Greedy Gaussian segmentation of multivariate time series

Hallac, David; Nystrup, Peter; Boyd, Stephen

doi:10.1007/s11634-018-0335-0

Cited by 66 publications

(51 citation statements)

References 54 publications

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“…To achieve this representation, it is necessary to simultaneously segment and cluster the time series. This problem is more difficult than standard time series segmentation [17,20], since multiple segments can belong to the same cluster. However, it is also harder than subsequence clustering [3,43] because each data point cannot be clustered independently (since neighboring points are encouraged to belong to the same cluster).…”

Section: Introductionmentioning

confidence: 99%

Toeplitz Inverse Covariance-Based Clustering of Multivariate Time Series Data

Hallac

Vare

Boyd

et al. 2017

Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining

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187

154

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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.

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Section: Introductionmentioning

confidence: 99%

Toeplitz Inverse Covariance-Based Clustering of Multivariate Time Series Data

Hallac

Vare

Boyd

et al. 2017

Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining

Self Cite

187

154

View full text Add to dashboard Cite

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“…In point clustering methods, instead, each multivariate observation at each time instance t is assigned to a cluster. In most popular approaches, however, this is done based on a distance metric (Grabarnik and Särkkä 2001, Focardi and Fabozzi 2004, Zolhavarieh et al 2014, Hendricks et al 2016, Hallac et al 2016.…”

Section: Introductionmentioning

confidence: 99%

Forecasting Market States

Procacci

Aste

2018

SSRN Journal

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We propose a novel methodology to define, analyse and forecast market states. In our approach market states are identified by a reference sparse precision matrix and a vector of expectation values. In our procedure each multivariate observation is associated to a given market state accordingly to a minimisation of a penalized Mahalanobis distance. The procedure is made computationally very efficient and can be used with a large number of assets. We demonstrate that this procedure is successfull at clustering different states of the markets in an unsupervised manner. In particular, we describe an experiment with one hundred log-returns and two states in which the methodology automatically associates states prevalently to pre-and post-crisis periods with one state gathering periods with average positive returns and the other state periods with average negative returns, therefore discovering spontaneously the common classification of 'bull' and 'bear' markets. In another experiment, with again one hundred log-returns and two states, we demonstrate that this procedure can be efficiently used to forecast off-sample future market states with significant prediction accuracy. This methodology opens the way to a range of applications in risk management and trading strategies in the context where the correlation structure plays a central role.

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“…[15,16,17,11]. A more exhaustive and recent list of references can be found for instance in [18,19].…”

Section: Data-driven Based Segmentationmentioning

confidence: 99%

Graph-based era segmentation of international financial integration

Bastidon

Parent

Jensen

et al. 2020

Physica A: Statistical Mechanics and its Applications

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Assessing world-wide financial integration constitutes a recurrent challenge in macroeconometrics, often addressed by visual inspections searching for data patterns. Econophysics literature enables us to build complementary, data-driven measures of financial integration using graphs. The present contribution investigates the potential and interests of a novel 3-step approach that combines several state-of-the-art procedures to i) compute graph-based representations of the multivariate dependence structure of asset prices time series representing the financial states of 32 countries world-wide ; ii) compute time series of 5 graph-based indices that characterize the time evolution of the topologies of the graph; iii) segment these time evolutions in piece-wise constant eras, using an optimization framework constructed on a multivariate multi-norm total variation penalized functional. The method shows first that it is possible to find endogenous stable eras of world-wide financial integration. Then, our results suggest that the most relevant globalization eras would be based on the historical patterns of global capital flows, while the major regulatory events of the 1970s would only appear as a cause of sub-segmentation.

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Greedy Gaussian segmentation of multivariate time series

Cited by 66 publications

References 54 publications

Toeplitz Inverse Covariance-Based Clustering of Multivariate Time Series Data

Toeplitz Inverse Covariance-Based Clustering of Multivariate Time Series Data

Forecasting Market States

Graph-based era segmentation of international financial integration

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