Model‐based clustering of regression time series data via APECM—an AECM algorithm sung to an even faster beat

Chen, Wei-Chen; Maitra, Ranjan

doi:10.1002/sam.10143

Cited by 24 publications

(31 citation statements)

References 36 publications

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“…Now, we will maximize the function (2) with respect to . The maximization with respect to the parameters η k does not change under the new parameterization and the explicit formula is provided [1]. Using the fact that W n,k is an AR(p) time series and conditioning on the first p observations, Eq.…”

Section: Proposed Parameter Estimationmentioning

confidence: 99%

“…To make this paper easier to read, the notation proposed [1] has been adopted completely. We start the discussion with the summary of the model proposed by the authors of the original paper.…”

Section: Introductionmentioning

confidence: 99%

“…, K }. The maximum likelihood (ML) estimation by means of the expectation-maximization (EM) algorithm [2] involves the calculation of posterior probabilities z (s+1) nk and maximization of the expected complete data log likelihood function Q |Z (s+1) = N n=1 K k=1 z (s+1) nk × (log η k + log φ Y n (y n |X n β k , k )) (1) with respect to parameters at the step s + 1. The authors provide explicit formulas for updating parameter estimates η (s+1) k and β (s+1) k .…”

Section: Introductionmentioning

confidence: 99%

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Efficient estimation in model‐based clustering of Gaussian regression time series

Melnykov

2012

Statistical Analysis

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This paper discusses an alternative approach to the estimation procedure presented in a recently published paper. The authors developed a model-based clustering approach for regression time series and proposed the APECM procedure as an acceleration method for the expectation-maximization algorithm. The process of the estimation of model parameters was discussed in great detail. In this paper, we show how the proposed procedure can be modified to achieve substantial acceleration and better stability. In particular, numerical maximization suggested for the estimation of parameters can be replaced with analytical closed-form expressions, and inverting high dimensional matrices can be avoided entirely. A convenient approach for assessing variability in parameter estimates is also provided. The results of conducted experiments are very promising.  2012Wiley Periodicals, Inc. Statistical Analysis and Data Mining 5: [95][96][97][98][99] 2012

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Section: Proposed Parameter Estimationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Efficient estimation in model‐based clustering of Gaussian regression time series

Melnykov

2012

Statistical Analysis

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“…Among many challenging applications addressed by this technique, there are the analysis of social networks (Handcock, Raftery, and Tantrum 2007), mass spectrometry data (Melnykov 2013b), and text classification (Nigam, McCallum, Thrun, and Mitchell 2000). Some work has been done in the direction of model-based clustering of time series (Liao 2005) and regression time series (Chen and Maitra 2011;Melnykov 2012). Despite a high number of interesting applications that can be addressed by grouping categorical sequences, this area has been given very limited attention in the literature on model-based clustering.…”

Section: Introductionmentioning

confidence: 99%

ClickClust: An R Package for Model-Based Clustering of Categorical Sequences

Melnykov¹

2016

J. Stat. Soft.

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The R package ClickClust is a new piece of software devoted to finite mixture modeling and model-based clustering of categorical sequences. As a special kind of time series, categorical sequences, also known as categorical time series, exhibit a time-dependent nature and are traditionally modeled by means of Markov chains. Clustering categorical sequences is an important problem with multiple applications, but grouping sequences of sites or web-pages, also known as clickstreams, is one of the most well-known problems that helps discover common navigation patterns and routes taken by users. This popular application is recognized in the package title ClickClust. The paper discusses methodological and algorithmic foundations of the package based on finite mixtures of Markov models. The number of Markov chain states can often be large leading to high-dimensional transition probability matrices. The high number of model parameters can affect clustering performance severely. As a remedy to this problem, backward and forward selection algorithms are proposed for grouping states. This extends the original clustering problem to a biclustering framework. Among other capabilities of ClickClust, there are the estimation of the variance-covariance matrix corresponding to model parameter estimates, prediction of future states visited, and the construction of a display named click-plot that helps illustrate the obtained clustering solutions. All available functions and the utility of the package are thoroughly discussed and illustrated on multiple examples.

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“…The problem of time series clustering has also been explored in the literature from different perspectives; see, e.g., [2,4,5,15,22,23,25].…”

Section: Introductionmentioning

confidence: 99%

A double clustering algorithm for financial time series based on extreme events

Luca

Zuccolotto

2016

Statistics &Amp; Risk Modeling

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This paper is concerned with a procedure for financial time series clustering, aimed at creating groups of time series characterized by similar behavior with regard to extreme events. The core of our proposal is a double clustering procedure: the former is based on the lower tail dependence of all the possible pairs of time series, the latter on the upper tail dependence. Tail dependence coefficients are estimated with copula functions. The final goal is to exploit the two clustering solutions in an algorithm designed to create a portfolio that maximizes the probability of joint positive extreme returns while minimizing the risk of joint negative extreme returns. In financial crisis scenarios, such a portfolio is expected to outperform portfolios generated by the traditional methods. We describe the results of a simulation study and, finally, we apply the procedure to a dataset composed of the 50 assets included in the EUROSTOXX index.

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Model‐based clustering of regression time series data via APECM—an AECM algorithm sung to an even faster beat

Cited by 24 publications

References 36 publications

Efficient estimation in model‐based clustering of Gaussian regression time series

Efficient estimation in model‐based clustering of Gaussian regression time series

ClickClust: An R Package for Model-Based Clustering of Categorical Sequences

A double clustering algorithm for financial time series based on extreme events

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