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SUMMARY: Biclustering is a generalization of clustering used to identify simultaneous grouping patterns in observations (rows) and features (columns) of a data matrix. Recently, the biclustering task has been formulated as a convex optimization problem. While this convex recasting of the problem has attractive properties, existing algorithms do not scale well. To address this problem and make convex biclustering a practical tool for analyzing larger data, we propose an implementation of fast convex biclustering called COBRAC to reduce the computing time by iteratively compressing problem size along with the solution path. We apply COBRAC to several gene expression datasets to demonstrate its effectiveness and efficiency. Besides the standalone version for COBRAC, we also developed a related online web server for online calculation and visualization of the downloadable interactive results. AVAILABILITY AND IMPLEMENTATION: The source code and test data are available at https://github.com/haidyi/cvxbiclustr or https://zenodo.org/record/4620218. The web server is available at https://cvxbiclustr.ericchi.com. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.
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Functional connectivity (FC) estimated from functional magnetic resonance imaging (fMRI) signals is important in understanding neural representation and information processing in cortical networks. However, due to a lack of "ground truth" FC pattern, the reliability and robustness of FC estimates are usually examined in downstream FC analysis tasks, such as performing participant's identification (also known as "fingerprinting"). In this paper, we propose to learn FC via a smooth graph learning framework. In particular, we treat each time frame of the fMRI time series as a graph signal on an underlying functional brain graph, and estimate the smooth graph functional connectivity (SGFC) by learning the weighted graph adjacency matrix based on graph signal smoothness assumption. We demonstrate that our approach gives rise to a natural and sparse graph representation of FC from which reliable graph measures can be extracted. Reliability of SGFC is evaluated in the context of fingerprinting and compared to correlation FC (CFC). SGFC achieves higher fingerprinting accuracy across several different experiment settings; the improvement is even more significant when a shorter fMRI scanning length is used for FC estimation. In addition to being reliable, we also validate the cognitive relevance of SGFC by using it to predict fluid intelligence. Finally, in evaluating topological measures of the sparse graph, SGFC reveals a more small-world and modular structure compared to CFC. Together, our results suggest that the smooth graph learning framework produces a naturally sparse, reliable, and cognitive-relevant representation of functional connectivity.
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Conectoma , Imagen por Resonancia Magnética , Matemática , Algoritmos , Conjuntos de Datos como Asunto , Humanos , Inteligencia , Reproducibilidad de los Resultados , Máquina de Vectores de SoporteRESUMEN
Large-scale brain dynamics are believed to lie in a latent, low-dimensional space. Typically, the embeddings of brain scans are derived independently from different cognitive tasks or resting-state data, ignoring a potentially large-and shared-portion of this space. Here, we establish that a shared, robust, and interpretable low-dimensional space of brain dynamics can be recovered from a rich repertoire of task-based functional magnetic resonance imaging (fMRI) data. This occurs when relying on nonlinear approaches as opposed to traditional linear methods. The embedding maintains proper temporal progression of the tasks, revealing brain states and the dynamics of network integration. We demonstrate that resting-state data embeds fully onto the same task embedding, indicating similar brain states are present in both task and resting-state data. Our findings suggest analysis of fMRI data from multiple cognitive tasks in a low-dimensional space is possible and desirable.
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Encéfalo/fisiología , Neuroimagen Funcional/métodos , Aprendizaje Automático , Imagen por Resonancia Magnética/métodos , Procesos Mentales/fisiología , Adulto , Encéfalo/diagnóstico por imagen , Conectoma/métodos , HumanosRESUMEN
A low-dimensional dynamical system is observed in an experiment as a high-dimensional signal, for example, a video of a chaotic pendulums system. Assuming that we know the dynamical model up to some unknown parameters, can we estimate the underlying system's parameters by measuring its time-evolution only once? The key information for performing this estimation lies in the temporal inter-dependencies between the signal and the model. We propose a kernel-based score to compare these dependencies. Our score generalizes a maximum likelihood estimator for a linear model to a general nonlinear setting in an unknown feature space. We estimate the system's underlying parameters by maximizing the proposed score. We demonstrate the accuracy and efficiency of the method using two chaotic dynamical systems-the double pendulum and the Lorenz '63 model.
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Graph signal processing (GSP) is an important methodology for studying data residing on irregular structures. As acquired data is increasingly taking the form of multi-way tensors, new signal processing tools are needed to maximally utilize the multi-way structure within the data. In this paper, we review modern signal processing frameworks generalizing GSP to multi-way data, starting from graph signals coupled to familiar regular axes such as time in sensor networks, and then extending to general graphs across all tensor modes. This widely applicable paradigm motivates reformulating and improving upon classical problems and approaches to creatively address the challenges in tensor-based data. We synthesize common themes arising from current efforts to combine GSP with tensor analysis and highlight future directions in extending GSP to the multi-way paradigm.
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If we pick n random points uniformly in [0, 1] d and connect each point to its c d log n-nearest neighbors, where d ≥ 2 is the dimension and c d is a constant depending on the dimension, then it is well known that the graph is connected with high probability. We prove that it suffices to connect every point to c d,1 log log n points chosen randomly among its c d,2 log n-nearest neighbors to ensure a giant component of size n - o(n) with high probability. This construction yields a much sparser random graph with ~ n log log n instead of ~ n log n edges that has comparable connectivity properties. This result has nontrivial implications for problems in data science where an affinity matrix is constructed: instead of connecting each point to its k nearest neighbors, one can often pick k' ⪠k random points out of the k nearest neighbors and only connect to those without sacrificing quality of results. This approach can simplify and accelerate computation; we illustrate this with experimental results in spectral clustering of large-scale datasets.
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Social neuroscientists often use magnetic resonance imaging (MRI) to understand the relationship between social experiences and their neural substrates. Although MRI is a powerful method, it has several limitations in the study of social experiences, first and foremost its low ecological validity. To address this limitation, researchers have conducted multimethod studies combining MRI with Ecological Momentary Assessment (EMA). However, there are no existing recommendations for best practices for conducting and reporting such studies. To address the absence of standards in the field, we conducted a systematic review of papers that combined the methods. A systematic search of peer-reviewed papers resulted in a pool of 11,558 articles. Inclusion criteria were studies in which participants completed (a) Structural or functional MRI and (b) an EMA protocol that included self-report. Seventy-one papers met inclusion criteria. The following review compares these studies based on several key parameters (e.g., sample size) with the aim of determining feasibility and current standards for design and reporting in the field. The review concludes with recommendations for future research. A special focus is given to the ways in which the two methods were combined analytically and suggestions for novel computational methods that could further advance the field of social neuroscience.
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Experimental work across species has demonstrated that spontaneously generated behaviors are robustly coupled to variations in neural activity within the cerebral cortex. Functional magnetic resonance imaging data suggest that temporal correlations in cortical networks vary across distinct behavioral states, providing for the dynamic reorganization of patterned activity. However, these data generally lack the temporal resolution to establish links between cortical signals and the continuously varying fluctuations in spontaneous behavior observed in awake animals. Here, we used wide-field mesoscopic calcium imaging to monitor cortical dynamics in awake mice and developed an approach to quantify rapidly time-varying functional connectivity. We show that spontaneous behaviors are represented by fast changes in both the magnitude and correlational structure of cortical network activity. Combining mesoscopic imaging with simultaneous cellular-resolution two-photon microscopy demonstrated that correlations among neighboring neurons and between local and large-scale networks also encode behavior. Finally, the dynamic functional connectivity of mesoscale signals revealed subnetworks not predicted by traditional anatomical atlas-based parcellation of the cortex. These results provide new insights into how behavioral information is represented across the neocortex and demonstrate an analytical framework for investigating time-varying functional connectivity in neural networks.
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Neocórtex , Neuronas , Ratones , Animales , Neuronas/fisiología , Imagen por Resonancia Magnética , Vigilia , Neocórtex/diagnóstico por imagen , Mapeo Encefálico/métodos , Vías Nerviosas/fisiologíaRESUMEN
Brain arterioles are active, multicellular complexes whose diameters oscillate at â¼ 0.1 Hz. We assess the physiological impact and spatiotemporal dynamics of vaso-oscillations in the awake mouse. First, vaso-oscillations in penetrating arterioles, which source blood from pial arterioles to the capillary bed, profoundly impact perfusion throughout neocortex. The modulation in flux during resting-state activity exceeds that of stimulus-induced activity. Second, the change in perfusion through arterioles relative to the change in their diameter is weak. This implies that the capillary bed dominates the hydrodynamic resistance of brain vasculature. Lastly, the phase of vaso-oscillations evolves slowly along arterioles, with a wavelength that exceeds the span of the cortical mantle and sufficient variability to establish functional cortical areas as parcels of uniform phase. The phase-gradient supports traveling waves in either direction along both pial and penetrating arterioles. This implies that waves along penetrating arterioles can mix, but not directionally transport, interstitial fluids.
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Circulación Cerebrovascular , Animales , Ratones , Arteriolas/fisiología , Circulación Cerebrovascular/fisiología , Masculino , Corteza Cerebral/fisiología , Corteza Cerebral/irrigación sanguínea , Ratones Endogámicos C57BL , Neocórtex/fisiología , Neocórtex/irrigación sanguíneaRESUMEN
Functional optical imaging in neuroscience is rapidly growing with the development of optical systems and fluorescence indicators. To realize the potential of these massive spatiotemporal datasets for relating neuronal activity to behavior and stimuli and uncovering local circuits in the brain, accurate automated processing is increasingly essential. We cover recent computational developments in the full data processing pipeline of functional optical microscopy for neuroscience data and discuss ongoing and emerging challenges.
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Many machine learning algorithms depend on weights that quantify row and column similarities of a data matrix. The choice of weights can dramatically impact the effectiveness of the algorithm. Nonetheless, the problem of choosing weights has arguably not been given enough study. When a data matrix is completely observed, Gaussian kernel affinities can be used to quantify the local similarity between pairs of rows and pairs of columns. Computing weights in the presence of missing data, however, becomes challenging. In this paper, we propose a new method to construct row and column affinities even when data are missing by building off a co-clustering technique. This method takes advantage of solving the optimization problem for multiple pairs of cost parameters and filling in the missing values with increasingly smooth estimates. It exploits the coupled similarity structure among both the rows and columns of a data matrix. We show these affinities can be used to perform tasks such as data imputation, clustering, and matrix completion on graphs.
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Emotion regulation habits have long been implicated in risk for depression. However, research in this area traditionally adopts an approach that ignores the multifaceted nature of emotion regulation strategies, the clinical heterogeneity of depression, and potential differential relations between emotion regulation features and individual symptoms. To address limitations associated with the dominant aggregate-level approach, this study aimed to identify which features of key emotion regulation strategies are most predictive and when those features are most predictive of individual symptoms of depression across different time lags. Leveraging novel developments in the field of machine learning, artificial neural network models with feature selection were estimated using data from 460 participants who participated in a 20-wave longitudinal study with weekly assessments. At each wave, participants completed measures of repetitive negative thinking, positive reappraisal, perceived stress, and depression symptoms. Results revealed that specific features of repetitive negative thinking (wondering "why cannot I get going?" and having thoughts or images about feelings of loneliness) and positive reappraisal (looking for positive sides) were important indicators for detecting various depressive symptoms, above and beyond perceived stress. These features had overlapping and unique predictive relations with individual cognitive, affective, and somatic symptoms. Examining temporal fluctuations in the predictive utility, results showed that the utility of these emotion regulation features was stable over time. These findings illuminate potential pathways through which emotion regulation features may confer risk for depression and help to identify actionable targets for its prevention and treatment. (PsycInfo Database Record (c) 2022 APA, all rights reserved).
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Pesimismo , Depresión/diagnóstico , Emociones/fisiología , Humanos , Estudios Longitudinales , Redes Neurales de la ComputaciónRESUMEN
Dimensionality reduction techniques are a key component of most microbiome studies, providing both the ability to tractably visualize complex microbiome datasets and the starting point for additional, more formal, statistical analyses. In this review, we discuss the motivation for applying dimensionality reduction techniques, the special characteristics of microbiome data such as sparsity and compositionality that make this difficult, the different categories of strategies that are available for dimensionality reduction, and examples from the literature of how they have been successfully applied (together with pitfalls to avoid). We conclude by describing the need for further development in the field, in particular combining the power of phylogenetic analysis with the ability to handle sparsity, compositionality, and non-normality, as well as discussing current techniques that should be applied more widely in future analyses.
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Optical imaging of calcium signals in the brain has enabled researchers to observe the activity of hundreds-to-thousands of individual neurons simultaneously. Current methods predominantly use morphological information, typically focusing on expected shapes of cell bodies, to better identify neurons in the field-of-view. The explicit shape constraints limit the applicability of automated cell identification to other important imaging scales with more complex morphologies, e.g., dendritic or widefield imaging. Specifically, fluorescing components may be broken up, incompletely found, or merged in ways that do not accurately describe the underlying neural activity. Here we present Graph Filtered Temporal Dictionary (GraFT), a new approach that frames the problem of isolating independent fluorescing components as a dictionary learning problem. Specifically, we focus on the time-traces-the main quantity used in scientific discovery-and learn a time trace dictionary with the spatial maps acting as the presence coefficients encoding which pixels the time-traces are active in. Furthermore, we present a novel graph filtering model which redefines connectivity between pixels in terms of their shared temporal activity, rather than spatial proximity. This model greatly eases the ability of our method to handle data with complex non-local spatial structure. We demonstrate important properties of our method, such as robustness to morphology, simultaneously detecting different neuronal types, and implicitly inferring number of neurons, on both synthetic data and real data examples. Specifically, we demonstrate applications of our method to calcium imaging both at the dendritic, somatic, and widefield scales.
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Algoritmos , Calcio , Encéfalo/diagnóstico por imagen , Encéfalo/fisiología , NeuronasRESUMEN
We present Low Distortion Local Eigenmaps (LDLE), a manifold learning technique which constructs a set of low distortion local views of a data set in lower dimension and registers them to obtain a global embedding. The local views are constructed using the global eigenvectors of the graph Laplacian and are registered using Procrustes analysis. The choice of these eigenvectors may vary across the regions. In contrast to existing techniques, LDLE can embed closed and non-orientable manifolds into their intrinsic dimension by tearing them apart. It also provides gluing instruction on the boundary of the torn embedding to help identify the topology of the original manifold. Our experimental results will show that LDLE largely preserved distances up to a constant scale while other techniques produced higher distortion. We also demonstrate that LDLE produces high quality embeddings even when the data is noisy or sparse.
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Microbiome data are sparse and high dimensional, so effective visualization of these data requires dimensionality reduction. To date, the most commonly used method for dimensionality reduction in the microbiome is calculation of between-sample microbial differences (beta diversity), followed by principal-coordinate analysis (PCoA). Uniform Manifold Approximation and Projection (UMAP) is an alternative method that can reduce the dimensionality of beta diversity distance matrices. Here, we demonstrate the benefits and limitations of using UMAP for dimensionality reduction on microbiome data. Using real data, we demonstrate that UMAP can improve the representation of clusters, especially when the clusters are composed of multiple subgroups. Additionally, we show that UMAP provides improved correlation of biological variation along a gradient with a reduced number of coordinates of the resulting embedding. Finally, we provide parameter recommendations that emphasize the preservation of global geometry. We therefore conclude that UMAP should be routinely used as a complementary visualization method for microbiome beta diversity studies. IMPORTANCE UMAP provides an additional method to visualize microbiome data. The method is extensible to any beta diversity metric used with PCoA, and our results demonstrate that UMAP can indeed improve visualization quality and correspondence with biological and technical variables of interest. The software to perform this analysis is available under an open-source license and can be obtained at https://github.com/knightlab-analyses/umap-microbiome-benchmarking; additionally, we have provided a QIIME 2 plugin for UMAP at https://github.com/biocore/q2-umap.
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The extraction of clusters from a dataset which includes multiple clusters and a significant background component is a non-trivial task of practical importance. In image analysis this manifests for example in anomaly detection and target detection. The traditional spectral clustering algorithm, which relies on the leading K eigenvectors to detect K clusters, fails in such cases. In this paper we propose the spectral embedding norm which sums the squared values of the first I normalized eigenvectors, where I can be significantly larger than K. We prove that this quantity can be used to separate clusters from the background in unbalanced settings, including extreme cases such as outlier detection. The performance of the algorithm is not sensitive to the choice of I, and we demonstrate its application on synthetic and real-world remote sensing and neuroimaging datasets.
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We consider the analysis of high dimensional data given in the form of a matrix with columns consisting of observations and rows consisting of features. Often the data is such that the observations do not reside on a regular grid, and the given order of the features is arbitrary and does not convey a notion of locality. Therefore, traditional transforms and metrics cannot be used for data organization and analysis. In this paper, our goal is to organize the data by defining an appropriate representation and metric such that they respect the smoothness and structure underlying the data. We also aim to generalize the joint clustering of observations and features in the case the data does not fall into clear disjoint groups. For this purpose, we propose multiscale data-driven transforms and metrics based on trees. Their construction is implemented in an iterative refinement procedure that exploits the co-dependencies between features and observations. Beyond the organization of a single dataset, our approach enables us to transfer the organization learned from one dataset to another and to integrate several datasets together. We present an application to breast cancer gene expression analysis: learning metrics on the genes to cluster the tumor samples into cancer sub-types and validating the joint organization of both the genes and the samples. We demonstrate that using our approach to combine information from multiple gene expression cohorts, acquired by different profiling technologies, improves the clustering of tumor samples.