Investigating Brain Functional Networks in a Riemannian Framework

The brain is a complex system of several interconnected components which can be categorized at different Spatio-temporal levels, evaluate the physical connections and the corresponding functionalities. To study brain connectivity at the macroscale, Magnetic Resonance Imaging (MRI) technique in all the different modalities has been exemplified to be an important tool. In particular, functional MRI (fMRI) enables to record the brain activity either at rest or in different conditions of cognitive task and assist in mapping the functional connectivity of the brain. The information of brain functional connectivity extracted from fMRI images can be defined using a graph representation, i.e. a mathematical object consisting of nodes, the brain regions, and edges, the link between regions. With this representation, novel insights have emerged about understanding brain connectivity and providing evidence that the brain networks are not randomly linked. Indeed, the brain network represents a small-world structure, with several different properties of segregation and integration that are accountable for specific functions and mental conditions. Moreover, network analysis enables to recognize and analyze patterns of brain functional connectivity characterizing a group of subjects. In recent decades, many developments have been made to understand the functioning of the human brain and many issues, related to the biological and the methodological perspective, are still need to be addressed. For example, sub-modular brain organization is still under debate, since it is necessary to understand how the brain is functionally organized. At the same time a comprehensive organization of functional connectivity is mostly unknown and also the dynamical reorganization of functional connectivity is appearing as a new frontier for analyzing brain dynamics. Moreover, the recognition of functional connectivity patterns in patients affected by mental disorders is still a challenging task, making plausible the development of new tools to solve them. Indeed, in this dissertation, we proposed novel methodological approaches to answer some of these biological and neuroscientific questions. We have investigated methods for analyzing and detecting heritability in twin's task-induced functional connectivity profiles. in this approach we are proposing a geodesic metric-based method for the estimation of similarity between functional connectivity, taking into account the manifold related properties of symmetric and positive definite matrices. Moreover, we also proposed a computational framework for classification and discrimination of brain connectivity graphs between healthy and pathological subjects affected by mental disorder, using geodesic metric-based clustering of brain graphs on manifold space. Within the same framework, we also propose an approach based on the dictionary learning method to encode the high dimensional connectivity data into a vectorial representation which is useful for classification and determining regions of brain graphs responsible for this segregation. We also propose an effective way to analyze the dynamical functional connectivity, building a similarity representation of fMRI dynamic functional connectivity states, exploiting modular properties of graph laplacians, geodesic clustering, and manifold learning

Comparison of brain connectomes using geodesic distance on manifold: A twins study

fMRI is a unique non-invasive approach for understanding the functional organization of the human brain, and task-based fMRI promotes identification of functionally relevant brain regions associated with a given task. Here, we use fMRI (using the Poffenberger Paradigm) data collected in mono- and dizygotic twin pairs to propose a novel approach for assessing similarity in functional networks. In particular, we compared network similarity between pairs of twins in task-relevant and task-orthogonal networks. The proposed method measures the similarity between functional networks using a geodesic distance between graph Laplacians. With method we show that networks are more similar in monozygotic twins compared to dizygotic twins. Furthermore, the similarity in monozygotic twins is higher for task-relevant, than task-orthogonal networks

Geodesic Clustering of Positive Definite Matrices For Classification of Mental Disorder Using Brain Functional Connectivity

Functional Magnetic Resonance Imaging (fMRI) is a commonly used technique to evaluate brain activity, and can be used to distinguish patients from healthy controls in a variety of diseases. In this work, we present a two-step approach to discriminate healthy subjects against those affected by either Autism Spectrum Disorder or Schizophrenia on the basis of their connectivity patterns. We exploited the property that connectivity patterns described by positive definite matrices define a Riemannian manifold. In this framework, to generate a vector representation used in the classification task, we performed a geodesic clustering of the connectivity matrices. Cluster centroids were then used as a dictionary allowing to encode all subjects graphs as vectors of geodesic distances. A linear Support Vector Machine was then used to classify subjects. To show the advantage of using geodesic distances for this problem, the same analysis was conducted using a Euclidean metric. Experiments show that employing Euclidean distances leads to a lower classification performance and possibly to the definition of the wrong number of clusters, whereas geodesic clustering results in a significantly improved accuracy

Automated Detection of Optic Disc for the Analysis of Retina Using Color Fundus Image

status: publishe

Geodesic Clustering of Positive Definite Matrices For Classification of Mental Disorder Using Brain Functional Connectivity

none6siFunctional Magnetic Resonance Imaging (fMRI) is a commonly used technique to evaluate brain activity, and can be used to distinguish patients from healthy controls in a variety of diseases. In this work, we present a two-step approach to discriminate healthy subjects against those affected by either Autism Spectrum Disorder or Schizophrenia on the basis of their connectivity patterns. We exploited the property that connectivity patterns described by positive definite matrices define a Riemannian manifold. In this framework, to generate a vector representation used in the classification task, we performed a geodesic clustering of the connectivity matrices. Cluster centroids were then used as a dictionary allowing to encode all subjects graphs as vectors of geodesic distances. A linear Support Vector Machine was then used to classify subjects. To show the advantage of using geodesic distances for this problem, the same analysis was conducted using a Euclidean metric. Experiments show that employing Euclidean distances leads to a lower classification performance and possibly to the definition of the wrong number of clusters, whereas geodesic clustering results in a significantly improved accuracy.noneYamin, Muhammad Abubakar; Tessadori, Jacopo; Akbar, Muhammad Usman; Dayan, Michael; Murino, Vittorio; Sona, DiegoYamin, Muhammad Abubakar; Tessadori, Jacopo; Akbar, Muhammad Usman; Dayan, Michael; Murino, Vittorio; Sona, Dieg

Dynamic Functional Connectivity For The Classification Of Multiple Sclerosis Phenotype: A Hidden Markov Model Approach

We present a pipeline for the classification of subjects according to multiple sclerosis phenotype. The approach is based on a hidden Markov model built on dynamic functional connectivity. More in detail, a sequence of correlation matrices is built from the fMRI time slices, then projected on the tangent Euclidean space. The number of considered dimensions is reduced through PCA, then dominant set clustering is applied to group similar correlation matrices in a limited number of ”mental” states, which are then used as the hidden states of the Markov model. Subjects in the test set are then classified according to the likelihood of their sequence of observations with the obtained class-wise Markov models. We demonstrate that our approach is capable of discriminating multiple sclerosis phenotypes and that the persistence of some of the identified states is a possible neurohpyisiological marker of disease severity

Investigating the Impact of Genetic Background on Brain Dynamic Functional Connectivity Through Machine Learning: A Twins Study

Functional magnetic resonance imaging (fMRI) is a popular approach for understanding the functional connectivity of human brain. Recently, dynamic functional connectivity has been used to analyze connectivity variations on resting state fMRI. Here, we use task based fMRI (using the Poffenberger Paradigm) data collected in mono- and dizygotic twin pairs. The task is to examine if the two groups of twins can be discriminated by using the dynamic connectivity, so to prove that genetic background has an effect on functional connectivity. To this aim, we have explored the dynamic connectivity patterns of task-relevant and task-orthogonal sub-networks using graph Laplacian representation in combination with a metric defined on the space of covariance matrices to compute the similarity between twins' dynamics in the mental state. Linear SVMs with an unsupervised feature selection (Laplacian Score) were then used to discriminate the two classes of twins.

Encoding Brain Networks Through Geodesic Clustering of Functional Connectivity for Multiple Sclerosis Classification

none9siAn important task in brain connectivity research is the classification of patients from healthy subjects. In this work, we present a two-step mathematical framework allowing to discriminate between two groups of people with an application to multiple sclerosis. The proposed approach exploits the properties of the connectivity matrices determined using the covariances between signals of a fixed set of brain areas. These positive semidefinite matrices lay on a Riemannian manifold, allowing to use a geodesic distance defined on this space. In order to generate a vector representation useful for classification purposes, but still preserving the network structure, we encoded the data exploiting the network attractors determined by a geodesic clustering of connectivity matrices. Then clustering centroids were used as a dictionary allowing to encode subject's connectivity matrices as a vector of geodesic distances. A Linear Support Vector Machine was then used to perform classification between subjects. To demonstrate the advantage of using geodesic metrics in this framework, we conducted the same analysis using Euclidean metric. Experimental results validate the fact that employing geodesic metric in this framework leads to a higher classification performance, whereas performance with a Euclidean metric was sub-optimal.noneYamin, Muhammad Abubakar; Valsasina, Paola; Dayan, Michael; Vascon, Sebastiano; Tessadori, Jacopo; Filippi, Massimo; Murino, Vittorio; Rocca, Maria A.; Sona, DiegoYamin, Muhammad Abubakar; Valsasina, Paola; Dayan, Michael; Vascon, Sebastiano; Tessadori, Jacopo; Filippi, Massimo; Murino, Vittorio; Rocca, Maria A.; Sona, Dieg

Encoding Brain Networks through Geodesic Clustering of Functional Connectivity for Multiple Sclerosis Classification

An important task in brain connectivity research is the classification of patients from healthy subjects. In this work, we present a two-step mathematical ramework allowing to discriminate between two groups of people with an application to multiple sclerosis. The proposed approach exploits the properties of the connectivity matrices determined using the covariances between signals of a fixed set of brain areas. These positive semidefinite matrices lay on a Riemannian manifold, allowing to use a geodesic distance defined on this space. In order to generate a vector representation useful for classification purposes, but still preserving the network structure, we encoded the data exploiting the network attractors determined by a geodesic clustering of connectivity matrices. Then clustering centroids were used as a dictionary allowing to encode subject\u2019s connectivity matrices as a vector of geodesic distances. A Linear Support Vector Machine was then used to perform classification between subjects. To demonstrate the advantage of using geodesic metrics in this framework, we conducted the same analysis using Euclidean metric. Experimental results validate the fact that employing geodesic metric in this framework leads to a higher classification performance, whereas performance with a Euclidean metric was sub-optimal