Tracking cortical activity from M/EEG using graph cuts with spatiotemporal constraints

Gramfort, Alexandre; Papadopoulo, Théodore; Baillet, Sylvain; Clerc, Maureen

doi:10.1016/j.neuroimage.2010.09.087

Cited by 7 publications

(7 citation statements)

References 47 publications

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“…More generally, the spatial geometry can be defined on a predefined graph. This is the case with brain imaging data, where the measurements of neural activity are provided at each vertex of the triangulated mesh of the brain and across several time points (Gramfort et al, 2011). Formally, each sample µ i in our dataset can be represented as a time sequence of discrete non-negative measures (µ i t ) t=1..T defined in some finite set X .…”

Section: Introductionmentioning

confidence: 99%

Averaging Spatio-temporal Signals using Optimal Transport and Soft Alignments

Janati¹,

Cuturi²,

Gramfort³

2022

Preprint

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Several fields in science, from genomics to neuroimaging, require monitoring populations (measures) that evolve with time. These complex datasets, describing dynamics with both time and spatial components, pose new challenges for data analysis. We propose in this work a new framework to carry out averaging of these datasets, with the goal of synthesizing a representative template trajectory from multiple trajectories. We show that this requires addressing three sources of invariance: shifts in time, space, and total population size (or mass/amplitude). Here we draw inspiration from dynamic time warping (DTW), optimal transport (OT) theory and its unbalanced extension (UOT) to propose a criterion that can address all three issues. This proposal leverages a smooth formulation of DTW (Soft-DTW) that is shown to capture temporal shifts, and UOT to handle both variations in space and size. Our proposed loss can be used to define spatio-temporal barycenters as Fréchet means. Using Fenchel duality, we show how these barycenters can be computed efficiently, in parallel, via a novel variant of entropy-regularized debiased UOT. Experiments on handwritten letters and brain imaging data confirm our theoretical findings and illustrate the effectiveness of the proposed loss for spatio-temporal data.

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Section: Introductionmentioning

confidence: 99%

Averaging Spatio-temporal Signals using Optimal Transport and Soft Alignments

Janati¹,

Cuturi²,

Gramfort³

2022

Preprint

Self Cite

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“…In Minimum Current Estimate-MCE or LASSO -( [16]), few sources are active at each time sample. The solution is obtained by solving the following functional for each time instant independently [16,17]:…”

Section: Introductionmentioning

confidence: 99%

Structural connectivity to reconstruct brain activation and effective connectivity between brain regions

Belaoucha¹,

Papadopoulo²

2020

J. Neural Eng.

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HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

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“…Multi-target tracking for example, involves the prediction of the time indexed positions of several objects or particles (Doucet et al, 2002). In brain imag-ing, magnetoencephalography (MEG) and functional magnetic resonance imaging (fMRI) yield measurements of neural activity in multiple positions and at multiple time points (Gramfort et al, 2011). Quantifying spatio-temporal variability in brain activity can allow to compare different clinial populations.…”

Section: Introductionmentioning

confidence: 99%

Spatio-Temporal Alignments: Optimal transport through space and time

Janati,

Cuturi,

Gramfort

2019

Preprint

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Comparing data defined over space and time is notoriously hard. It involves quantifying both spatial and temporal variability while taking into account the chronological structure of the data. Dynamic Time Warping (DTW) computes a minimal cost alignment between time series that preserves the chronological order but is inherently blind to spatio-temporal shifts. In this paper, we propose Spatio-Temporal Alignments (STA), a new differentiable formulation of DTW that captures spatial and temporal variability. Spatial differences between time samples are captured using regularized Optimal transport. While temporal alignment cost exploits a smooth variant of DTW called soft-DTW. We show how smoothing DTW leads to alignment costs that increase quadratically with time shifts. The costs are expressed using an unbalanced Wasserstein distance to cope with observations that are not probabilities. Experiments on handwritten letters and brain imaging data confirm our theoretical findings and illustrate the effectiveness of STA as a dissimilarity for spatio-temporal data.

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Tracking cortical activity from M/EEG using graph cuts with spatiotemporal constraints

Cited by 7 publications

References 47 publications

Averaging Spatio-temporal Signals using Optimal Transport and Soft Alignments

Averaging Spatio-temporal Signals using Optimal Transport and Soft Alignments

Structural connectivity to reconstruct brain activation and effective connectivity between brain regions

Spatio-Temporal Alignments: Optimal transport through space and time

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