Evaluating Graph Signal Processing for Neuroimaging Through Classification and Dimensionality Reduction
- 1. 24/01 /17 1 INTERSEMESTRE NEUROIMAGERIE - ANALYSE D'IRMF CÉRÉBRALE EVALUATING GRAPH SIGNAL PROCESSING FOR NEUROIMAGING THROUGH CLASSIFICATION AND DIMENSIONALITY REDUCTION Mathilde Ménoret Nicolas Farrugia Bastien Pasdeloup Vincent Gripon GlobalSIP 2017 Montreal November 14th 2017
- 2. 2NEUROIMAGING AND NETWORK SCIENCE Fornito et al. 2015 Nature Neuro The application of Graph Theory for neuroimaging is now widespread in the neuroimaging community.
- 3. 3WHY GRAPH SIGNAL PROCESSING ? ► Graph Signal Processing (GSP) attempts to generalize univariate signal processing (eg Fourier analysis) to irregular domains ► Graph Laplacian : L = D - A A : Adjacency matrix, D : degree matrix ► Graph Signals are a mapping of a signal on the graph nodes ► Graph Fourier Transform exploits the eigenvectors of L (harmonics) ► Classical signal processing can be obtained by taking a ring graph ► Applications of GSP - Decomposition of signals in the Graph Fourier domain - Filtering - … ► Properties of the graph Laplacian for brain graphs
- 4. 4THE NEXT STEP ? ► Laplacian eigenvectors of a graph based on brain structure (gray and white matter) can predict spontaneous brain activity (Atasoy, Donelly & Pearson, 2017, Nature communications)
- 5. 5THE NEXT STEP ? ► Laplacian eigenvectors can be interpreted functionally (Margulies et al. 2016, PNAS, here termed “connectivity gradients”) -> Therefore GSP appears as an ideal framework to analyse, predict and interpret brain activity.
- 6. 6GSP APPLIED TO NEUROIMAGING ► Graph Frequencies + PCA (Huang et al. 2016) : statistical analysis on a motor learning task and fMRI data. ► Dimensionality reduction (Rui et al. 2016) by learning subspaces on graph frequencies on MEG data. ► Denoising and dimensionality reduction on EEG data using graph laplacian – SPHARA (Graichen et al. 2015) ► Low rank estimation / denoising (Liu et al. 2016) ► Measure derived from graph signal smoothness combined with graph modularity (Modular Dirichlet Energy) to analyse an EEG experiment (Smith et al 2017)
- 7. 7OUR CONTRIBUTION ► Goal: use GSP for supervised classification of brain activity (fMRI) ► Key Questions - Can GSP improve classification accuracy? - What is the influence of the graph? - Can GSP be exploited for dimensionality reduction in the context of brain data? ► Experiments - Simulated fMRI data - Haxby dataset All results are presented here using classification with linear support vector machines. Menoret, Farrugia, Pasdeloup & Gripon “Evaluating Graph Signal Processing for Neuroimaging through Classification and Dimensionality Reduction”, https://arxiv.org/abs/1703.01842
- 8. Haxby et al. 2001, Science Brain parcellation to create regions of interests (ROIs) Geometry : baricenter of ROIs BASC Atlas, Bellec et al. Neuroimage 2010
- 9. Contrast Condition 1 – Condition 2 fMRI simulation: neuRosim Simulated activity in 6 areas in two conditions (Faces Vs Houses): • Bilateral Primary Visual Cortex V1 (similar activation for both conditions), • Bilateral Fusiform Face Area (stronger activation for faces) • Bilateral Parahippocampal Place area (stronger activation for houses). Simulated noise on spatial locations and activation amplitude. Simulations were grouped in “Easy” or “Difficult” cases depending on noise.
- 10. 10DIFFERENT TYPES OF GRAPHS ► Graphs based on 3D coordinates - Weights = gaussian kernel on distances between ROI coordinates - All weights (Full) or Thresholded (Geometric) ► Functional graphs - Weights = statistical measures of similarity between ROI signals - Absolute values of Correlation or Covariance ► Graph based on smoothness priors (Kalofolias) ► Mixed graphs - Thresholded geometric support + covariance weights - Fundis = product of Full and Covariance ► N.B. Graph Fourier Transforms are isometries
- 11. 11DIMENSIONALITY REDUCTION TECHNIQUES From initial data : ► PCA or ICA - Select k first components ► K-best features selected by Analysis of Variance (k-best ANOVA) - Perform all univariate ANOVA comparing conditions - Select k nodes that discriminate best the conditions From low (LF) and high frequencies (HF) in the GFT domain : ► Select k first (resp. last) eigenvalues of L to get GFT LF (resp. GFT HF) ► Graph Sampling - Calculate the graph weighted coherence for LF and HF - Extract k nodes concentrating most energy
- 12. * -> next results are shown only for the semilocal graph SIMULATED DATA – 50 COMPONENTS
- 13. Contrast Condition 1 – Condition 2 SVM weights after GS SVM weight after ANOVA feature selection RESULTS USING SIMULATED DATA
- 14. RESULTS SIMULATION AND HAXBY SEMILOCAL GRAPH
- 15. Contrast House-Face SVM weight after Graph Sampling (Semilocal) Dim: 50 RESULTS ON HAXBY DATASET
- 16. GSP FOR BRAIN DECODING - CONCLUSIONS 16 ► Dimensionality reduction combined with GSP is a promising avenue ► Classification - On simulated data, GSP using semi-local graph and graph sampling yields significant performance improvements in a difficult scenario - On a real dataset : when keeping few dimensions, GSP + semilocal and graph sampling may improve classification accuracy ► Perspectives - Use a structural graph from dMRI ? - Role of classification technique ? (linear SVC used so far)