相关论文
1974 - Geophysics
MAXIMUM‐ENTROPY SPATIAL PROCESSING OF ARRAY DATA

The procedure of maximum‐entropy spectral analysis (MESA), used in the processing of time series data, also applies to wavenumber (bearing) analysis of signals received from a spatially distributed linear array of sensors. The method is precisely the use of autoregressive spectral analysis in the space dimension rather than in time. There are also close links to the predictive deconvolution method used in geophysical work, and to the process of constructing noise‐whitening filters in communication theory, as well as to least‐squares model building. In this note, we review the maximum‐entropy procedure pointing out all these links. The specific algorithm appropriate to a uniformly spaced line array of sensors is given, as well as one possible algorithm for use in the case of nonuniform sensor spacing.

2011 - 2011 IEEE 11th International Conference on Data Mining
SPO: Structure Preserving Oversampling for Imbalanced Time Series Classification

This paper presents a novel structure preserving over sampling (SPO) technique for classifying imbalanced time series data. SPO generates synthetic minority samples based on multivariate Gaussian distribution by estimating the covariance structure of the minority class and regularizing the unreliable eigen spectrum. By preserving the main covariance structure and intelligently creating protective variances in the trivial eigen feature dimensions, the synthetic samples expand effectively into the void area in the data space without being too closely tied with existing minority-class samples. Extensive experiments based on several public time series datasets demonstrate that our proposed SPO in conjunction with support vector machines can achieve better performances than existing over sampling methods and state-of-the-art methods in time series classification.

2011 - IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing
Unsupervised Land Cover Change Detection: Meaningful Sequential Time Series Analysis

An automated land cover change detection method is proposed that uses coarse spatial resolution hyper-temporal earth observation satellite time series data. The study compared three different unsupervised clustering approaches that operate on short term Fourier transform coefficients computed over subsequences of 8-day composite MODerate-resolution Imaging Spectroradiometer (MODIS) surface reflectance data that were extracted with a temporal sliding window. The method uses a feature extraction process that creates meaningful sequential time series that can be analyzed and processed for change detection. The method was evaluated on real and simulated land cover change examples and obtained a change detection accuracy exceeding 76% on real land cover conversion and more than 70% on simulated land cover conversion.

2014 - ICML
Stochastic Variational Inference for Bayesian Time Series Models

Bayesian models provide powerful tools for analyzing complex time series data, but performing inference with large datasets is a challenge. Stochastic variational inference (SVI) provides a new framework for approximating model posteriors with only a small number of passes through the data, enabling such models to be fit at scale. However, its application to time series models has not been studied. In this paper we develop SVI algorithms for several common Bayesian time series models, namely the hidden Markov model (HMM), hidden semi-Markov model (HSMM), and the non-parametric HDP-HMM and HDP-HSMM. In addition, because HSMM inference can be expensive even in the minibatch setting of SVI, we develop fast approximate updates for HSMMs with durations distributions that are negative binomials or mixtures of negative binomials.

2000 - Econometric Theory
TESTS OF COMMON STOCHASTIC TRENDS

This paper is concerned with tests in multivariate time series models made up of random walk (with drift) and stationary components. When the stationary component is white noise, a Lagrange multiplier test of the hypothesis that the covariance matrix of the disturbances driving the multivariate random walk is null is shown to be locally best invariant, something that does not automatically follow in the multivariate case. The asymptotic distribution of the test statistic is derived for the general model. The test is then extended to deal with a serially correlated stationary component. The main contribution of the paper is to propose a test of the validity of a specified value for the rank of the covariance matrix of the disturbances driving the multivariate random walk. This rank is equal to the number of common trends, or levels, in the series. The test is very simple insofar as it does not require any models to be estimated, even if serial correlation is present. Its use with real data is illustrated in the context of a stochastic volatility model, and the relationship with tests in the cointegration literature is discussed.

2012 - The Science of the total environment
High-frequency water quality time series in precipitation and streamflow: from fragmentary signals to scientific challenge.

Eighteen months of 7-hourly analyses of rainfall and stream water chemistry are presented, spanning a wide range of chemical determinands and building on over 20 years of weekly records for the moorland headwaters of the river Severn. The high-frequency time series data show that hydrochemical responses to major hydrological and biological drivers of short-term variability in rainfall and rivers are not captured by conventional low-frequency monitoring programmes. A wealth of flow related, flow independent, diurnal, seasonal and annual fluctuations indicate a cacophony of interactions within the catchment and stream. The complexity of the chemical dynamics is visually obvious, although there appears to be no clear way of translating this complexity into a simple algorithm. The work provides a proof of concept for the complex structure of catchment functioning revealed by extensive high-frequency measurements coupled with high analytical sensitivity and reproducibility. It provides new insights into hydrogeochemical functioning and a novel resource for catchment modelling.

1993
Time Series of Continuous Proportions

SUMMARY A vector of continuous proportions consists of the proportions of some total accounted for by its constituent components. An example is the proportions of world motor vehicle production by Japan, the USA and all other countries. We consider the situation where time series data are available and where interest focuses on the proportions rather than the actual amounts. Reasons for analysing such times series include estimation of the underlying trend, estimation of the effect of covariates and interventions, and forecasting. We develop a state space model for time series of continuous proportions. Conditionally on the unobserved state, the observations are assumed to follow the Dirichlet distribution, often considered to be the most natural distribution on the simplex. The state follows the Dirichlet conjugate distribution which is introduced here. Thus the model, although based on the Dirichlet distribution, does not have its restrictive independence properties. Covariates, trends, seasonality and interventions may be incorporated in a natural way. The model has worked well when applied to several examples, and we illustrate with components of world motor vehicle production.

2015 - Eng. Appl. Artif. Intell.
Joint mutual information-based input variable selection for multivariate time series modeling

Abstract For modeling of multivariate time series, input variable selection is a key problem. This paper presents the estimation of joint mutual information and its application in input variable selection problems. Mutual information is a commonly used measure for variable selection. To improve the performance of input variable selection, we propose a novel high-dimensional mutual information estimator based on copula entropy, which is estimated by the truncated k -nearest neighbor method. Simulations on high dimensional Gaussian distributions substantiate the effectiveness of the proposed mutual information estimator. A relationship between the joint mutual information and the copula entropy is derived, which is used for joint mutual information estimation. Then the proposed estimator is applied to input variable selection for multivariate time series modeling based on the criterion of max dependency and max–min dependency. A stop criterion is proposed to terminate the selection process automatically. Simulation results show that the input variable selection method works well on both synthetic and real life dataset.

2000 - Human Brain Mapping
A multistep Unsupervised Fuzzy Clustering Analysis of fMRI time series

A paradigm independent multistage strategy based on the Unsupervised Fuzzy Clustering Analysis (UFCA) and its potential for fMRI data analysis are presented. The influence of the fuzziness index is studied using Receiver Operating Characteristics (ROC) methodology and an interval of choice, around the widely used value 2, is shown to yield the best performance. The ill‐balanced data problem is also overcome using a pre‐processing step to reduce the number of voxels presented to the method. Statistical and anatomical criteria are proposed to exclude some voxels and enhance the UFCA sensitivity. An original postprocessing step aiming at statistically characterizing the obtained clusters is also developed. Two similarity criteria are used: the correlation coefficient on temporal profiles and a novel fuzzy overlap coefficient on membership degree maps. This final step provides a useful analysis tool to study intra‐individual reproducibility of the classes across series (stimulation vs. stimulation, noise vs. noise or stimulation vs. noise). Finally, a comparison between this technique and some existing or locally developed postprocessing algorithms is presented using ROC methods. Its sensitivity and robustness is compared to the classical FCA or other techniques as a function of several parameters such as Contrast‐to‐Noise Ratio (CNR) and noise amplitude. Even without knowledge about the paradigm, the hemodynamic response function and the number of clusters, the performances of the proposed strategy are comparable to those of the classical approaches where extensive prior knowledge has to be added. Hum. Brain Mapping 10:160–178, 2000. © 2000 Wiley‐Liss, Inc.

2004 - Journal of Applied Statistics
Applying State Space to SPC: Monitoring Multivariate Time Series

Monitoring cross-sectional and serially interdependent processes has become a new issue in statistical process control (SPC). In up-to-date SPC literature, Kalman filtering was reported to monitor univariate autocorrelated processes. This paper applies a Kalman filter or state-space method for SPC to monitoring multivariate time series. We use Aoki's approach to estimate the parameter matrices of a state-space model. Multivariate Hotelling T 2 control charts are employed to monitor the residuals of the state-space. Examples of this approach are illustrated.

2010 - KDD
DUST: a generalized notion of similarity between uncertain time series

Large-scale sensor deployments and an increased use of privacy-preserving transformations have led to an increasing interest in mining uncertain time series data. Traditional distance measures such as Euclidean distance or dynamic time warping are not always effective for analyzing uncertain time series data. Recently, some measures have been proposed to account for uncertainty in time series data. However, we show in this paper that their applicability is limited. In specific, these approaches do not provide an intuitive way to compare two uncertain time series and do not easily accommodate multiple error functions. In this paper, we provide a theoretical framework that generalizes the notion of similarity between uncertain time series. Secondly, we propose DUST, a novel distance measure that accommodates uncertainty and degenerates to the Euclidean distance when the distance is large compared to the error. We provide an extensive experimental validation of our approach for the following applications: classification, top-k motif search, and top-k nearest-neighbor queries.

2018 - Remote. Sens.
Classification and Mapping of Paddy Rice by Combining Landsat and SAR Time Series Data

Rice is an important food resource, and the demand for rice has increased as population has expanded. Therefore, accurate paddy rice classification and monitoring are necessary to identify and forecast rice production. Satellite data have been often used to produce paddy rice maps with more frequent update cycle (e.g., every year) than field surveys. Many satellite data, including both optical and SAR sensor data (e.g., Landsat, MODIS, and ALOS PALSAR), have been employed to classify paddy rice. In the present study, time series data from Landsat, RADARSAT-1, and ALOS PALSAR satellite sensors were synergistically used to classify paddy rice through machine learning approaches over two different climate regions (sites A and B). Six schemes considering the composition of various combinations of input data by sensor and collection date were evaluated. Scheme 6 that fused optical and SAR sensor time series data at the decision level yielded the highest accuracy (98.67% for site A and 93.87% for site B). Performance of paddy rice classification was better in site A than site B, which consists of heterogeneous land cover and has low data availability due to a high cloud cover rate. This study also proposed Paddy Rice Mapping Index (PMI) considering spectral and phenological characteristics of paddy rice. PMI represented well the spatial distribution of paddy rice in both regions. Google Earth Engine was adopted to produce paddy rice maps over larger areas using the proposed PMI-based approach.

2013 - ArXiv
An Introductory Study on Time Series Modeling and Forecasting

Modeling and forecasting of time series data has fundamental importance in various practical domains. The aim of this book is to present a concise description of some popular time series forecasting models with their salient features. Three important classes of time series models, viz. stochastic, neural networks and support vector machines are studied together with their inherent forecasting strengths and weaknesses. The book also meticulously discusses about several basic issues related to time series analysis, such as stationarity, parsimony, overfitting, etc. Our study is enriched by presenting the empirical forecasting results, conducted on six real-world time series datasets. Five performance measures are used to evaluate the forecasting accuracies of different models as well as to compare the models. For each of the six time series datasets, we further show the obtained forecast diagram which graphically depicts the closeness between the original and predicted observations.

2014 - Remote. Sens.
Automated Spatiotemporal Landslide Mapping over Large Areas Using RapidEye Time Series Data

In the past, different approaches for automated landslide identification based on multispectral satellite remote sensing were developed to focus on the analysis of the spatial distribution of landslide occurrences related to distinct triggering events. However, many regions, including southern Kyrgyzstan, experience ongoing process activity requiring continual multi-temporal analysis. For this purpose, an automated object-oriented landslide mapping approach has been developed based on RapidEye time series data complemented by relief information. The approach builds on analyzing temporal NDVI-trajectories for the separation between landslide-related surface changes and other land cover changes. To accommodate the variety of landslide phenomena occurring in the 7500 km2 study area, a combination of pixel-based multiple thresholds and object-oriented analysis has been implemented including the discrimination of uncertainty-related landslide likelihood classes. Applying the approach to the whole study area for the time period between 2009 and 2013 has resulted in the multi-temporal identification of 471 landslide objects. A quantitative accuracy assessment for two independent validation sites has revealed overall high mapping accuracy (Quality Percentage: 80%), proving the suitability of the developed approach for efficient spatiotemporal landslide mapping over large areas, representing an important prerequisite for objective landslide hazard and risk assessment at the regional scale.

2007 - Journal of Hydrology
Flood prediction using Time Series Data Mining

Summary This paper describes a novel approach to river flood prediction using Time Series Data Mining which combines chaos theory and data mining to characterize and predict events in complex, nonperiodic and chaotic time series. Geophysical phenomena, including earthquakes, floods and rainfall, represent a class of nonlinear systems termed chaotic, in which the relationships between variables in a system are dynamic and disproportionate, however completely deterministic. Chaos theory provides a structured explanation for irregular behavior and anomalies in systems that are not inherently stochastic. While nonlinear approaches such as Artificial Neural Networks, Hidden Markov Models and Nonlinear Prediction are useful in forecasting of daily discharge values in a river, the focus of these approaches is on forecasting magnitudes of future discharge values rather than the prediction of floods. The described Time Series Data Mining methodology focuses on the prediction of events where floods constitute the events in a river daily discharge time series. The methodology is demonstrated using data collected at the St. Louis gauging station located on the Mississippi River in the USA. Results associated with the impact of earliness of prediction and the acceptable risk-level vs. prediction accuracy are presented.

2000 - Public opinion quarterly
The origins and consequences of public trust in government: a time series analysis.

The study of citizens' trust in the national government has been primarily individual-level, cross-sectional analysis. In the current research, we develop a quarterly time series measure of trust in the U.S. national government from 1980 to 1997 and conduct the first multivariate time series examination of public trust in government. We find that negative perceptions of the economy, scandals associated with Congress, and increasing public concern about crime each lead to declining public trust in government. Declining trust in government in turn leads to less positive evaluations of Congress and reduced support for government action to address a range of domestic policy concerns. These results provide new evidence of the influence of public concern about crime and the centrality of Congress in understanding public evaluations of the national government and new evidence of how declining levels of trust in government may influence elections and domestic policy making.

2004
FastDTW: Toward Accurate Dynamic Time Warping in Linear Time and Space

The dynamic time warping (DTW) algorithm is able to find the optimal alignment between two time series. It is often used to determine time series similarity, classification, and to find corresponding regions between two time series. DTW has a quadratic time and space complexity that limits its use to only small time series data sets. In this paper we introduce FastDTW, an approximation of DTW that has a linear time and space complexity. FastDTW uses a multilevel approach that recursively projects a solution from a coarse resolution and refines the projected solution. We prove the linear time and space complexity of FastDTW both theoretically and empirically. We also analyze the accuracy of FastDTW compared to two other existing approximate DTW algorithms: Sakoe-Chuba Bands and Data Abstraction. Our results show a large improvement in accuracy over the existing methods.

2014 - Comput. Stat. Data Anal.
Discriminant analysis of multivariate time series: Application to diagnosis based on ECG signals

In analysing ECG data, the main aim is to differentiate between the signal patterns of healthy subjects and those of individuals with specific heart conditions. We propose an approach for classifying multivariate ECG signals based on discriminant and wavelet analyses. For this purpose we use multiple-scale wavelet variances and wavelet correlations to distinguish between the patterns of multivariate ECG signals based on the variability of the individual components of each ECG signal and on the relationships between every pair of these components. Using the results of other ECG classification studies in the literature as references, we demonstrate that our approach applied to 12-lead ECG signals from a particular database compares favourably. We also demonstrate with real and synthetic ECG data that our approach to classifying multivariate time series out-performs other well-known approaches for classifying multivariate time series.

2018 - Applied Energy
Multivariate exploration of non-intrusive load monitoring via spatiotemporal pattern network

Non-intrusive load monitoring (NILM) of electrical demand for the purpose of identifying load components has thus far mostly been studied using univariate data, e.g., using only whole building electricity consumption time series to identify a certain type of end-use such as lighting load. However, using additional variables in the form of multivariate time series data may provide more information in terms of extracting distinguishable features in the context of energy disaggregation. In this work, a novel probabilistic graphical modeling approach, namely the spatiotemporal pattern network (STPN) is proposed for energy disaggregation using multivariate time-series data. The STPN framework is shown to be capable of handling diverse types of multivariate time-series to improve the energy disaggregation performance. The technique outperforms the state of the art factorial hidden Markov models (FHMM) and combinatorial optimization (CO) techniques in multiple real-life test cases. Furthermore, based on two homes’ aggregate electric consumption data, a similarity metric is defined for the energy disaggregation of one home using a trained model based on the other home (i.e., out-of-sample case). The proposed similarity metric allows us to enhance scalability via learning supervised models for a few homes and deploying such models to many other similar but unmodeled homes with significantly high disaggregation accuracy.

2002 - Proceedings of the eighth ACM SIGKDD international conference on Knowledge discovery and data mining
A unifying framework for detecting outliers and change points from non-stationary time series data

We are concerned with the issues of outlier detection and change point detection from a data stream. In the area of data mining, there have been increased interest in these issues since the former is related to fraud detection, rare event discovery, etc., while the latter is related to event/trend by change detection, activity monitoring, etc. Specifically, it is important to consider the situation where the data source is non-stationary, since the nature of data source may change over time in real applications. Although in most previous work outlier detection and change point detection have not been related explicitly, this paper presents a unifying framework for dealing with both of them on the basis of the theory of on-line learning of non-stationary time series. In this framework a probabilistic model of the data source is incrementally learned using an on-line discounting learning algorithm, which can track the changing data source adaptively by forgetting the effect of past data gradually. Then the score for any given data is calculated to measure its deviation from the learned model, with a higher score indicating a high possibility of being an outlier. Further change points in a data stream are detected by applying this scoring method into a time series of moving averaged losses for prediction using the learned model. Specifically we develop an efficient algorithms for on-line discounting learning of auto-regression models from time series data, and demonstrate the validity of our framework through simulation and experimental applications to stock market data analysis.

Toeplitz Inverse Covariance-Based Clustering of Multivariate Time Series Data

Stephen P. Boyd
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Jure Leskovec
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Stephen Boyd
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David Hallac
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Sagar Vare
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J. Leskovec
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David Hallac
|
Sagar Vare

Abstract:Subsequence clustering of multivariate time series is a useful tool for discovering repeated patterns in temporal data. Once these patterns have been discovered, seemingly complicated datasets can be interpreted as a temporal sequence of only a small number of states, or clusters. For example, raw sensor data from a fitness-tracking application can be expressed as a timeline of a select few actions (i.e., walking, sitting, running). However, discovering these patterns is challenging because it requires simultaneous segmentation and clustering of the time series. Furthermore, interpreting the resulting clusters is difficult, especially when the data is high-dimensional. Here we propose a new method of model-based clustering, which we call Toeplitz Inverse Covariance-based Clustering (TICC). Each cluster in the TICC method is defined by a correlation network, or Markov random field (MRF), characterizing the interdependencies between different observations in a typical subsequence of that cluster. Based on this graphical representation, TICC simultaneously segments and clusters the time series data. We solve the TICC problem through alternating minimization, using a variation of the expectation maximization (EM) algorithm. We derive closed-form solutions to efficiently solve the two resulting subproblems in a scalable way, through dynamic programming and the alternating direction method of multipliers (ADMM), respectively. We validate our approach by comparing TICC to several state-of-the-art baselines in a series of synthetic experiments, and we then demonstrate on an automobile sensor dataset how TICC can be used to learn interpretable clusters in real-world scenarios.

参考文献

[1]  Pradeep Ravikumar,et al.  QUIC: quadratic approximation for sparse inverse covariance estimation , 2014, J. Mach. Learn. Res..

[2]  Eamonn J. Keogh,et al.  Scaling up dynamic time warping for datamining applications , 2000, KDD '00.

[3]  Nir Friedman,et al.  Probabilistic Graphical Models - Principles and Techniques , 2009 .

[4]  Stephen P. Boyd,et al.  Conic Optimization via Operator Splitting and Homogeneous Self-Dual Embedding , 2013, Journal of Optimization Theory and Applications.

[5]  Alexandre d'Aspremont,et al.  Model Selection Through Sparse Max Likelihood Estimation Model Selection Through Sparse Maximum Likelihood Estimation for Multivariate Gaussian or Binary Data , 2022 .

[6]  Andrew J. Viterbi,et al.  Error bounds for convolutional codes and an asymptotically optimum decoding algorithm , 1967, IEEE Trans. Inf. Theory.

[7]  U. Brandes.  A faster algorithm for betweenness centrality , 2001 .

[8]  Johannes Peltola,et al.  Activity classification using realistic data from wearable sensors , 2006, IEEE Transactions on Information Technology in Biomedicine.

[9]  Martin J. Wainwright,et al.  Log-determinant relaxation for approximate inference in discrete Markov random fields , 2006, IEEE Transactions on Signal Processing.

[10]  Eric R. Ziegel,et al.  The Elements of Statistical Learning , 2003, Technometrics.

[11]  Eamonn J. Keogh,et al.  Accelerating Dynamic Time Warping Clustering with a Novel Admissible Pruning Strategy , 2015, KDD.

[12]  J. Zico Kolter,et al.  Sparse Gaussian Conditional Random Fields: Algorithms, Theory, and Application to Energy Forecasting , 2013, ICML.

[13]  Eamonn J. Keogh,et al.  Searching and Mining Trillions of Time Series Subsequences under Dynamic Time Warping , 2012, KDD.

[14]  Dit-Yan Yeung,et al.  Time series clustering with ARMA mixtures , 2004, Pattern Recognit..

[15]  Thomas Martinetz,et al.  'Neural-gas' network for vector quantization and its application to time-series prediction , 1993, IEEE Trans. Neural Networks.

[16]  A. H. Shirazi,et al.  Network analysis of a financial market based on genuine correlation and threshold method , 2011 .

[17]  Patrick Danaher,et al.  The joint graphical lasso for inverse covariance estimation across multiple classes , 2011, Journal of the Royal Statistical Society. Series B, Statistical methodology.

[18]  Aristides Gionis,et al.  Finding recurrent sources in sequences , 2003, RECOMB '03.

[19]  Fabian Mörchen,et al.  Extracting interpretable muscle activation patterns with time series knowledge mining , 2005, Int. J. Knowl. Based Intell. Eng. Syst..

[20]  Eamonn J. Keogh,et al.  A symbolic representation of time series, with implications for streaming algorithms , 2003, DMKD '03.

[21]  Heikki Mannila,et al.  Rule Discovery from Time Series , 1998, KDD.

[22]  P. Rousseeuw.  Silhouettes: a graphical aid to the interpretation and validation of cluster analysis , 1987 .

[23]  Tim Oates,et al.  Visualizing Variable-Length Time Series Motifs , 2012, SDM.

[24]  Marco Cuturi,et al.  Fast Global Alignment Kernels , 2011, ICML.

[25]  Stephen P. Boyd,et al.  Greedy Gaussian segmentation of multivariate time series , 2016, Advances in Data Analysis and Classification.

[26]  Stephen P. Boyd,et al.  Proximal Algorithms , 2013, Found. Trends Optim..

[27]  Kazuya Takeda,et al.  Driver Modeling Based on Driving Behavior and Its Evaluation in Driver Identification , 2007, Proceedings of the IEEE.

[28]  Padhraic Smyth,et al.  Clustering Sequences with Hidden Markov Models , 1996, NIPS.

[29]  Michael I. Jordan.  Graphical Models , 2003 .

[30]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[31]  Evgenia Dimitriadou.  Convex Clustering Methods and Clustering Indexes , 2015 .

[32]  Eamonn Keogh.  Exact Indexing of Dynamic Time Warping , 2002, VLDB.

[33]  A. Raftery,et al.  Model-based Gaussian and non-Gaussian clustering , 1993 .

[34]  Saeed Aghabozorgi,et al.  A Review of Subsequence Time Series Clustering , 2014, TheScientificWorldJournal.

[35]  Adrian E. Raftery,et al.  MCLUST Version 3: An R Package for Normal Mixture Modeling and Model-Based Clustering , 2006 .

[36]  Donald J. Berndt,et al.  Using Dynamic Time Warping to Find Patterns in Time Series , 1994, KDD Workshop.

[37]  M. Hestenes.  Multiplier and gradient methods , 1969 .

[38]  Eamonn J. Keogh,et al.  Clustering of time-series subsequences is meaningless: implications for previous and future research , 2004, Knowledge and Information Systems.

[39]  Pradeep Ravikumar,et al.  BIG & QUIC: Sparse Inverse Covariance Estimation for a Million Variables , 2013, NIPS.

[40]  Robert M. Gray,et al.  Toeplitz and Circulant Matrices: A Review , 2005, Found. Trends Commun. Inf. Theory.

[41]  Robert M. Gray,et al.  Toeplitz And Circulant Matrices: A Review (Foundations and Trends(R) in Communications and Information Theory) , 2006 .

[42]  Li Wei,et al.  Experiencing SAX: a novel symbolic representation of time series , 2007, Data Mining and Knowledge Discovery.

[43]  R. Tibshirani,et al.  Sparse inverse covariance estimation with the graphical lasso. , 2008, Biostatistics.

[44]  Stephen P. Boyd,et al.  Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers , 2011, Found. Trends Mach. Learn..

[45]  Heikki Mannila,et al.  Time series segmentation for context recognition in mobile devices , 2001, Proceedings 2001 IEEE International Conference on Data Mining.

[46]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[47]  M. Yuan,et al.  Model selection and estimation in regression with grouped variables , 2006 .

[48]  Leonhard Held,et al.  Gaussian Markov Random Fields: Theory and Applications , 2005 .

[49]  Su-In Lee,et al.  Node-based learning of multiple Gaussian graphical models , 2013, J. Mach. Learn. Res..

引用
SummerTime: Variable-length Time Series Summarization with Application to Physical Activity Analysis
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TATC: Predicting Alzheimer's Disease with Actigraphy Data
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Drive2Vec: Multiscale State-Space Embedding of Vehicular Sensor Data
2018 21st International Conference on Intelligent Transportation Systems (ITSC)
2018
Forecasting market states
Machine Learning and AI in Finance
2018
Subspace clustering for situation assessment in aquatic drones
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Spatial-Temporal Demand Forecasting and Competitive Supply via Graph Convolutional Networks
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Early Recognition of Driving Intention for Lane Change Based on Recurrent Hidden Semi-Markov Model
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Modeling Combinatorial Evolution in Time Series Prediction
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Pattern Recognition in Multivariate Time Series: Towards an Automated Event Detection Method for Smart Manufacturing Systems
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Developing Measures of Cognitive Impairment in the Real World from Consumer-Grade Multimodal Sensor Streams
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Soybean Price Pattern Discovery Via Toeplitz Inverse Covariance-Based Clustering
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Steps towards end-to-end neural speaker diarization. (Étapes vers un système neuronal de bout en bout pour la tâche de segmentation et de regroupement en locuteurs)
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