaly detection gene expression data base generative adversarial network generative adversarial time series datum adversarial network experimental datum fourier series nearest neighbor support vector regression time series analysi missing datum data based moving average gene expression datum time series model series analysi lyapunov exponent series datum outlier detection dynamic time warping time series forecasting data mining algorithm panel datum time series prediction series model multivariate time series finite time unit root dynamic time linear and nonlinear series forecasting time warping distance measure financial time series series prediction integrated moving average experimental comparison multivariate time financial time dependent variable chaotic time series nonlinear time vegetation index nonlinear time series arima model fuzzy time large time anomaly detection method fuzzy time series chaotic time autoregressive integrated moving time series based air pollutant time series classification representation method fokker-planck equation series representation similarity analysi series classification univariate time series time series clustering unsupervised anomaly detection periodic pattern nearest neighbor classification time series dataset series data mining time series regression anomaly detection approach time series database series clustering observed time series forecasting time series local similarity long time series time series similarity series database fmri time series complex time indian stock market time series representation symbolic aggregate approximation complex time series forecasting time series data set series similarity fmri time time series anomaly large time series series data analysi series anomaly detection analyzing time series expression time series interrupted time series ucr time series time correction modeling time series clustering time series mining time series interrupted time series data based fourier series representation simple exponential smoothing early classification forecast time series time series subsequence sensor networks pose distributed index piecewise constant approximation quality time series mining time microarray time series incomplete time series massive time series large-scale time series analysing time series microarray time neural time series mri time neural time series data generated time series experiment visualizing time series called time series data set