Assessment of the number of components in Gaussian mixture models in the presence of multiple local maximizers

Kim, Dae-Young; Seo, Byungtae

doi:10.1016/j.jmva.2013.11.018

Cited by 45 publications

(13 citation statements)

References 23 publications

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“…However, an alternative interpretation might be that BIC was simply being parsimonious, and that flower dimensions alone might not be enough to confidently separate the species. A much more detailed look at clustering the iris data, considering many more possible modeling choices, is found in Kim and Seo (2014). However, this simple look is enough to discuss the relevant ideas.…”

Section: Introductionmentioning

confidence: 99%

Sensitivity and Specificity of Information Criteria

Dziak

Coffman

Lanza

et al. 2018

Preprint

143

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Latent class analysis • Likelihood ratio testing • Model selection Key Points:• Information criteria such as AIC and BIC are motivated by different theoretical frameworks.• However, when comparing pairs of nested models, they reduce algebraically to likelihood ratio tests with differing alpha levels.• This perspective makes it easier to understand their different emphases on sensitivity versus specificity, and why BIC but not AIC possesses model selection consistency.• This perspective is useful for comparisons, but it does not mean that the information criteria are only likelihood ratio tests. Information criteria can be used in ways these tests themselves are not as well suited for, such as for model averaging.

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Section: Introductionmentioning

confidence: 99%

Sensitivity and Specificity of Information Criteria

Dziak

Coffman

Lanza

et al. 2018

Preprint

143

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show abstract

“…Firstly, the number of Gaussian components, K, is chosen, and the G-UMM is initialised and trained on an input data set (that may or may not contain any transient faults) in the space of the raw signals or in an appropriate feature space. K should be chosen sufficiently large, such that the G-UMM can accurately describe the distribution of the data, while remaining small enough to avoid over-fitting (Kim & Seo, 2014;McKenzie & Alder, 1994) and produce physically interpretable clusters where possible to aid the setting of the parameters of the HMM in the following step. The HMM is used in order to include the temporal relationship into the fault detection scheme.…”

Section: G-umm -Hmm Based Fault Detectionmentioning

confidence: 99%

Gas Turbine Engine Condition Monitoring Using Gaussian Mixture and Hidden Markov Models

Jacobs

Edwards

et al. 2020

IJPHM

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This paper investigates the problem of condition monitoring of complex dynamic systems, specifically the detection, localisation and quantification of transient faults. A data driven approach is developed for fault detection where the multidimensional data sequence is viewed as a stochastic process whose behaviour can be described by a hidden Markov model with two hidden states — i.e. ‘healthy / nominal’ and ‘unhealthy / faulty’. The fault detection is performed by first clustering in a multidimensional data space to define normal operating behaviour using a Gaussian-Uniform mixture model. The health status of the system at each data point is then determined by evaluating the posterior probabilities of the hidden states of a hidden Markov model. This allows the temporal relationship between sequential data points to be incorporated into the fault detection scheme. The proposed scheme is robust to noise and requires minimal tuning. A real-world case study is performed based on the detection of transient faults in the variable stator vane actuator of a gas turbine engine to demonstrate the successful application of the scheme. The results are used to demonstrate the generation of simple and easily interpretable analytics that can be used to monitor the evolution of the fault across time.

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“…In our experiments, we have noticed that in low dimensions, this problem does not arise when initialized with k-means. This is a well-known phenomenon that happens because the likelihood is unbounded, and, in this case, increases by fitting the covariance matrix of a component on just one datapoint (Bishop, 2006;Kim and Seo, 2014). Intuitively, the likelihood of a GMM can increase by (a) decreasing the variance over a single datapoint or (b) extending a better fit over a large number of points.…”

Section: High Dimensional Datamentioning

confidence: 99%

Model-based Clustering using Automatic Differentiation: Confronting Misspecification and High-Dimensional Data

Kasa

Rajan

2019

Preprint

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Gaussian Mixture Models (GMMs) are used for model-based clustering in a variety of applications. In this paper, we study two practically important but relatively less explored cases of fitting GMMs (1) when there is misspecification and (2) on high-dimensional data. Our empirical analyses reveal limitations of likelihood based model selection in both Expectation Maximization (EM) and Gradient Descent (GD) based inference methods. We design new KL divergence based model selection criteria and GD-based inference methods that use the criteria in fitting GMM on low-and high-dimensional data as well as for selecting the number of clusters. Our experiments on simulated and real datasets show the superiority of our approach over state-of-theart methods for clustering 1 .

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Assessment of the number of components in Gaussian mixture models in the presence of multiple local maximizers

Cited by 45 publications

References 23 publications

Sensitivity and Specificity of Information Criteria

Sensitivity and Specificity of Information Criteria

Gas Turbine Engine Condition Monitoring Using Gaussian Mixture and Hidden Markov Models

Model-based Clustering using Automatic Differentiation: Confronting Misspecification and High-Dimensional Data

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