Advances in Spectral Learning with Applications to Text Analysis and Brain Imaging

Spectral learning algorithms are becoming increasingly popular in data-rich domains, driven in part by recent advances in large scale randomized SVD, and in spectral estimation of Hidden Markov Models. Extensions of these methods lead to statistical estimation algorithms which are not only fast, scalable, and useful on real data sets, but are also provably correct. Following this line of research, we make two contributions. First, we propose a set of spectral algorithms for text analysis and natural language processing. In particular, we propose fast and scalable spectral algorithms for learning word embeddings -- low dimensional real vectors (called Eigenwords) that capture the “meaning” of words from their context. Second, we show how similar spectral methods can be applied to analyzing brain images. State-of-the-art approaches to learning word embeddings are slow to train or lack theoretical grounding; We propose three spectral algorithms that overcome these limitations. All three algorithms harness the multi-view nature of text data i.e. the left and right context of each word, and share three characteristics: 1). They are fast to train and are scalable. 2). They have strong theoretical properties. 3). They can induce context-specific embeddings i.e. different embedding for “river bank” or “Bank of America”. \end{enumerate} They also have lower sample complexity and hence higher statistical power for rare words. We provide theory which establishes relationships between these algorithms and optimality criteria for the estimates they provide. We also perform thorough qualitative and quantitative evaluation of Eigenwords and demonstrate their superior performance over state-of-the-art approaches. Next, we turn to the task of using spectral learning methods for brain imaging data. Methods like Sparse Principal Component Analysis (SPCA), Non-negative Matrix Factorization (NMF) and Independent Component Analysis (ICA) have been used to obtain state-of-the-art accuracies in a variety of problems in machine learning. However, their usage in brain imaging, though increasing, is limited by the fact that they are used as out-of-the-box techniques and are seldom tailored to the domain specific constraints and knowledge pertaining to medical imaging, which leads to difficulties in interpretation of results. In order to address the above shortcomings, we propose Eigenanatomy (EANAT), a general framework for sparse matrix factorization. Its goal is to statistically learn the boundaries of and connections between brain regions by weighing both the data and prior neuroanatomical knowledge. Although EANAT incorporates some neuroanatomical prior knowledge in the form of connectedness and smoothness constraints, it can still be difficult for clinicians to interpret the results in specific domains where network-specific hypotheses exist. We thus extend EANAT and present a novel framework for prior-constrained sparse decomposition of matrices derived from brain imaging data, called Prior Based Eigenanatomy (p-Eigen). We formulate our solution in terms of a prior-constrained l1 penalized (sparse) principal component analysis. Experimental evaluation confirms that p-Eigen extracts biologically-relevant, patient-specific functional parcels and that it significantly aids classification of Mild Cognitive Impairment when compared to state-of-the-art competing approaches

Recent publications from the Alzheimer's Disease Neuroimaging Initiative: Reviewing progress toward improved AD clinical trials

INTRODUCTION: The Alzheimer's Disease Neuroimaging Initiative (ADNI) has continued development and standardization of methodologies for biomarkers and has provided an increased depth and breadth of data available to qualified researchers. This review summarizes the over 400 publications using ADNI data during 2014 and 2015. METHODS: We used standard searches to find publications using ADNI data. RESULTS: (1) Structural and functional changes, including subtle changes to hippocampal shape and texture, atrophy in areas outside of hippocampus, and disruption to functional networks, are detectable in presymptomatic subjects before hippocampal atrophy; (2) In subjects with abnormal β-amyloid deposition (Aβ+), biomarkers become abnormal in the order predicted by the amyloid cascade hypothesis; (3) Cognitive decline is more closely linked to tau than Aβ deposition; (4) Cerebrovascular risk factors may interact with Aβ to increase white-matter (WM) abnormalities which may accelerate Alzheimer's disease (AD) progression in conjunction with tau abnormalities; (5) Different patterns of atrophy are associated with impairment of memory and executive function and may underlie psychiatric symptoms; (6) Structural, functional, and metabolic network connectivities are disrupted as AD progresses. Models of prion-like spreading of Aβ pathology along WM tracts predict known patterns of cortical Aβ deposition and declines in glucose metabolism; (7) New AD risk and protective gene loci have been identified using biologically informed approaches; (8) Cognitively normal and mild cognitive impairment (MCI) subjects are heterogeneous and include groups typified not only by "classic" AD pathology but also by normal biomarkers, accelerated decline, and suspected non-Alzheimer's pathology; (9) Selection of subjects at risk of imminent decline on the basis of one or more pathologies improves the power of clinical trials; (10) Sensitivity of cognitive outcome measures to early changes in cognition has been improved and surrogate outcome measures using longitudinal structural magnetic resonance imaging may further reduce clinical trial cost and duration; (11) Advances in machine learning techniques such as neural networks have improved diagnostic and prognostic accuracy especially in challenges involving MCI subjects; and (12) Network connectivity measures and genetic variants show promise in multimodal classification and some classifiers using single modalities are rivaling multimodal classifiers. DISCUSSION: Taken together, these studies fundamentally deepen our understanding of AD progression and its underlying genetic basis, which in turn informs and improves clinical trial desig

Non-linear Recovery of Sparse Signal Representations with Applications to Temporal and Spatial Localization

Foundations of signal processing are heavily based on Shannon's sampling theorem for acquisition, representation and reconstruction. This theorem states that signals should not contain frequency components higher than the Nyquist rate, which is half of the sampling rate. Then, the signal can be perfectly reconstructed from its samples. Increasing evidence shows that the requirements imposed by Shannon's sampling theorem are too conservative for many naturally-occurring signals, which can be accurately characterized by sparse representations that require lower sampling rates closer to the signal's intrinsic information rates. Finite rate of innovation (FRI) is a new theory that allows to extract underlying sparse signal representations while operating at a reduced sampling rate. The goal of this PhD work is to advance reconstruction techniques for sparse signal representations from both theoretical and practical points of view. Specifically, the FRI framework is extended to deal with applications that involve temporal and spatial localization of events, including inverse source problems from radiating fields. We propose a novel reconstruction method using a model-fitting approach that is based on minimizing the fitting error subject to an underlying annihilation system given by the Prony's method. First, we showed that this is related to the problem known as structured low-rank matrix approximation as in structured total least squares problem. Then, we proposed to solve our problem under three different constraints using the iterative quadratic maximum likelihood algorithm. Our analysis and simulation results indicate that the proposed algorithms improve the robustness of the results with respect to common FRI reconstruction schemes. We have further developed the model-fitting approach to analyze spontaneous brain activity as measured by functional magnetic resonance imaging (fMRI). For this, we considered the noisy fMRI time course for every voxel as a convolution between an underlying activity inducing signal (i.e., a stream of Diracs) and the hemodynamic response function (HRF). We then validated this method using experimental fMRI data acquired during an event-related study. The results showed for the first time evidence for the practical usage of FRI for fMRI data analysis. We also addressed the problem of retrieving a sparse source distribution from the boundary measurements of a radiating field. First, based on Green's theorem, we proposed a sensing principle that allows to relate the boundary measurements to the source distribution. We focused on characterizing these sensing functions with particular attention for those that can be derived from holomorphic functions as they allow to control spatial decay of the sensing functions. With this selection, we developed an FRI-inspired non-iterative reconstruction algorithm. Finally, we developed an extension to the sensing principle (termed eigensensing) where we choose the spatial eigenfunctions of the Laplace operator as the sensing functions. With this extension, we showed that eigensensing principle allows to extract partial Fourier measurements of the source functions from boundary measurements. We considered photoacoustic tomography as a potential application of these theoretical developments

Automatic Detection of Brain Functional Disorder Using Imaging Data

Recently, Attention Deficit Hyperactive Disorder (ADHD) is getting a lot of attention mainly for two reasons. First, it is one of the most commonly found childhood behavioral disorders. Around 5-10% of the children all over the world are diagnosed with ADHD. Second, the root cause of the problem is still unknown and therefore no biological measure exists to diagnose ADHD. Instead, doctors need to diagnose it based on the clinical symptoms, such as inattention, impulsivity and hyperactivity, which are all subjective. Functional Magnetic Resonance Imaging (fMRI) data has become a popular tool to understand the functioning of the brain such as identifying the brain regions responsible for different cognitive tasks or analyzing the statistical differences of the brain functioning between the diseased and control subjects. ADHD is also being studied using the fMRI data. In this dissertation we aim to solve the problem of automatic diagnosis of the ADHD subjects using their resting state fMRI (rs-fMRI) data. As a core step of our approach, we model the functions of a brain as a connectivity network, which is expected to capture the information about how synchronous different brain regions are in terms of their functional activities. The network is constructed by representing different brain regions as the nodes where any two nodes of the network are connected by an edge if the correlation of the activity patterns of the two nodes is higher than some threshold. The brain regions, represented as the nodes of the network, can be selected at different granularities e.g. single voxels or cluster of functionally homogeneous voxels. The topological differences of the constructed networks of the ADHD and control group of subjects are then exploited in the classification approach. We have developed a simple method employing the Bag-of-Words (BoW) framework for the classification of the ADHD subjects. We represent each node in the network by a 4-D feature vector: node degree and 3-D location. The 4-D vectors of all the network nodes of the training data are then grouped in a number of clusters using K-means; where each such cluster is termed as a word. Finally, each subject is represented by a histogram (bag) of such words. The Support Vector Machine (SVM) classifier is used for the detection of the ADHD subjects using their histogram representation. The method is able to achieve 64% classification accuracy. The above simple approach has several shortcomings. First, there is a loss of spatial information while constructing the histogram because it only counts the occurrences of words ignoring the spatial positions. Second, features from the whole brain are used for classification, but some of the brain regions may not contain any useful information and may only increase the feature dimensions and noise of the system. Third, in our study we used only one network feature, the degree of a node which measures the connectivity of the node, while other complex network features may be useful for solving the proposed problem. In order to address the above shortcomings, we hypothesize that only a subset of the nodes of the network possesses important information for the classification of the ADHD subjects. To identify the important nodes of the network we have developed a novel algorithm. The algorithm generates different random subset of nodes each time extracting the features from a subset to compute the feature vector and perform classification. The subsets are then ranked based on the classification accuracy and the occurrences of each node in the top ranked subsets are measured. Our algorithm selects the highly occurring nodes for the final classification. Furthermore, along with the node degree, we employ three more node features: network cycles, the varying distance degree and the edge weight sum. We concatenate the features of the selected nodes in a fixed order to preserve the relative spatial information. Experimental validation suggests that the use of the features from the nodes selected using our algorithm indeed help to improve the classification accuracy. Also, our finding is in concordance with the existing literature as the brain regions identified by our algorithms are independently found by many other studies on the ADHD. We achieved a classification accuracy of 69.59% using this approach. However, since this method represents each voxel as a node of the network which makes the number of nodes of the network several thousands. As a result, the network construction step becomes computationally very expensive. Another limitation of the approach is that the network features, which are computed for each node of the network, captures only the local structures while ignore the global structure of the network. Next, in order to capture the global structure of the networks, we use the Multi-Dimensional Scaling (MDS) technique to project all the subjects from an unknown network-space to a low dimensional space based on their inter-network distance measures. For the purpose of computing distance between two networks, we represent each node by a set of attributes such as the node degree, the average power, the physical location, the neighbor node degrees, and the average powers of the neighbor nodes. The nodes of the two networks are then mapped in such a way that for all pair of nodes, the sum of the attribute distances, which is the inter-network distance, is minimized. To reduce the network computation cost, we enforce that the maximum relevant information is preserved with minimum redundancy. To achieve this, the nodes of the network are constructed with clusters of highly active voxels while the activity levels of the voxels are measured based on the average power of their corresponding fMRI time-series. Our method shows promise as we achieve impressive classification accuracies (73.55%) on the ADHD-200 data set. Our results also reveal that the detection rates are higher when classification is performed separately on the male and female groups of subjects. So far, we have only used the fMRI data for solving the ADHD diagnosis problem. Finally, we investigated the answers of the following questions. Do the structural brain images contain useful information related to the ADHD diagnosis problem? Can the classification accuracy of the automatic diagnosis system be improved combining the information of the structural and functional brain data? Towards that end, we developed a new method to combine the information of structural and functional brain images in a late fusion framework. For structural data we input the gray matter (GM) brain images to a Convolutional Neural Network (CNN). The output of the CNN is a feature vector per subject which is used to train the SVM classifier. For the functional data we compute the average power of each voxel based on its fMRI time series. The average power of the fMRI time series of a voxel measures the activity level of the voxel. We found significant differences in the voxel power distribution patterns of the ADHD and control groups of subjects. The Local binary pattern (LBP) texture feature is used on the voxel power map to capture these differences. We achieved 74.23% accuracy using GM features, 77.30% using LBP features and 79.14% using combined information. In summary this dissertation demonstrated that the structural and functional brain imaging data are useful for the automatic detection of the ADHD subjects as we achieve impressive classification accuracies on the ADHD-200 data set. Our study also helps to identify the brain regions which are useful for ADHD subject classification. These findings can help in understanding the pathophysiology of the problem. Finally, we expect that our approaches will contribute towards the development of a biological measure for the diagnosis of the ADHD subjects

Assessment of a multi-measure functional connectivity approach

Efforts to find differences in brain activity patterns of subjects with neurological and psychiatric disorders that could help in their diagnosis and prognosis have been increasing in recent years and promise to revolutionise clinical practice and our understanding of such illnesses in the future. Resting-state functional magnetic resonance imaging (rsfMRI) data has been increasingly used to evaluate said activity and to characterize the connectivity between distinct brain regions, commonly organized in functional connectivity (FC) matrices. Here, machine learning methods were used to assess the extent to which multiple FC matrices, each determined with a different statistical method, could change classification performance relative to when only one matrix is used, as is common practice. Used statistical methods include correlation, coherence, mutual information, transfer entropy and non-linear correlation, as implemented in the MULAN toolbox. Classification was made using random forests and support vector machine (SVM) classifiers. Besides the previously mentioned objective, this study had three other goals: to individually investigate which of these statistical methods yielded better classification performances, to confirm the importance of the blood-oxygen-level-dependent (BOLD) signal in the frequency range 0.009-0.08 Hz for FC based classifications as well as to assess the impact of feature selection in SVM classifiers. Publicly available rs-fMRI data from the Addiction Connectome Preprocessed Initiative (ACPI) and the ADHD-200 databases was used to perform classification of controls vs subjects with Attention-Deficit/Hyperactivity Disorder (ADHD). Maximum accuracy and macro-averaged f-measure values of 0.744 and 0.677 were respectively achieved in the ACPI dataset and of 0.678 and 0.648 in the ADHD-200 dataset. Results show that combining matrices could significantly improve classification accuracy and macro-averaged f-measure if feature selection is made. Also, the results of this study suggest that mutual information methods might play an important role in FC based classifications, at least when classifying subjects with ADHD

Brain Computations and Connectivity [2nd edition]

This is an open access title available under the terms of a CC BY-NC-ND 4.0 International licence. It is free to read on the Oxford Academic platform and offered as a free PDF download from OUP and selected open access locations. Brain Computations and Connectivity is about how the brain works. In order to understand this, it is essential to know what is computed by different brain systems; and how the computations are performed. The aim of this book is to elucidate what is computed in different brain systems; and to describe current biologically plausible computational approaches and models of how each of these brain systems computes. Understanding the brain in this way has enormous potential for understanding ourselves better in health and in disease. Potential applications of this understanding are to the treatment of the brain in disease; and to artificial intelligence which will benefit from knowledge of how the brain performs many of its extraordinarily impressive functions. This book is pioneering in taking this approach to brain function: to consider what is computed by many of our brain systems; and how it is computed, and updates by much new evidence including the connectivity of the human brain the earlier book: Rolls (2021) Brain Computations: What and How, Oxford University Press. Brain Computations and Connectivity will be of interest to all scientists interested in brain function and how the brain works, whether they are from neuroscience, or from medical sciences including neurology and psychiatry, or from the area of computational science including machine learning and artificial intelligence, or from areas such as theoretical physics

Geometric Data Analysis: Advancements of the Statistical Methodology and Applications

Data analysis has become fundamental to our society and comes in multiple facets and approaches. Nevertheless, in research and applications, the focus was primarily on data from Euclidean vector spaces. Consequently, the majority of methods that are applied today are not suited for more general data types. Driven by needs from fields like image processing, (medical) shape analysis, and network analysis, more and more attention has recently been given to data from non-Euclidean spaces–particularly (curved) manifolds. It has led to the field of geometric data analysis whose methods explicitly take the structure (for example, the topology and geometry) of the underlying space into account. This thesis contributes to the methodology of geometric data analysis by generalizing several fundamental notions from multivariate statistics to manifolds. We thereby focus on two different viewpoints. First, we use Riemannian structures to derive a novel regression scheme for general manifolds that relies on splines of generalized Bézier curves. It can accurately model non-geodesic relationships, for example, time-dependent trends with saturation effects or cyclic trends. Since Bézier curves can be evaluated with the constructive de Casteljau algorithm, working with data from manifolds of high dimensions (for example, a hundred thousand or more) is feasible. Relying on the regression, we further develop a hierarchical statistical model for an adequate analysis of longitudinal data in manifolds, and a method to control for confounding variables. We secondly focus on data that is not only manifold- but even Lie group-valued, which is frequently the case in applications. We can only achieve this by endowing the group with an affine connection structure that is generally not Riemannian. Utilizing it, we derive generalizations of several well-known dissimilarity measures between data distributions that can be used for various tasks, including hypothesis testing. Invariance under data translations is proven, and a connection to continuous distributions is given for one measure. A further central contribution of this thesis is that it shows use cases for all notions in real-world applications, particularly in problems from shape analysis in medical imaging and archaeology. We can replicate or further quantify several known findings for shape changes of the femur and the right hippocampus under osteoarthritis and Alzheimer's, respectively. Furthermore, in an archaeological application, we obtain new insights into the construction principles of ancient sundials. Last but not least, we use the geometric structure underlying human brain connectomes to predict cognitive scores. Utilizing a sample selection procedure, we obtain state-of-the-art results

Gaze-Based Human-Robot Interaction by the Brunswick Model

We present a new paradigm for human-robot interaction based on social signal processing, and in particular on the Brunswick model. Originally, the Brunswick model copes with face-to-face dyadic interaction, assuming that the interactants are communicating through a continuous exchange of non verbal social signals, in addition to the spoken messages. Social signals have to be interpreted, thanks to a proper recognition phase that considers visual and audio information. The Brunswick model allows to quantitatively evaluate the quality of the interaction using statistical tools which measure how effective is the recognition phase. In this paper we cast this theory when one of the interactants is a robot; in this case, the recognition phase performed by the robot and the human have to be revised w.r.t. the original model. The model is applied to Berrick, a recent open-source low-cost robotic head platform, where the gazing is the social signal to be considered