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A Gaussian Process Model for Unsupervised Analysis of High Dimensional Shape Data

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Machine Learning in Medical Imaging (MLMI 2021)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 12966))

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Applications of medical image analysis are often faced with the challenge of modelling high-dimensional data with relatively few samples. In many settings, normal or healthy samples are prevalent while pathological samples are rarer, highly diverse, and/or difficult to model. In such cases, a robust model of the normal population in the high-dimensional space can be useful for characterizing pathologies. In this context, there is utility in hybrid models, such as probabilistic PCA, which learns a low-dimensional model, commensurates with the available data, and combines it with a generic, isotropic noise model for the remaining dimensions. However, the isotropic noise model ignores the inherent correlations that are evident in so many high-dimensional data sets associated with images and shapes in medicine. This paper describes a method for estimating a Gaussian model for collections of images or shapes that exhibit underlying correlations, e.g., in the form of smoothness. The proposed method incorporates a Gaussian-process noise model within a generative formulation. For optimization, we derive a novel expectation maximization (EM) algorithm. We demonstrate the efficacy of the method on synthetic examples and on anatomical shape data.

Supported by the National Institutes of Health under R21-EB026061, NIBIB-U24EB029011, NIAMS-R01AR076120, NHLBI-R01HL135568, NIBIB-R01EB016701, and NIGMS-P41GM103545. Authors thank Erin Anstadt, MD and Jesse A Goldstein, MD for providing cranial shapes. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health.

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Tao, W., Bhalodia, R., Whitaker, R. (2021). A Gaussian Process Model for Unsupervised Analysis of High Dimensional Shape Data. In: Lian, C., Cao, X., Rekik, I., Xu, X., Yan, P. (eds) Machine Learning in Medical Imaging. MLMI 2021. Lecture Notes in Computer Science(), vol 12966. Springer, Cham.

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