Learning distributions of shape trajectories from longitudinal datasets: a hierarchical model on a manifold of diffeomorphisms

We propose a method to learn a distribution of shape trajectories from longitudinal data, i.e. the collection of individual objects repeatedly observed at multiple time-points. The method allows to compute an average spatiotemporal trajectory of shape changes at the group level, and the individual variations of this trajectory both in terms of geometry and time dynamics. First, we formulate a non-linear mixed-effects statistical model as the combination of a generic statistical model for manifold-valued longitudinal data, a deformation model defining shape trajectories via the action of a finite-dimensional set of diffeomorphisms with a manifold structure, and an efficient numerical scheme to compute parallel transport on this manifold. Second, we introduce a MCMC-SAEM algorithm with a specific approach to shape sampling, an adaptive scheme for proposal variances, and a log-likelihood tempering strategy to estimate our model. Third, we validate our algorithm on 2D simulated data, and then estimate a scenario of alteration of the shape of the hippocampus 3D brain structure during the course of Alzheimer's disease. The method shows for instance that hippocampal atrophy progresses more quickly in female subjects, and occurs earlier in APOE4 mutation carriers. We finally illustrate the potential of our method for classifying pathological trajectories versus normal ageing

Learning distributions of shape trajectories from longitudinal datasets: a hierarchical model on a manifold of diffeomorphisms

International audienceWe propose a method to learn a distribution of shape tra-jectories from longitudinal data, i.e. the collection of individual objects repeatedly observed at multiple time-points. The method allows to compute an average spatiotemporal trajectory of shape changes at the group level, and the individual variations of this trajectory both in terms of geometry and time dynamics. First, we formulate a non-linear mixed-effects statistical model as the combination of a generic statistical model for manifold-valued longitudinal data, a deformation model defining shape trajectories via the action of a finite-dimensional set of diffeomorphisms with a man-ifold structure, and an efficient numerical scheme to compute parallel transport on this manifold. Second, we introduce a MCMC-SAEM algorithm with a specific approach to shape sampling, an adaptive scheme for proposal variances , and a log-likelihood tempering strategy to estimate our model. Third, we validate our algorithm on 2D simulated data, and then estimate a scenario of alteration of the shape of the hippocampus 3D brain structure during the course of Alzheimer's disease. The method shows for instance that hippocampal atrophy progresses more quickly in female subjects, and occurs earlier in APOE4 mutation carriers. We finally illustrate the potential of our method for classifying pathological trajectories versus normal ageing

Hierarchical modeling of Alzheimer's disease progression from a large longitudinal MRI data set

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Non-Redundant Combination of Hand-Crafted and Deep Learning Radiomics: Application to the Early Detection of Pancreatic Cancer

We address the problem of learning Deep Learning Radiomics (DLR) that are not redundant with Hand-Crafted Radiomics (HCR). To do so, we extract DLR features using a VAE while enforcing their independence with HCR features by minimizing their mutual information. The resulting DLR features can be combined with hand-crafted ones and leveraged by a classifier to predict early markers of cancer. We illustrate our method on four early markers of pancreatic cancer and validate it on a large independent test set. Our results highlight the value of combining non-redundant DLR and HCR features, as evidenced by an improvement in the Area Under the Curve compared to baseline methods that do not address redundancy or solely rely on HCR features.Comment: CaPTion workshop MICCAI 202

Predicting the Progression of Mild Cognitive Impairment Using Machine Learning: A Systematic and Quantitative Review

Context. Automatically predicting if a subject with Mild Cognitive Impairment (MCI) is going to progress to Alzheimer's disease (AD) dementia in the coming years is a relevant question regarding clinical practice and trial inclusion alike. A large number of articles have been published, with a wide range of algorithms, input variables, data sets and experimental designs. It is unclear which of these factors are determinant for the prediction, and affect the predictive performance that can be expected in clinical practice. We performed a systematic review of studies focusing on the automatic prediction of the progression of MCI to AD dementia. We systematically and statistically studied the influence of different factors on predictive performance. Method. The review included 172 articles, 93 of which were published after 2014. 234 experiments were extracted from these articles. For each of them, we reported the used data set, the feature types (defining 10 categories), the algorithm type (defining 12 categories), performance and potential methodological issues. The impact of the features and algorithm on the performance was evaluated using t-tests on the coefficients of mixed effect linear regressions. Results. We found that using cognitive, fluorodeoxyglucose-positron emission tomog-raphy or potentially electroencephalography and magnetoencephalography variables significantly improves predictive performance compared to not including them (p=0.046, 0.009 and 0.003 respectively), whereas including T1 magnetic resonance imaging, amyloid positron emission tomography or cerebrospinal fluid AD biomarkers does not show a significant effect. On the other hand, the algorithm used in the method does not have a significant impact on performance. We identified several methodological issues. Major issues, found in 23.5% of studies, include the absence of a test set, or its use for feature selection or parameter tuning. Other issues, found in 15.0% of studies, pertain to the usability of the method in clinical practice. We also highlight that short-term predictions are likely not to be better than predicting that subjects stay stable over time. Finally, we highlight possible biases in publications that tend not to publish methods with poor performance on large data sets, which may be censored as negative results. Conclusion. Using machine learning to predict MCI to AD dementia progression is a promising and dynamic field. Among the most predictive modalities, cognitive scores are the cheapest and less invasive, as compared to imaging. The good performance they offer question the wide use of imaging for predicting diagnosis evolution, and call for further exploring fine cognitive assessments. Issues identified in the studies highlight the importance of establishing good practices and guidelines for the use of machine learning as a decision support system in clinical practice

Learning distributions of shape trajectories from longitudinal datasets: a hierarchical model on a manifold of diffeomorphisms

International audienceWe propose a method to learn a distribution of shape tra-jectories from longitudinal data, i.e. the collection of individual objects repeatedly observed at multiple time-points. The method allows to compute an average spatiotemporal trajectory of shape changes at the group level, and the individual variations of this trajectory both in terms of geometry and time dynamics. First, we formulate a non-linear mixed-effects statistical model as the combination of a generic statistical model for manifold-valued longitudinal data, a deformation model defining shape trajectories via the action of a finite-dimensional set of diffeomorphisms with a man-ifold structure, and an efficient numerical scheme to compute parallel transport on this manifold. Second, we introduce a MCMC-SAEM algorithm with a specific approach to shape sampling, an adaptive scheme for proposal variances , and a log-likelihood tempering strategy to estimate our model. Third, we validate our algorithm on 2D simulated data, and then estimate a scenario of alteration of the shape of the hippocampus 3D brain structure during the course of Alzheimer's disease. The method shows for instance that hippocampal atrophy progresses more quickly in female subjects, and occurs earlier in APOE4 mutation carriers. We finally illustrate the potential of our method for classifying pathological trajectories versus normal ageing

Learning the spatiotemporal variability in longitudinal shape data sets

In this paper, we propose a generative statistical model to learn the spatiotemporal variability in longitudinal shape data sets, which contain repeated observations of a set of objects or individuals over time. From all the short-term sequences of individual data, the method estimates a long-term normative scenario of shape changes and a tubular coordinate system around this trajectory. Each individual data sequence is therefore (i) mapped onto a specific portion of the trajectory accounting for differences in pace of progression across individuals, and (ii) shifted in the shape space to account for intrinsic shape differences across individuals that are independent of the progression of the observed process. The parameters of the model are estimated using a stochastic approximation of the expectation-maximization algorithm. The proposed approach is validated on a simulated data set, illustrated on the analysis of facial expression in video sequences, and applied to the modeling of the progressive atrophy of the hippocampus in Alzheimer's disease patients. These experiments show that one can use the method to reconstruct data at the precision of the noise, to highlight significant factors that may modulate the progression, and to simulate entirely synthetic longitudinal data sets reproducing the variability of the observed process

Auto-encoding meshes of any topology with the current-splatting and exponentiation layers

International audienceDeep learning has met key applications in image computing, but still lacks processing paradigms for meshes, i.e. collections of elementary geometrical parts such as points, segments or triangles. Meshes are both a powerful representation for geometrical objects, and a challenge for network architectures because of their inherent irregular structure. This work contributes to adapt classical deep learning paradigms to this particular type of data in three ways. First, we introduce the current-splatting layer which embeds meshes in a metric space, allowing the downstream network to process them without any assumption on their topology: they may be composed of varied numbers of elements or connected components, contain holes, or bear high levels of geometrical noise. Second, we adapt to meshes the exponentiation layer which, from an upstream image array, generates shapes with a diffeomorphic control over their topology. Third, we take advantage of those layers to devise a variational auto-encoding architecture, which we interpret as a generative statistical model that learns adapted low-dimensional representations for mesh data sets. An explicit norm-control layer ensures the correspondence between the latent-space Euclidean metric and the shape-space log-Euclidean one. We illustrate this method on simulated and real data sets, and show the practical relevance of the learned representation for visualization, classification and mesh synthesis

Learning low-dimensional representations of shape data sets with diffeomorphic autoencoders

Auteur collectif : Alzheimer’s Disease Neuroimaging InitiativeInternational audienceContemporary deformation-based morphometry offers parametric classes of diffeomorphisms that can be searched to compute the optimal transformation that warps a shape into another, thus defining a similarity metric for shape objects. Extending such classes to capture the geometrical variability in always more varied statistical situations represents an active research topic. This quest for genericity however leads to computationally-intensive estimation problems. Instead, we propose in this work to learn the best-adapted class of diffeomorphisms along with its parametrization, for a shape data set of interest. Optimization is carried out with an auto-encoding variational inference approach, offering in turn a coherent model-estimator pair that we name diffeomorphic auto-encoder. The main contributions are: (i) an original network-based method to construct diffeomorphisms, (ii) a current-splatting layer that allows neural network architectures to process meshes, (iii) illustrations on simulated and real data sets that show differences in the learned statistical distributions of shapes when compared to a standard approach

Learning low-dimensional representations of shape data sets with diffeomorphic autoencoders

Auteur collectif : Alzheimer’s Disease Neuroimaging InitiativeInternational audienceContemporary deformation-based morphometry offers parametric classes of diffeomorphisms that can be searched to compute the optimal transformation that warps a shape into another, thus defining a similarity metric for shape objects. Extending such classes to capture the geometrical variability in always more varied statistical situations represents an active research topic. This quest for genericity however leads to computationally-intensive estimation problems. Instead, we propose in this work to learn the best-adapted class of diffeomorphisms along with its parametrization, for a shape data set of interest. Optimization is carried out with an auto-encoding variational inference approach, offering in turn a coherent model-estimator pair that we name diffeomorphic auto-encoder. The main contributions are: (i) an original network-based method to construct diffeomorphisms, (ii) a current-splatting layer that allows neural network architectures to process meshes, (iii) illustrations on simulated and real data sets that show differences in the learned statistical distributions of shapes when compared to a standard approach