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Despite the digital nature of magnetic resonance imaging, the resulting observations are most frequently reported and stored in text documents. There is a trove of information untapped in medical health records, case reports, and medical publications. In this paper, we propose to mine brain medical publications to learn the spatial distribution associated with anatomical terms. The problem is formulated in terms of minimization of a risk on distributions which leads to a least-deviation cost function. An efficient algorithm in the dual then learns the mapping from documents to brain structures. Empirical results using coordinates extracted from the brain-imaging literature show that i) models must adapt to semantic variation in the terms used to describe a given anatomical structure, ii) voxel-wise parameterization leads to higher likelihood of locations reported in unseen documents, iii) least-deviation cost outperforms least-square. As a proof of concept for our method, we use our model of spatial distributions to predict the distribution of specific neurological conditions from text-only reports.

For statistical learning, categorical variables in a table are usually considered as discrete entities and encoded separately to feature vectors, e.g., with one-hot encoding. "Dirty" non-curated data gives rise to categorical variables with a very high cardinality but redundancy: several categories reflect the same entity. In databases, this issue is typically solved with a deduplication step. We show that a simple approach that exposes the redundancy to the learning algorithm brings significant gains. We study a generalization of one-hot encoding, similarity encoding, that builds feature vectors from similarities across categories. We perform a thorough empirical validation on non-curated tables, a problem seldom studied in machine learning. Results on seven real-world datasets show that similarity encoding brings significant gains in prediction in comparison with known encoding methods for categories or strings, notably one-hot encoding and bag of character n-grams. We draw practical recommendations for encoding dirty categories: 3-gram similarity appears to be a good choice to capture morphological resemblance. For very high-cardinality, dimensionality reduction significantly reduces the computational cost with little loss in performance: random projections or choosing a subset of prototype categories still outperforms classic encoding approaches.

Cognitive neuroscience is enjoying rapid increase in extensive public brain-imaging datasets. It opens the door to large-scale statistical models. Finding a unified perspective for all available data calls for scalable and automated solutions to an old challenge: how to aggregate heterogeneous information on brain function into a universal cognitive system that relates mental operations/cognitive processes/psychological tasks to brain networks? We cast this challenge in a machine-learning approach to predict conditions from statistical brain maps across different studies. For this, we leverage multi-task learning and multi-scale dimension reduction to learn low-dimensional representations of brain images that carry cognitive information and can be robustly associated with psychological stimuli. Our multi-dataset classification model achieves the best prediction performance on several large reference datasets, compared to models without cognitive-aware low-dimension representations, it brings a substantial performance boost to the analysis of small datasets, and can be introspected to identify universal template cognitive concepts., Comment: Advances in Neural Information Processing Systems, Dec 2017, Long Beach, United States. 2017

Predictive models ground many state-of-the-art developments in statistical brain image analysis: decoding, MVPA, searchlight, or extraction of biomarkers. The principled approach to establish their validity and usefulness is cross-validation, testing prediction on unseen data. Here, I would like to raise awareness on error bars of cross-validation, which are often underestimated. Simple experiments show that sample sizes of many neuroimaging studies inherently lead to large error bars, eg $\pm$10% for 100 samples. The standard error across folds strongly underestimates them. These large error bars compromise the reliability of conclusions drawn with predictive models, such as biomarkers or methods developments where, unlike with cognitive neuroimaging MVPA approaches, more samples cannot be acquired by repeating the experiment across many subjects. Solutions to increase sample size must be investigated, tackling possible increases in heterogeneity of the data.

We present a matrix-factorization algorithm that scales to input matrices with both huge number of rows and columns. Learned factors may be sparse or dense and/or non-negative, which makes our algorithm suitable for dictionary learning, sparse component analysis, and non-negative matrix factorization. Our algorithm streams matrix columns while subsampling them to iteratively learn the matrix factors. At each iteration, the row dimension of a new sample is reduced by subsampling, resulting in lower time complexity compared to a simple streaming algorithm. Our method comes with convergence guarantees to reach a stationary point of the matrix-factorization problem. We demonstrate its efficiency on massive functional Magnetic Resonance Imaging data (2 TB), and on patches extracted from hyperspectral images (103 GB). For both problems, which involve different penalties on rows and columns, we obtain significant speed-ups compared to state-of-the-art algorithms., Comment: IEEE Transactions on Signal Processing, Institute of Electrical and Electronics Engineers, A Para\^itre

We present a matrix factorization algorithm that scales to input matrices that are large in both dimensions (i.e., that contains morethan 1TB of data). The algorithm streams the matrix columns while subsampling them, resulting in low complexity per iteration andreasonable memory footprint. In contrast to previous online matrix factorization methods, our approach relies on low-dimensional statistics from past iterates to control the extra variance introduced by subsampling. We present a convergence analysis that guarantees us to reach a stationary point of the problem. Large speed-ups can be obtained compared to previous online algorithms that do not perform subsampling, thanks to the feature redundancy that often exists in high-dimensional settings.

Resting-state functional Magnetic Resonance Imaging (R-fMRI) holds the promise to reveal functional biomarkers of neuropsychiatric disorders. However, extracting such biomarkers is challenging for complex multi-faceted neuropatholo-gies, such as autism spectrum disorders. Large multi-site datasets increase sample sizes to compensate for this complexity, at the cost of uncontrolled heterogeneity. This heterogeneity raises new challenges, akin to those face in realistic diagnostic applications. Here, we demonstrate the feasibility of inter-site classification of neuropsychiatric status, with an application to the Autism Brain Imaging Data Exchange (ABIDE) database, a large (N=871) multi-site autism dataset. For this purpose, we investigate pipelines that extract the most predictive biomarkers from the data. These R-fMRI pipelines build participant-specific connectomes from functionally-defined brain areas. Connectomes are then compared across participants to learn patterns of connectivity that differentiate typical controls from individuals with autism. We predict this neuropsychiatric status for participants from the same acquisition sites or different, unseen, ones. Good choices of methods for the various steps of the pipeline lead to 67% prediction accuracy on the full ABIDE data, which is significantly better than previously reported results. We perform extensive validation on multiple subsets of the data defined by different inclusion criteria. These enables detailed analysis of the factors contributing to successful connectome-based prediction. First, prediction accuracy improves as we include more subjects, up to the maximum amount of subjects available. Second, the definition of functional brain areas is of paramount importance for biomarker discovery: brain areas extracted from large R-fMRI datasets outperform reference atlases in the classification tasks., Comment: in NeuroImage, Elsevier, 2016

In this work, we revisit fast dimension reduction approaches, as with random projections and random sampling. Our goal is to summarize the data to decrease computational costs and memory footprint of subsequent analysis. Such dimension reduction can be very efficient when the signals of interest have a strong structure, such as with images. We focus on this setting and investigate feature clustering schemes for data reductions that capture this structure. An impediment to fast dimension reduction is that good clustering comes with large algorithmic costs. We address it by contributing a linear-time agglomerative clustering scheme, Recursive Nearest Agglomeration (ReNA). Unlike existing fast agglomerative schemes, it avoids the creation of giant clusters. We empirically validate that it approximates the data as well as traditional variance-minimizing clustering schemes that have a quadratic complexity. In addition, we analyze signal approximation with feature clustering and show that it can remove noise, improving subsequent analysis steps. As a consequence, data reduction by clustering features with ReNA yields very fast and accurate models, enabling to process large datasets on budget. Our theoretical analysis is backed by extensive experiments on publicly-available data that illustrate the computation efficiency and the denoising properties of the resulting dimension reduction scheme., Comment: IEEE Transactions on Pattern Analysis and Machine Intelligence, Institute of Electrical and Electronics Engineers, In press

Spatially-sparse predictors are good models for brain decoding: they give accurate predictions and their weight maps are interpretable as they focus on a small number of regions. However, the state of the art, based on total variation or graph-net, is computationally costly. Here we introduce sparsity in the local neighborhood of each voxel with social-sparsity, a structured shrinkage operator. We find that, on brain imaging classification problems, social-sparsity performs almost as well as total-variation models and better than graph-net, for a fraction of the computational cost. It also very clearly outlines predictive regions. We give details of the model and the algorithm., Comment: in Pattern Recognition in NeuroImaging, Jun 2016, Trento, Italy. 2016

Decoding, ie prediction from brain images or signals, calls for empirical evaluation of its predictive power. Such evaluation is achieved via cross-validation, a method also used to tune decoders' hyper-parameters. This paper is a review on cross-validation procedures for decoding in neuroimaging. It includes a didactic overview of the relevant theoretical considerations. Practical aspects are highlighted with an extensive empirical study of the common decoders in within-and across-subject predictions, on multiple datasets --anatomical and functional MRI and MEG-- and simulations. Theory and experiments outline that the popular " leave-one-out " strategy leads to unstable and biased estimates, and a repeated random splits method should be preferred. Experiments outline the large error bars of cross-validation in neuroimaging settings: typical confidence intervals of 10%. Nested cross-validation can tune decoders' parameters while avoiding circularity bias. However we find that it can be more favorable to use sane defaults, in particular for non-sparse decoders., Comment: NeuroImage, Elsevier, 2016

We consider structure discovery of undirected graphical models from observational data. Inferring likely structures from few examples is a complex task often requiring the formulation of priors and sophisticated inference procedures. Popular methods rely on estimating a penalized maximum likelihood of the precision matrix. However, in these approaches structure recovery is an indirect consequence of the data-fit term, the penalty can be difficult to adapt for domain-specific knowledge, and the inference is computationally demanding. By contrast, it may be easier to generate training samples of data that arise from graphs with the desired structure properties. We propose here to leverage this latter source of information as training data to learn a function, parametrized by a neural network that maps empirical covariance matrices to estimated graph structures. Learning this function brings two benefits: it implicitly models the desired structure or sparsity properties to form suitable priors, and it can be tailored to the specific problem of edge structure discovery, rather than maximizing data likelihood. Applying this framework, we find our learnable graph-discovery method trained on synthetic data generalizes well: identifying relevant edges in both synthetic and real data, completely unknown at training time. We find that on genetics, brain imaging, and simulation data we obtain performance generally superior to analytical methods.

Sparse matrix factorization is a popular tool to obtain interpretable data decompositions, which are also effective to perform data completion or denoising. Its applicability to large datasets has been addressed with online and randomized methods, that reduce the complexity in one of the matrix dimension, but not in both of them. In this paper, we tackle very large matrices in both dimensions. We propose a new factoriza-tion method that scales gracefully to terabyte-scale datasets, that could not be processed by previous algorithms in a reasonable amount of time. We demonstrate the efficiency of our approach on massive functional Magnetic Resonance Imaging (fMRI) data, and on matrix completion problems for recommender systems, where we obtain significant speed-ups compared to state-of-the art coordinate descent methods.

We present a method for fast resting-state fMRI spatial decomposi-tions of very large datasets, based on the reduction of the temporal dimension before applying dictionary learning on concatenated individual records from groups of subjects. Introducing a measure of correspondence between spatial decompositions of rest fMRI, we demonstrates that time-reduced dictionary learning produces result as reliable as non-reduced decompositions. We also show that this reduction significantly improves computational scalability.

Functional brain networks are well described and estimated from data with Gaussian Graphical Models (GGMs), e.g. using sparse inverse covariance estimators. Comparing functional connectivity of subjects in two populations calls for comparing these estimated GGMs. Our goal is to identify differences in GGMs known to have similar structure. We characterize the uncertainty of differences with confidence intervals obtained using a parametric distribution on parameters of a sparse estimator. Sparse penalties enable statistical guarantees and interpretable models even in high-dimensional and low-sample settings. Characterizing the distributions of sparse models is inherently challenging as the penalties produce a biased estimator. Recent work invokes the sparsity assumptions to effectively remove the bias from a sparse estimator such as the lasso. These distributions can be used to give confidence intervals on edges in GGMs, and by extension their differences. However, in the case of comparing GGMs, these estimators do not make use of any assumed joint structure among the GGMs. Inspired by priors from brain functional connectivity we derive the distribution of parameter differences under a joint penalty when parameters are known to be sparse in the difference. This leads us to introduce the debiased multi-task fused lasso, whose distribution can be characterized in an efficient manner. We then show how the debiased lasso and multi-task fused lasso can be used to obtain confidence intervals on edge differences in GGMs. We validate the techniques proposed on a set of synthetic examples as well as neuro-imaging dataset created for the study of autism.

The total variation (TV) penalty, as many other analysis-sparsity problems, does not lead to separable factors or a proximal operatorwith a closed-form expression, such as soft thresholding for the $\ell\_1$ penalty. As a result, in a variational formulation of an inverse problem or statisticallearning estimation, it leads to challenging non-smooth optimization problemsthat are often solved with elaborate single-step first-order methods. When thedata-fit term arises from empirical measurements, as in brain imaging, it isoften very ill-conditioned and without simple structure. In this situation, in proximal splitting methods, the computation cost of thegradient step can easily dominate each iteration. Thus it is beneficialto minimize the number of gradient steps.We present fAASTA, a variant of FISTA, that relies on an internal solver forthe TV proximal operator, and refines its tolerance to balance computationalcost of the gradient and the proximal steps. We give benchmarks andillustrations on "brain decoding": recovering brain maps from noisymeasurements to predict observed behavior. The algorithm as well as theempirical study of convergence speed are valuable for any non-exact proximaloperator, in particular analysis-sparsity problems.

The use of brain images as markers for diseases or behavioral differences is challenged by the small effects size and the ensuing lack of power, an issue that has incited researchers to rely more systematically on large cohorts. Coupled with resolution increases, this leads to very large datasets. A striking example in the case of brain imaging is that of the Human Connectome Project: 20 Terabytes of data and growing. The resulting data deluge poses severe challenges regarding the tractability of some processing steps (discriminant analysis, multivariate models) due to the memory demands posed by these data. In this work, we revisit dimension reduction approaches, such as random projections, with the aim of replacing costly function evaluations by cheaper ones while decreasing the memory requirements. Specifically, we investigate the use of alternate schemes, based on fast clustering, that are well suited for signals exhibiting a strong spatial structure, such as anatomical and functional brain images. Our contribution is twofold: i) we propose a linear-time clustering scheme that bypasses the percolation issues inherent in these algorithms and thus provides compressions nearly as good as traditional quadratic-complexity variance-minimizing clustering schemes, ii) we show that cluster-based compression can have the virtuous effect of removing high-frequency noise, actually improving subsequent estimations steps. As a consequence, the proposed approach yields very accurate models on several large-scale problems yet with impressive gains in computational efficiency, making it possible to analyze large datasets., Comment: ICML Workshop on Statistics, Machine Learning and Neuroscience (Stamlins 2015), Jul 2015, Lille, France

Functional Magnetic Resonance Images acquired during resting-state provide information about the functional organization of the brain through measuring correlations between brain areas. Independent components analysis is the reference approach to estimate spatial components from weakly structured data such as brain signal time courses; each of these components may be referred to as a brain network and the whole set of components can be conceptualized as a brain functional atlas. Recently, new methods using a sparsity prior have emerged to deal with low signal-to-noise ratio data. However, even when using sophisticated priors, the results may not be very sparse and most often do not separate the spatial components into brain regions. This work presents post-processing techniques that automatically sparsify brain maps and separate regions properly using geometric operations, and compares these techniques according to faithfulness to data and stability metrics. In particular, among threshold-based approaches, hysteresis thresholding and random walker segmentation, the latter improves significantly the stability of both dense and sparse models.

Imaging neuroscience links brain activation maps to behavior and cognition via correlational studies. Due to the nature of the individual experiments, based on eliciting neural response from a small number of stimuli, this link is incomplete, and unidirectional from the causal point of view. To come to conclusions on the function implied by the activation of brain regions, it is necessary to combine a wide exploration of the various brain functions and some inversion of the statistical inference. Here we introduce a methodology for accumulating knowledge towards a bidirectional link between observed brain activity and the corresponding function. We rely on a large corpus of imaging studies and a predictive engine. Technically, the challenges are to find commonality between the studies without denaturing the richness of the corpus. The key elements that we contribute are labeling the tasks performed with a cognitive ontology, and modeling the long tail of rare paradigms in the corpus. To our knowledge, our approach is the first demonstration of predicting the cognitive content of completely new brain images. To that end, we propose a method that predicts the experimental paradigms across different studies., Comment: NIPS (Neural Information Processing Systems), United States (2013)

Scikit-learn is an increasingly popular machine learning li- brary. Written in Python, it is designed to be simple and efficient, accessible to non-experts, and reusable in various contexts. In this paper, we present and discuss our design choices for the application programming interface (API) of the project. In particular, we describe the simple and elegant interface shared by all learning and processing units in the library and then discuss its advantages in terms of composition and reusability. The paper also comments on implementation details specific to the Python ecosystem and analyzes obstacles faced by users and developers of the library.

Functional connectomes capture brain interactions via synchronized fluctuations in the functional magnetic resonance imaging signal. If measured during rest, they map the intrinsic functional architecture of the brain. With task-driven experiments they represent integration mechanisms between specialized brain areas. Analyzing their variability across subjects and conditions can reveal markers of brain pathologies and mechanisms underlying cognition. Methods of estimating functional connectomes from the imaging signal have undergone rapid developments and the literature is full of diverse strategies for comparing them. This review aims to clarify links across functional-connectivity methods as well as to expose different steps to perform a group study of functional connectomes.

As neuroimaging databases grow in size and complexity, the time researchers spend investigating and managing the data increases to the expense of data analysis. As a result, investigators rely more and more heavily on scripting using high-level languages to automate data management and processing tasks. For this, a structured and programmatic access to the data store is necessary. Web services are a first step toward this goal. They however lack in functionality and ease of use because they provide only low level interfaces to databases. We introduce here PyXNAT, a Python module that interacts with The Extensible Neuroimaging Archive Toolkit (XNAT) through native Python calls across multiple operating systems. The choice of Python enables PyXNAT to expose the XNAT Web Services and unify their features with a higher level and more expressive language. PyXNAT provides XNAT users direct access to all the scientific packages in Python. Finally PyXNAT aims to be efficient and easy to use, both as a backend library to build XNAT clients and as an alternative frontend from the command line.

Typical cohorts in brain imaging studies are not large enough for systematic testing of all the information contained in the images. To build testable working hypotheses, investigators thus rely on analysis of previous work, sometimes formalized in a so-called meta-analysis. In brain imaging, this approach underlies the specification of regions of interest (ROIs) that are usually selected on the basis of the coordinates of previously detected effects. In this paper, we propose to use a database of images, rather than coordinates, and frame the problem as transfer learning: learning a discriminant model on a reference task to apply it to a different but related new task. To facilitate statistical analysis of small cohorts, we use a sparse discriminant model that selects predictive voxels on the reference task and thus provides a principled procedure to define ROIs. The benefits of our approach are twofold. First it uses the reference database for prediction, i.e. to provide potential biomarkers in a clinical setting. Second it increases statistical power on the new task. We demonstrate on a set of 18 pairs of functional MRI experimental conditions that our approach gives good prediction. In addition, on a specific transfer situation involving different scanners at different locations, we show that voxel selection based on transfer learning leads to higher detection power on small cohorts., Comment: MICCAI, Nice : France (2012)

Researchers in functional neuroimaging mostly use activation coordinates to formulate their hypotheses. Instead, we propose to use the full statistical images to define regions of interest (ROIs). This paper presents two machine learning approaches, transfer learning and selection transfer, that are compared upon their ability to identify the common patterns between brain activation maps related to two functional tasks. We provide some preliminary quantification of these similarities, and show that selection transfer makes it possible to set a spatial scale yielding ROIs that are more specific to the context of interest than with transfer learning. In particular, selection transfer outlines well known regions such as the Visual Word Form Area when discriminating between different visual tasks., Comment: PRNI 2012 : 2nd International Workshop on Pattern Recognition in NeuroImaging, London : United Kingdom (2012)

Medical images can be used to predict a clinical score coding for the severity of a disease, a pain level or the complexity of a cognitive task. In all these cases, the predicted variable has a natural order. While a standard classifier discards this information, we would like to take it into account in order to improve prediction performance. A standard linear regression does model such information, however the linearity assumption is likely not be satisfied when predicting from pixel intensities in an image. In this paper we address these modeling challenges with a supervised learning procedure where the model aims to order or rank images. We use a linear model for its robustness in high dimension and its possible interpretation. We show on simulations and two fMRI datasets that this approach is able to predict the correct ordering on pairs of images, yielding higher prediction accuracy than standard regression and multiclass classification techniques.

Inferring the functional specificity of brain regions from functional Magnetic Resonance Images (fMRI) data is a challenging statistical problem. While the General Linear Model (GLM) remains the standard approach for brain mapping, supervised learning techniques (a.k.a.} decoding) have proven to be useful to capture multivariate statistical effects distributed across voxels and brain regions. Up to now, much effort has been made to improve decoding by incorporating prior knowledge in the form of a particular regularization term. In this paper we demonstrate that further improvement can be made by accounting for non-linearities using a ranking approach rather than the commonly used least-square regression. Through simulation, we compare the recovery properties of our approach to linear models commonly used in fMRI based decoding. We demonstrate the superiority of ranking with a real fMRI dataset.

Functional neuroimaging can measure the brain?s response to an external stimulus. It is used to perform brain mapping: identifying from these observations the brain regions involved. This problem can be cast into a linear supervised learning task where the neuroimaging data are used as predictors for the stimulus. Brain mapping is then seen as a support recovery problem. On functional MRI (fMRI) data, this problem is particularly challenging as i) the number of samples is small due to limited acquisition time and ii) the variables are strongly correlated. We propose to overcome these difficulties using sparse regression models over new variables obtained by clustering of the original variables. The use of randomization techniques, e.g. bootstrap samples, and clustering of the variables improves the recovery properties of sparse methods. We demonstrate the benefit of our approach on an extensive simulation study as well as two fMRI datasets., Comment: Appears in Proceedings of the 29th International Conference on Machine Learning (ICML 2012)

Correlations in the signal observed via functional Magnetic Resonance Imaging (fMRI), are expected to reveal the interactions in the underlying neural populations through hemodynamic response. In particular, they highlight distributed set of mutually correlated regions that correspond to brain networks related to different cognitive functions. Yet graph-theoretical studies of neural connections give a different picture: that of a highly integrated system with small-world properties: local clustering but with short pathways across the complete structure. We examine the conditional independence properties of the fMRI signal, i.e. its Markov structure, to find realistic assumptions on the connectivity structure that are required to explain the observed functional connectivity. In particular we seek a decomposition of the Markov structure into segregated functional networks using decomposable graphs: a set of strongly-connected and partially overlapping cliques. We introduce a new method to efficiently extract such cliques on a large, strongly-connected graph. We compare methods learning different graph structures from functional connectivity by testing the goodness of fit of the model they learn on new data. We find that summarizing the structure as strongly-connected networks can give a good description only for very large and overlapping networks. These results highlight that Markov models are good tools to identify the structure of brain connectivity from fMRI signals, but for this purpose they must reflect the small-world properties of the underlying neural systems.

Ultrafast synchrotron microtomography has been used to study in-situ and in real time the initial stages of silicate glass melt formation from crystalline granular raw materials. Significant and unexpected rearrangements of grains occur below the nominal eutectic temperature, and several drastically different solid-state reactions are observed to take place at different types of intergranular contacts. These reactions have a profound influence on the formation and the composition of the liquids produced, and control the formation of defects., Comment: 4 pages, 4 figures

Scikit-learn is a Python module integrating a wide range of state-of-the-art machine learning algorithms for medium-scale supervised and unsupervised problems. This package focuses on bringing machine learning to non-specialists using a general-purpose high-level language. Emphasis is put on ease of use, performance, documentation, and API consistency. It has minimal dependencies and is distributed under the simplified BSD license, encouraging its use in both academic and commercial settings. Source code, binaries, and documentation can be downloaded from http://scikit-learn.org., Comment: Update authors list and URLs

We propose a method that combines signals from many brain regions observed in functional Magnetic Resonance Imaging (fMRI) to predict the subject's behavior during a scanning session. Such predictions suffer from the huge number of brain regions sampled on the voxel grid of standard fMRI data sets: the curse of dimensionality. Dimensionality reduction is thus needed, but it is often performed using a univariate feature selection procedure, that handles neither the spatial structure of the images, nor the multivariate nature of the signal. By introducing a hierarchical clustering of the brain volume that incorporates connectivity constraints, we reduce the span of the possible spatial configurations to a single tree of nested regions tailored to the signal. We then prune the tree in a supervised setting, hence the name supervised clustering, in order to extract a parcellation (division of the volume) such that parcel-based signal averages best predict the target information. Dimensionality reduction is thus achieved by feature agglomeration, and the constructed features now provide a multi-scale representation of the signal. Comparisons with reference methods on both simulated and real data show that our approach yields higher prediction accuracy than standard voxel-based approaches. Moreover, the method infers an explicit weighting of the regions involved in the regression or classification task.

In the Python world, NumPy arrays are the standard representation for numerical data. Here, we show how these arrays enable efficient implementation of numerical computations in a high-level language. Overall, three techniques are applied to improve performance: vectorizing calculations, avoiding copying data in memory, and minimizing operation counts. We first present the NumPy array structure, then show how to use it for efficient computation, and finally how to share array data with other libraries.

While medical imaging typically provides massive amounts of data, the extraction of relevant information for predictive diagnosis remains a difficult challenge. Functional MRI (fMRI) data, that provide an indirect measure of task-related or spontaneous neuronal activity, are classically analyzed in a mass-univariate procedure yielding statistical parametric maps. This analysis framework disregards some important principles of brain organization: population coding, distributed and overlapping representations. Multivariate pattern analysis, i.e., the prediction of behavioural variables from brain activation patterns better captures this structure. To cope with the high dimensionality of the data, the learning method has to be regularized. However, the spatial structure of the image is not taken into account in standard regularization methods, so that the extracted features are often hard to interpret. More informative and interpretable results can be obtained with the l_1 norm of the image gradient, a.k.a. its Total Variation (TV), as regularization. We apply for the first time this method to fMRI data, and show that TV regularization is well suited to the purpose of brain mapping while being a powerful tool for brain decoding. Moreover, this article presents the first use of TV regularization for classification.

Mayavi is an open-source, general-purpose, 3D scientific visualization package. It seeks to provide easy and interactive tools for data visualization that fit with the scientific user's workflow. For this purpose, Mayavi provides several entry points: a full-blown interactive application; a Python library with both a MATLAB-like interface focused on easy scripting and a feature-rich object hierarchy; widgets associated with these objects for assembling in a domain-specific application, and plugins that work with a general purpose application-building framework. In this article, we present an overview of the various features of Mayavi, we then provide insight on the design and engineering decisions made in implementing Mayavi, and finally discuss a few novel applications.

Spontaneous brain activity, as observed in functional neuroimaging, has been shown to display reproducible structure that expresses brain architecture and carries markers of brain pathologies. An important view of modern neuroscience is that such large-scale structure of coherent activity reflects modularity properties of brain connectivity graphs. However, to date, there has been no demonstration that the limited and noisy data available in spontaneous activity observations could be used to learn full-brain probabilistic models that generalize to new data. Learning such models entails two main challenges: i) modeling full brain connectivity is a difficult estimation problem that faces the curse of dimensionality and ii) variability between subjects, coupled with the variability of functional signals between experimental runs, makes the use of multiple datasets challenging. We describe subject-level brain functional connectivity structure as a multivariate Gaussian process and introduce a new strategy to estimate it from group data, by imposing a common structure on the graphical model in the population. We show that individual models learned from functional Magnetic Resonance Imaging (fMRI) data using this population prior generalize better to unseen data than models based on alternative regularization schemes. To our knowledge, this is the first report of a cross-validated model of spontaneous brain activity. Finally, we use the estimated graphical model to explore the large-scale characteristics of functional architecture and show for the first time that known cognitive networks appear as the integrated communities of functional connectivity graph., Comment: in Advances in Neural Information Processing Systems, Vancouver : Canada (2010)

Functional brain connectivity, as revealed through distant correlations in the signals measured by functional Magnetic Resonance Imaging (fMRI), is a promising source of biomarkers of brain pathologies. However, establishing and using diagnostic markers requires probabilistic inter-subject comparisons. Principled comparison of functional-connectivity structures is still a challenging issue. We give a new matrix-variate probabilistic model suitable for inter-subject comparison of functional connectivity matrices on the manifold of Symmetric Positive Definite (SPD) matrices. We show that this model leads to a new algorithm for principled comparison of connectivity coefficients between pairs of regions. We apply this model to comparing separately post-stroke patients to a group of healthy controls. We find neurologically-relevant connection differences and show that our model is more sensitive that the standard procedure. To the best of our knowledge, these results are the first report of functional connectivity differences between a single-patient and a group and thus establish an important step toward using functional connectivity as a diagnostic tool.

Spatial Independent Components Analysis (ICA) is increasingly used in the context of functional Magnetic Resonance Imaging (fMRI) to study cognition and brain pathologies. Salient features present in some of the extracted Independent Components (ICs) can be interpreted as brain networks, but the segmentation of the corresponding regions from ICs is still ill-controlled. Here we propose a new ICA-based procedure for extraction of sparse features from fMRI datasets. Specifically, we introduce a new thresholding procedure that controls the deviation from isotropy in the ICA mixing model. Unlike current heuristics, our procedure guarantees an exact, possibly conservative, level of specificity in feature detection. We evaluate the sensitivity and specificity of the method on synthetic and fMRI data and show that it outperforms state-of-the-art approaches.

Spatial Independent Component Analysis (ICA) is an increasingly used data-driven method to analyze functional Magnetic Resonance Imaging (fMRI) data. To date, it has been used to extract meaningful patterns without prior information. However, ICA is not robust to mild data variation and remains a parameter-sensitive algorithm. The validity of the extracted patterns is hard to establish, as well as the significance of differences between patterns extracted from different groups of subjects. We start from a generative model of the fMRI group data to introduce a probabilistic ICA pattern-extraction algorithm, called CanICA (Canonical ICA). Thanks to an explicit noise model and canonical correlation analysis, our method is auto-calibrated and identifies the group-reproducible data subspace before performing ICA. We compare our method to state-of-the-art multi-subject fMRI ICA methods and show that the features extracted are more reproducible.

We propose a scheme for testing the weak equivalence principle (Universality of Free Fall) using an atom-interferometric measurement of the local differential acceleration between two atomic species with a large mass ratio as test masses. A apparatus in free fall can be used to track atomic free-fall trajectories over large distances. We show how the differential acceleration can be extracted from the interferometric signal using Bayesian statistical estimation, even in the case of a large mass and laser wavelength difference. We show that this statistical estimation method does not suffer from acceleration noise of the platform and does not require repeatable experimental conditions. We specialize our discussion to a dual potassium/rubidium interferometer and extend our protocol with other atomic mixtures. Finally, we discuss the performances of the UFF test developed for the free-fall (0-g) airplane in the ICE project (\verb"http://www.ice-space.fr")

We describe the operation of a light pulse interferometer using cold 87Rb atoms in reduced gravity. Using a series of two Raman transitions induced by light pulses, we have obtained Ramsey fringes in the low gravity environment achieved during parabolic flights. With our compact apparatus, we have operated in a regime which is not accessible on ground. In the much lower gravity environment and lower vibration level of a satellite, our cold atom interferometer could measure accelerations with a sensitivity orders of magnitude better than the best ground based accelerometers and close to proven spaced-based ones.

We report on light-shift tomography of a cloud of 87 Rb atoms in a far-detuned optical-dipole trap at 1565 nm. Our method is based on standard absorption imaging, but takes advantage of the strong light-shift of the excited state of the imaging transition, which is due to a quasi-resonance of the trapping laser with a higher excited level. We use this method to (i) map the equipotentials of a crossed optical-dipole trap, and (ii) study the thermalisation of an atomic cloud by following the evolution of the potential-energy of atoms during the free-evaporation process.