Maximum Likelihood Estimation for the Offset-Normal Shape Distributions Using EM

Kume, Alfred; Welling, Max

doi:10.1198/jcgs.2010.09190

Cited by 14 publications

(28 citation statements)

References 14 publications

(9 reference statements)

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“…We acknowledge that, in a parametric framework, a similar analysis could also be performed by using the model proposed by Kume and Welling (2010). In fact, based on a likelihood approach, nested models could be compared using the generalised likelihood ratio test using the difference in the deviances having an asymptotic χ 2 -distribution.…”

Section: Discussionmentioning

confidence: 99%

Nonparametric combination-based tests in dynamic shape analysis

Brombin

Salmaso

Fontanella

et al. 2015

Journal of Nonparametric Statistics

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Landmark-based geometric morphometric methods are probably the most widely used approaches for shape analysis. Much work has been done for static or cross-sectional shape analysis while considerably less research has focused on dynamic or longitudinal shapes. The question of analysing shape changes over time is a fundamental issue in many research fields. In this paper, as a motivating example, we consider the problem of describing the dynamics of facial expressions for which medical and sociological studies call for a proper differential analysis to distinguish their different characteristics. We address the problem from an inferential point of view testing whether landmark positions change over time, within each facial expression, and whether these changes are different between different expressions. As the shape changes over time completely depend on geometrical landmarks, part of the problem becomes finding the subset of landmarks which best describes the dynamics of the expressions. In this paper, we show by means of a motivating example related to the analysis of the FG-NET (Face and Gesture Recognition Research Network) database with facial expressions and emotions from the Technical University Munich [Wallhoff, F. (2006), Database with Facial Expressions and Emotions from Technical University of Munich (FEEDTUM)'], that NonParametric Combination (NPC) tests can be effective tools when testing whether there is a difference between dynamics of facial expressions or testing which of the landmarks are more informative in explaining their dynamics. In particular, we start analysing data by means of bivariate linear mixed-effects models and then we improve inferential results using the NPC methodology

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Section: Discussionmentioning

confidence: 99%

Nonparametric combination-based tests in dynamic shape analysis

Brombin

Salmaso

Fontanella

et al. 2015

Journal of Nonparametric Statistics

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“…Following Kume and Welling (2010), we first develop the Expectation-Maximization (EM) algorithm (Dempster et al, 1977) to calculate the maximum likelihood estimate (MLE) of θ , denoted by θ̃ , for low-dimensional shape data, that is, p ≪ n . The key idea of the EM algorithm is to introduce missing data and then maximize the conditional expectation of the complete-data log-likelihood function, called Q function.…”

Section: Methodsmentioning

confidence: 99%

“…Most existing methods for shape data primarily extend standard clustering algorithms, such as K-means or mean-shift algorithm, by replacing the Euclidean metric by the metric of the curved shape space (Srivastava et al, 2005; Subbarao and Meer, 2009; Amaral et al, 2010). Furthermore, Kume and Welling (2010) developed a mixture model of offset-normal distributions, which explicitly models the spatial covariance matrix of all landmarks in each cluster. All these methods, however, do not address the noisy data in the high-dimensional feature space, the high-dimensional spatial correlation matrix, and the shape variation associated with explanatory attributes.…”

Section: Introductionmentioning

confidence: 99%

“…We use the offset-normal shape distribution (Dryden and Mardia, 1991; Kume and Welling, 2010) to characterize the variability of shape data in the curved shape space. To handle high dimensionality, we use a penalized clustering framework as an effective and powerful method to perform both variable selection and clustering (Pan and Shen, 2007; Guo et al, 2010).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Clustering High-Dimensional Landmark-Based Two-Dimensional Shape Data

Huang

Styner

Zhu

2015

Journal of the American Statistical Association

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An important goal in image analysis is to cluster and recognize objects of interest according to the shapes of their boundaries. Clustering such objects faces at least four major challenges including a curved shape space, a high-dimensional feature space, a complex spatial correlation structure, and shape variation associated with some covariates (e.g., age or gender). The aim of this paper is to develop a penalized model-based clustering framework to cluster landmark-based planar shape data, while explicitly addressing these challenges. Specifically, a mixture of offset-normal shape factor analyzers (MOSFA) is proposed with mixing proportions defined through a regression model (e.g., logistic) and an offset-normal shape distribution in each component for data in the curved shape space. A latent factor analysis model is introduced to explicitly model the complex spatial correlation. A penalized likelihood approach with both adaptive pairwise fusion Lasso penalty function and L2 penalty function is used to automatically realize variable selection via thresholding and deliver a sparse solution. Our real data analysis has confirmed the excellent finite-sample performance of MOSFA in revealing meaningful clusters in the corpus callosum shape data obtained from the Attention Deficit Hyperactivity Disorder-200 (ADHD-200) study.

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“…For shape analysis one needs to remove registration, either by integration (marginalization) or by optimization. Marginalization usually leads to very complicated models (Dryden and Mardia, 1991;Kume and Welling, 2010), and a Bayesian alternative using Markov chain Monte Carlo methods deals with the integration via simulation (Green and Mardia, 2006). Alternatively, one can work in the quotient space (Kendall, 1984), where one optimizes over registrations.…”

Section: Marginalization Versus Optimizationmentioning

confidence: 99%