We propose a new sparsification method for the singular value decomposition—called the constrained singular value decomposition (CSVD)—that can incorporate multiple constraints such as sparsification and orthogonality for the left and right singular vectors. The CSVD can combine different constraints because it implements each constraint as a projection onto a convex set, and because it integrates these constraints as projections onto the intersection of multiple convex sets. We show that, with appropriate sparsification constants, the algorithm is guaranteed to converge to a stable point. We also propose and analyze the convergence of an efficient algorithm for the specific case of the projection onto the balls defined by the norms L₁ and L₂. We illustrate the CSVD and compare it to the standard singular value decomposition and to a non-orthogonal related sparsification method with: 1) a simulated example, 2) a small set of face images (corresponding to a configuration with a number of variables much larger than the number of observations), and 3) a psychometric application with a large number of observations and a small number of variables. The companion R-package, csvd, that implements the algorithms described in this paper, along with reproducible examples, are available for download from https://github.com/vguillemot/csvd.

Haralick texture features are common texture descriptors in image analysis. To compute the Haralick features, the image gray-levels are reduced, a process called quantization. The resulting features depend heavily on the quantization step, so Haralick features are not reproducible unless the same quantization is performed. The aim of this work was to develop Haralick features that are invariant to the number of quantization gray-levels. By redefining the gray-level co-occurrence matrix (GLCM) as a discretized probability density function, it becomes asymptotically invariant to the quantization. The invariant and original features were compared using logistic regression classification to separate two classes based on the texture features. Classifiers trained on the invariant features showed higher accuracies, and had similar performance when training and test images had very different quantizations. In conclusion, using the invariant Haralick features, an image pattern will give the same texture feature values independent of image quantization.

Predictive models can be used on high-dimensional brain images to decode cognitive states or diagnosis/prognosis of a clinical condition/evolution. Spatial regularization through structured sparsity offers new perspectives in this context and reduces the risk of overfitting the model while providing interpretable neuroimaging signatures by forcing the solution to adhere to domain-specific constraints. Total variation (TV) is a promising candidate for structured penalization: it enforces spatial smoothness of the solution while segmenting predictive regions from the background. We consider the problem of minimizing the sum of a smooth convex loss, a non-smooth convex penalty (whose proximal operator is known) and a wide range of possible complex, non-smooth convex structured penalties such as TV or overlapping group Lasso. Existing solvers are either limited in the functions they can minimize or in their practical capacity to scale to high-dimensional imaging data. Nesterov’s smoothing technique can be used to minimize a large number of non-smooth convex structured penalties. However, reasonable precision requires a small smoothing parameter, which slows down the convergence speed to unacceptable levels. To benefit from the versatility of Nesterov’s smoothing technique, we propose a first order continuation algorithm, CONESTA, which automatically generates a sequence of decreasing smoothing parameters. The generated sequence maintains the optimal convergence speed toward any globally desired precision. Our main contributions are: gap to probe the current distance to the global optimum in order to adapt the smoothing parameter and the To propose an expression of the duality convergence speed. This expression is applicable to many penalties and can be used with other solvers than CONESTA. We also propose an expression for the particular smoothing parameter that minimizes the number of iterations required to reach a given precision. Furthermore, we provide a convergence proof and its rate, which is an improvement over classical proximal gradient smoothing methods. We demonstrate on both simulated and high-dimensional structural neuroimaging data that CONESTA significantly outperforms many state-of-the-art solvers in regard to convergence speed and precision.

The Haralick texture features are common in the image analysis literature, partly because of their simplicity and because their values can be interpreted. It was recently observed that the Haralick texture features are very sensitive to the size of the GLCM that was used to compute them, which led to a new formulation that is invariant to the GLCM size. However, these new features still depend on the sample size used to compute the GLCM, i.e. the size of the input image region-of-interest (ROI).

The purpose of this work was to investigate the performance of density estimation methods for approximating the GLCM and subsequently the corresponding invariant features.

Three density estimation methods were evaluated, namely a piece-wise constant distribution, the Parzen-windows method, and the Gaussian mixture model. The methods were evaluated on 29 different image textures and 20 invariant Haralick texture features as well as a wide range of different ROI sizes.

The results indicate that there are two types of features: those that have a clear minimum error for a particular GLCM size for each ROI size, and those whose error decreases monotonically with increased GLCM size. For the first type of features, the Gaussian mixture model gave the smallest errors, and in particular for small ROI sizes (less than about 20×20).

In conclusion, the Gaussian mixture model is the preferred method for the first type of features (in particular for small ROIs). For the second type of features, simply using a large GLCM size is preferred.

ObjectiveStructural MRI (sMRI) increasingly offers insight into abnormalities inherent to schizophrenia. Previous machine learning applications suggest that individual classification is feasible and reliable and, however, is focused on the predictive performance of the clinical status in cross‐sectional designs, which has limited biological perspectives. Moreover, most studies depend on relatively small cohorts or single recruiting site. Finally, no study controlled for disease stage or medication's effect. These elements cast doubt on previous findings’ reproducibility.

MethodWe propose a machine learning algorithm that provides an interpretable brain signature. Using large datasets collected from 4 sites (276 schizophrenia patients, 330 controls), we assessed cross‐site prediction reproducibility and associated predictive signature. For the first time, we evaluated the predictive signature regarding medication and illness duration using an independent dataset of first‐episode patients.

ResultsMachine learning classifiers based on neuroanatomical features yield significant intersite prediction accuracies (72%) together with an excellent predictive signature stability. This signature provides a neural score significantly correlated with symptom severity and the extent of cognitive impairments. Moreover, this signature demonstrates its efficiency on first‐episode psychosis patients (73% accuracy).

ConclusionThese results highlight the existence of a common neuroanatomical signature for schizophrenia, shared by a majority of patients even from an early stage of the disorder.

Purpose

The linear least squares (LLS) estimator provides a fast approach to parameter estimation in the linearized two-compartment exchange model. However, the LLS method may introduce a bias through correlated noise in the system matrix of the model. The purpose of this work is to present a new estimator for the linearized two-compartment exchange model that takes this noise into account.

Method

To account for the noise in the system matrix, we developed an estimator based on the weighted total least squares (WTLS) method. Using simulations, the proposed WTLS estimator was compared, in terms of accuracy and precision, to an LLS estimator and a nonlinear least squares (NLLS) estimator.

Results

The WTLS method improved the accuracy compared to the LLS method to levels comparable to the NLLS method. This improvement was at the expense of increased computational time; however, the WTLS was still faster than the NLLS method. At high signal-to-noise ratio all methods provided similar precisions while inconclusive results were observed at low signal-to-noise ratio.

Conclusion

The proposed method provides improvements in accuracy compared to the LLS method, however, at an increased computational cost. Magn Reson Med, 2017. © 2017 International Society for Magnetic Resonance in Medicine.

Despite significant progress in the field, the detection of fMRI signal changes during hallucinatory events remains difficult and time-consuming. This article first proposes a machine-learning algorithm to automatically identify resting-state fMRI periods that precede hallucinations versus periods that do not. When applied to whole-brain fMRI data, state-of-the-art classification methods, such as support vector machines (SVM), yield dense solutions that are difficult to interpret. We proposed to extend the existing sparse classification methods by taking the spatial structure of brain images into account with structured sparsity using the total variation penalty. Based on this approach, we obtained reliable classifying performances associated with interpretable predictive patterns, composed of two clearly identifiable clusters in speech-related brain regions. The variation in transition-to-hallucination functional patterns not only from one patient to another but also from one occurrence to the next (e.g., also depending on the sensory modalities involved) appeared to be the major difficulty when developing effective classifiers. Consequently, second, this article aimed to characterize the variability within the prehallucination patterns using an extension of principal component analysis with spatial constraints. The principal components (PCs) and the associated basis patterns shed light on the intrinsic structures of the variability present in the dataset. Such results are promising in the scope of innovative fMRI-guided therapy for drug-resistant hallucinations, such as fMRI-based neurofeedback.

Principal component analysis (PCA) is an exploratory tool widely used in data analysis to uncover the dominant patterns of variability within a population. Despite its ability to represent a data set in a low-dimensional space, PCA’s interpretability remains limited. Indeed, the components produced by PCA are often noisy or exhibit no visually meaningful patterns. Furthermore, the fact that the components are usually non-sparse may also impede interpretation, unless arbitrary thresholding is applied. However, in neuroimaging, it is essential to uncover clinically interpretable phenotypic markers that would account for the main variability in the brain images of a population. Recently, some alternatives to the standard PCA approach, such as sparse PCA (SPCA), have been proposed, their aim being to limit the density of the components. Nonetheless, sparsity alone does not entirely solve the interpretability problem in neuroimaging, since it may yield scattered andunstable components. We hypothesized that the incorporation of prior information regarding the structure of the data may lead to improved relevance and interpretability of brain patterns. We therefore present a simple extension of the popular PCA framework that adds structured sparsity penalties on the loading vectors in order to identify the few stable regions in the brain images that capture most of the variability. Such structured sparsity can be obtained by combining, e.g., l1 and total variation (TV) penalties, where the TV regularization encodes information on the underlying structure of the data. This paper presents the structured SPCA (denoted SPCA-TV) optimization framework and its resolution. We demonstrate SPCA-TV’s effectiveness and versatility on three different data sets. It can be applied to any kind of structured data, such as, e.g., N-dimensional array images or meshes of cortical surfaces. The gains of SPCA-TV over unstructured approaches (such as SPCA and ElasticNet PCA) or structured approach (such as GraphNet PCA) are significant, since SPCA-TV reveals the variability within a data set in the form of intelligible brain patterns that are easier to interpret and more stable across different samples.