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Deep neural networks are a family of computational models that have led to a dramatical improvement of the state of the art in several domains such as image, voice or text analysis. These methods provide a framework to model complex,…

Multi-modal biological, imaging, and neuropsychological markers have demonstrated promising performance for distinguishing Alzheimer's disease (AD) patients from cognitively normal elders. However, it remains difficult to early predict when…

In this paper we show the similarities and differences of two deep neural networks by comparing the manifolds composed of activation vectors in each fully connected layer of them. The main contribution of this paper includes 1) a new data…

Recent methods in geometric deep learning have introduced various neural networks to operate over data that lie on Riemannian manifolds. Such networks are often necessary to learn well over graphs with a hierarchical structure or to learn…

We introduce deep neural networks for the analysis of anatomical shapes that learn a low-dimensional shape representation from the given task, instead of relying on hand-engineered representations. Our framework is modular and consists of…

Multimodal medical image fusion is a crucial task that combines complementary information from different imaging modalities into a unified representation, thereby enhancing diagnostic accuracy and treatment planning. While deep learning…

Geometric deep learning has gained much attention in recent years due to more available data acquired from non-Euclidean domains. Some examples include point clouds for 3D models and wireless sensor networks in communications. Graphs are…

Depth prediction plays a key role in understanding a 3D scene. Several techniques have been developed throughout the years, among which Convolutional Neural Network has recently achieved state-of-the-art performance on estimating depth from…

Non-Euclidean constraints are inherent in many kinds of data in computer vision and machine learning, typically as a result of specific invariance requirements that need to be respected during high-level inference. Often, these geometric…

Early diagnosis, playing an important role in preventing progress and treating the Alzheimer's disease (AD), is based on classification of features extracted from brain images. The features have to accurately capture main AD-related…

Manifold-valued data naturally arises in medical imaging. In cognitive neuroscience, for instance, brain connectomes base the analysis of coactivation patterns between different brain regions on the analysis of the correlations of their…

Deep learning has shown outstanding performance in identifying intricate structures in complex high-dimensional data, especially in the domain of computer vision. The application of deep learning to early detection and automated…

Collecting and accessing a large amount of medical data is very time-consuming and laborious, not only because it is difficult to find specific patients but also because it is required to resolve the confidentiality of a patient's medical…

We propose two graph neural network layers for graphs with features in a Riemannian manifold. First, based on a manifold-valued graph diffusion equation, we construct a diffusion layer that can be applied to an arbitrary number of nodes and…

Disease progression modeling (DPM) using longitudinal data is a challenging task in machine learning for healthcare that can provide clinicians with better tools for diagnosis and monitoring of disease. Existing DPM algorithms neglect…

Ability of deep networks to extract high level features and of recurrent networks to perform time-series inference have been studied. In view of universality of one hidden layer network at approximating functions under weak constraints, the…

Alzheimer's disease (AD) is a progressive and incurable neurodegenerative disease which destroys brain cells and causes loss to patient's memory. An early detection can prevent the patient from further damage of the brain cells and hence…

Many tasks require mapping continuous input data (e.g. images) to discrete task outputs (e.g. class labels). Yet, how neural networks learn to perform such discrete computations on continuous data manifolds remains poorly understood. Here,…

Deep neural networks have been demonstrated to achieve phenomenal success in many domains, and yet their inner mechanisms are not well understood. In this paper, we investigate the curvature of image manifolds, i.e., the manifold deviation…

Joint models for longitudinal and time-to-event data are commonly used in longitudinal studies to forecast disease trajectories over time. Despite the many advantages of joint modeling, the standard forms suffer from limitations that arise…