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Morten Mørup
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Journal Articles
Publisher: Journals Gateway
Neural Computation (2017) 29 (10): 2712–2741.
Published: 01 October 2017
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Cluster analysis of functional magnetic resonance imaging (fMRI) data is often performed using gaussian mixture models, but when the time series are standardized such that the data reside on a hypersphere, this modeling assumption is questionable. The consequences of ignoring the underlying spherical manifold are rarely analyzed, in part due to the computational challenges imposed by directional statistics. In this letter, we discuss a Bayesian von Mises–Fisher (vMF) mixture model for data on the unit hypersphere and present an efficient inference procedure based on collapsed Markov chain Monte Carlo sampling. Comparing the vMF and gaussian mixture models on synthetic data, we demonstrate that the vMF model has a slight advantage inferring the true underlying clustering when compared to gaussian-based models on data generated from both a mixture of vMFs and a mixture of gaussians subsequently normalized. Thus, when performing model selection, the two models are not in agreement. Analyzing multisubject whole brain resting-state fMRI data from healthy adult subjects, we find that the vMF mixture model is considerably more reliable than the gaussian mixture model when comparing solutions across models trained on different groups of subjects, and again we find that the two models disagree on the optimal number of components. The analysis indicates that the fMRI data support more than a thousand clusters, and we confirm this is not a result of overfitting by demonstrating better prediction on data from held-out subjects. Our results highlight the utility of using directional statistics to model standardized fMRI data and demonstrate that whole brain segmentation of fMRI data requires a very large number of functional units in order to adequately account for the discernible statistical patterns in the data.
Journal Articles
Publisher: Journals Gateway
Neural Computation (2016) 28 (10): 2250–2290.
Published: 01 October 2016
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The brain consists of specialized cortical regions that exchange information between each other, reflecting a combination of segregated (local) and integrated (distributed) processes that define brain function. Functional magnetic resonance imaging (fMRI) is widely used to characterize these functional relationships, although it is an ongoing challenge to develop robust, interpretable models for high-dimensional fMRI data. Gaussian mixture models (GMMs) are a powerful tool for parcellating the brain, based on the similarity of voxel time series. However, conventional GMMs have limited parametric flexibility: they only estimate segregated structure and do not model interregional functional connectivity, nor do they account for network variability across voxels or between subjects. To address these issues, this letter develops the functional segregation and integration model (FSIM). This extension of the GMM framework simultaneously estimates spatial clustering and the most consistent group functional connectivity structure. It also explicitly models network variability, based on voxel- and subject-specific network scaling profiles. We compared the FSIM to standard GMM in a predictive cross-validation framework and examined the importance of different model parameters, using both simulated and experimental resting-state data. The reliability of parcellations is not significantly altered by flexibility of the FSIM, whereas voxel- and subject-specific network scaling profiles significantly improve the ability to predict functional connectivity in independent test data. Moreover, the FSIM provides a set of interpretable parameters to characterize both consistent and variable aspects functional connectivity structure. As an example of its utility, we use subject-specific network profiles to identify brain regions where network expression predicts subject age in the experimental data. Thus, the FSIM is effective at summarizing functional connectivity structure in group-level fMRI, with applications in modeling the relationships between network variability and behavioral/demographic variables.
Journal Articles
Publisher: Journals Gateway
Neural Computation (2014) 26 (6): 1236–1237.
Published: 01 June 2014
Journal Articles
Publisher: Journals Gateway
Neural Computation (2012) 24 (9): 2434–2456.
Published: 01 September 2012
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Many networks of scientific interest naturally decompose into clusters or communities with comparatively fewer external than internal links; however, current Bayesian models of network communities do not exert this intuitive notion of communities. We formulate a nonparametric Bayesian model for community detection consistent with an intuitive definition of communities and present a Markov chain Monte Carlo procedure for inferring the community structure. A Matlab toolbox with the proposed inference procedure is available for download. On synthetic and real networks, our model detects communities consistent with ground truth, and on real networks, it outperforms existing approaches in predicting missing links. This suggests that community structure is an important structural property of networks that should be explicitly modeled.
Journal Articles
Publisher: Journals Gateway
Neural Computation (2008) 20 (8): 2112–2131.
Published: 01 August 2008
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There is a increasing interest in analysis of large-scale multiway data. The concept of multiway data refers to arrays of data with more than two dimensions, that is, taking the form of tensors. To analyze such data, decomposition techniques are widely used. The two most common decompositions for tensors are the Tucker model and the more restricted PARAFAC model. Both models can be viewed as generalizations of the regular factor analysis to data of more than two modalities. Nonnegative matrix factorization (NMF), in conjunction with sparse coding, has recently been given much attention due to its part-based and easy interpretable representation. While NMF has been extended to the PARAFAC model, no such attempt has been done to extend NMF to the Tucker model. However, if the tensor data analyzed are nonnegative, it may well be relevant to consider purely additive (i.e., nonnegative) Tucker decompositions). To reduce ambiguities of this type of decomposition, we develop updates that can impose sparseness in any combination of modalities, hence, proposed algorithms for sparse nonnegative Tucker decompositions (SN-TUCKER). We demonstrate how the proposed algorithms are superior to existing algorithms for Tucker decompositions when the data and interactions can be considered nonnegative. We further illustrate how sparse coding can help identify what model (PARAFAC or Tucker) is more appropriate for the data as well as to select the number of components by turning off excess components. The algorithms for SN-TUCKER can be downloaded from Mørup (2007).