Kernel-based classification for brain connectivity graphs on the Riemannian manifold of positive definite matrices

Dodero, Luca; Minh, Hà Quang; Biagio, Marco San; Murino, Vittorio; Sona, Diego

doi:10.1109/isbi.2015.7163812

Cited by 46 publications

(44 citation statements)

References 13 publications

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“…Partial correlation between nodes is useful to rule out indirect effects in the correlation structure, but calls for shrunk estimates (Smith et al, 2011;Varoquaux et al, 2010b). Mathematical arguments have also led to representations tailored to the manifold-structure of covariance matrices (Varoquaux et al, 2010a;Ng et al, 2014;Dodero et al, 2015;Colclough et al, 2017). We benchmark the simplest of these, a tangent representation of the manifold which underlies the more complex developments (see Appendix A for a quick introduction to this formalism).…”

Section: Representation Of Brain Functional Connectomesmentioning

confidence: 99%

“…With this covariance structure, we study three different parametrizations of functional interactions: full correlation, partial correlation (Smith et al, 2011;Varoquaux and Craddock, 2013) and the tangent space of covariance matrices. The latter is less frequently used but has solid mathematical foundations and a variety of groups have reported good decoding per-formances with this framework (Varoquaux et al, 2010a;Barachant et al, 2013;Ng et al, 2014;Dodero et al, 2015;Qiu et al, 2015;Rahim et al, 2017;Wong et al, 2018). We compared two variants, using as a reference point the Euclidean mean (Varoquaux et al, 2010a) or the geometric mean (Ng et al, 2014); in both cases we rely on Nilearn implementation (Abraham et al, 2014b).…”

Section: Connectivity Parametrizationmentioning

confidence: 99%

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Benchmarking functional connectome-based predictive models for resting-state fMRI

et al. 2019

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Functional connectomes reveal biomarkers of individual psychological or clinical traits. However, there is great variability in the analytic pipelines typically used to derive them from rest-fMRI cohorts. Here, we consider a specific type of studies, using predictive models on the edge weights of functional connectomes, for which we highlight the best modeling choices. We systematically study the prediction performances of models in 6 different cohorts and a total of 2 000 individuals, encompassing neuro-degenerative (Alzheimer's, Post-traumatic stress disorder), neuro-psychiatric (Schizophrenia, Autism), drug impact (Cannabis use) clinical settings and psychological trait (fluid intelligence). The typical prediction procedure from rest-fMRI consists of three main steps: defining brain regions, representing the interactions, and supervised learning. For each step we benchmark typical choices: 8 different ways of defining regions-either pre-defined or generated from the rest-fMRI data-3 measures to build functional connectomes from the extracted time-series, and 10 classification models to compare functional interactions across subjects. Our benchmarks summarize more than 240 different pipelines and outline modeling choices that show consistent prediction performances in spite of variations in the populations and sites. We find that regions defined from functional data work best; that it is beneficial to capture between-region interactions with tangent-based parametrization of covariances, a midway between correlations and partial correlation; and that simple linear predictors such as a logistic regression give the best predictions. Our work is a step forward to establishing reproducible imaging-based biomarkers for clinical settings.

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Section: Representation Of Brain Functional Connectomesmentioning

confidence: 99%

Section: Connectivity Parametrizationmentioning

confidence: 99%

Benchmarking functional connectome-based predictive models for resting-state fMRI

et al. 2019

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“…Some other approaches try to design a suitable kernel relating to the specific problem. Dudero et al [2] proposed a mathematical framework based on Riemannian geometry and kernel methods that could be applied to connectivity matrices for the classification tasks. They have trained and tested proposed kernel using crossvalidation method and reported the accuracy of 60.76%.…”

Section: Related Workmentioning

confidence: 99%

Graph theoretical approach for screening autism on brain complex networks

et al. 2019

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Autism spectrum disorder has been known as a prevalent brain disorder of children in recent years. Numerous studies have indicated differences between functional brain networks of disordered and typically developed brains. Nevertheless, no automatic and effective methodology has been established for the identification of this disorder using functional magnetic resonance images (fMRI). In this research, we investigate differences between Autistic and typically developed brain networks by modeling fMRI data to brain complex networks and propose a method for classification of the aforementioned groups. In this method, applying graphlet counts, as the frequency of predefined non-isomorphic subgraphs, feature vectors have been extracted and using an ensemble classifier, data has been classified into two defined groups. Results, showing 6.5% improvement according to the best baseline method, has reached 69.81% of accuracy for disorder classification.

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“…obtaining the dynamic Laplacian connectivity (dLC), where D t is the degree matrix of W t at each time t. The graph Laplacian is PSD and it can be easily regularized to a positive definite matrix by the modification L t = L t + γI, where γ > 0 is a regularization parameter and I is the identity matrix [11]. In our settings we used γ = 10 −9 .…”

Section: Graph Laplacian and Modularitymentioning

confidence: 99%

“…The graph Laplacian matrix is often used to study modular organization [8,9] and it has recently been proposed to explore dynamical process of network systems [10]. Moreover, the Laplacian matrix is positive semi-definite (PSD) and it can be combined with the Riemannian geometry [11]. Therefore, we characterize dissimilarity between dFC patterns using Riemannian metrics.…”

Section: Introductionmentioning

confidence: 99%

Traces of human functional activity: Moment-to-moment fluctuations in fMRI data

Dodero

Sona

Meskaldji

et al. 2016

2016 IEEE 13th International Symposium on Biomedical Imaging (ISBI)

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Dynamic functional connectivity (dFC) measured by functional magnetic resonance imaging (fMRI) shows evidence of large-scale networks with highly dynamic (re)configurations.We propose a novel approach to extract traces of human brain function by the construction of a trajectory in a meaningful low-dimensional space. This allows studying dFC in more detail and identify possible meaningful brain states from the moment-to-moment fluctuations of the brain signals during resting state or naturalistic conditions such as passive movie watching. Specifically, we explored dynamic organization of sub-networks derived from the time-dependent graph Laplacian in combination with Riemannian manifold distance to measure dissimilarity over time of dFC and to subsequently build the trajectory of brain activity. As a proof-of-principle, we show results for an fMRI dataset containing both rest and movie epochs in 15 healthy participants. The movie condition varied (i.e., fearful, joyful, and neutral movie excerpts) and clearly influenced the subsequent resting-state period in terms of FC brain state.

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Kernel-based classification for brain connectivity graphs on the Riemannian manifold of positive definite matrices

Cited by 46 publications

References 13 publications

Benchmarking functional connectome-based predictive models for resting-state fMRI

Benchmarking functional connectome-based predictive models for resting-state fMRI

Graph theoretical approach for screening autism on brain complex networks

Traces of human functional activity: Moment-to-moment fluctuations in fMRI data

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