Abstract
Resting-state functional connectivity states are often identified as clusters of dynamic connectivity patterns. However, existing clustering approaches do not distinguish major states from rarely occurring minor states and hence are sensitive to noise. To address this issue, we propose to model major states using a non-linear generative process guided by a Gaussian-mixture distribution in a low-dimensional latent space, while separately modeling the connectivity patterns of minor states by a non-informative uniform distribution. We embed this truncated Gaussian-Mixture model in a Variational AutoEncoder framework to obtain a general joint clustering and outlier detection approach, called tGM-VAE. When applied to synthetic data with known ground-truth, tGM-VAE is more accurate in clustering dynamic connectivity patterns than existing approaches. On the rs-fMRI data of 593 healthy adolescents from the National Consortium on Alcohol and Neurodevelopment in Adolescence (NCANDA) study, tGM-VAE identified meaningful major connectivity states. The dwell time of these states significantly correlated with age.
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References
Buckner, R., Krienen, F., Yeo, B.: Opportunities and limitations of intrinsic functional connectivity MRI. Nat. Neurosci. 16(7), 832–837 (2013)
Allen, E., Damaraju, E., Plis, S., et al.: Tracking whole-brain connectivity dynamics in the resting state. Cerebral Cortex 24(3), 663–676 (2014)
Zalesky, A., Fornito, A., Cocchi, L., Gollo, L.L., Breakspear, M.: Time-resolved resting-state brain networks. PNAS 111(28), 10341–10346 (2014)
Damarajua, E., Allen, E., Belgerc, A., et al.: Dynamic functional connectivity analysis reveals transient states of dysconnectivity in schizophrenia. NeuroImage: Clin. 5, 298–308 (2014)
Yu, Q., Erhardt, E.B., Sui, J., et al.: Assessing dynamic brain graphs of time-varying connectivity in fMRI data: application to healthy controls and patients with schizophrenia. NeuroImage 107, 345–355 (2015)
Taghia, J., Ryali, S., et al.: Bayesian switching factor analysis for estimating time-varying functional connectivity in fMRI. NeuroImage 155, 271–290 (2017)
Nielsen, S., Madsen, K., Røge, R., Schmidt, M.N., Mørup, M.: Nonparametric modeling of dynamic functional connectivity in fMRI data. In: Machine Learning and Interpretation in Neuroimaging Workshop (2015)
Blei, D.M., Jordan, M.I.: Variational inference for dirichlet process mixtures. Bayesian Anal. 1(1), 121–144 (2017)
Nalisnick, E., Smyth, P.: Stick-breaking variational autoencoders. In: ICLR (2017)
Zhao, Q., Kwon, D., Pohl, K.M.: A riemannian framework for longitudinal analysis of resting-state functional connectivity. In: Frangi, A.F., Schnabel, J.A., Davatzikos, C., Alberola-López, C., Fichtinger, G. (eds.) MICCAI 2018. LNCS, vol. 11072, pp. 145–153. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-00931-1_17
Kingma, D., Welling, M.: Auto-encoding variational bayes. In: ICLR (2013)
Kingma, D.P., Rezende, D.J., Mohamed, S., Welling, M.: Semi-supervised learning with deep generative models. In: NIPS (2014)
Dilokthanakul, N., Mediano, P.A., Garnelo, M.: Deep unsupervised clustering with Gaussian mixture variational autoencoder (2017, preprint). arxiv.org/abs/1611.02648
Jiang, Z., Zheng, Y., Tan, H., Tang, B., Zhou, H.: Variational deep embedding: an unsupervised and generative approach to clustering. In: IJCAI (2017)
Abbasnejad, E., Dick, A.R., van den Hengel, A.: Infinite variational autoencoder for semi-supervised learning. In: CVPR (2017)
Higgins, I., Matthey, L., Pal, A., et al.: Beta-VAE: learning basic visual concepts with a constrained variational framework. In: ICLR (2017)
Ebbers, J., et al.: Hidden Markov model variational autoencoder for acoustic unit discovery. In: InterSpeech (2017)
Müller-Oehring, E., Kwon, D., Nagel, B., Sullivan, E., et al.: Influences of age, sex, and moderate alcohol drinking on the intrinsic functional architecture of adolescent brains. Cerebral Cortex 28(3), 1049–1063 (2017)
Rohlfing, T., Zahr, N., Sullivan, E., Pfefferbaum, A.: The SRI24 multichannel atlas of normal adult human brain structure. Hum. Brain Mapp. 31(5), 798–819 (2014)
Chen, Y., Wiesel, A., Eldar, Y.C., Hero, A.O.: Shrinkage algorithms for MMSE covariance estimation. IEEE Trans. Sig. Process. 58(10), 5016–5029 (2010)
Pfefferbaum, A., et al.: Altered brain developmental trajectories in adolescents after initiating drinking. Am. J. Psychiatry 175(4), 370–380 (2017)
Chen, Y., Wang, W., et al.: Age-related decline in the variation of dynamic functional connectivity: a resting state analysis. Front Aging Neurosci. 9(23), 1–11 (2017)
Acknowledgement
This research was supported in part by NIH grants U24AA021697-06, AA005965, AA013521, AA017168.
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Zhao, Q., Honnorat, N., Adeli, E., Pfefferbaum, A., Sullivan, E.V., Pohl, K.M. (2019). Variational Autoencoder with Truncated Mixture of Gaussians for Functional Connectivity Analysis. In: Chung, A., Gee, J., Yushkevich, P., Bao, S. (eds) Information Processing in Medical Imaging. IPMI 2019. Lecture Notes in Computer Science(), vol 11492. Springer, Cham. https://doi.org/10.1007/978-3-030-20351-1_68
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DOI: https://doi.org/10.1007/978-3-030-20351-1_68
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