Quantifying the Statistical Impact of GRAPPA in fcMRI Data with a Real-Valued Isomorphism

The interpolation of missing spatial frequencies through the generalized auto-calibrating partially parallel acquisitions (GRAPPA) parallel magnetic resonance imaging (MRI) model implies a correlation is induced between the acquired and reconstructed frequency measurements. As the parallel image reconstruction algorithms in many medical MRI scanners are based on the GRAPPA model, this study aims to quantify the statistical implications that the GRAPPA model has in functional connectivity studies. The linear mathematical framework derived in the work of Rowe , 2007, is adapted to represent the complex-valued GRAPPA image reconstruction operation in terms of a real-valued isomorphism, and a statistical analysis is performed on the effects that the GRAPPA operation has on reconstructed voxel means and correlations. The interpolation of missing spatial frequencies with the GRAPPA model is shown to result in an artificial correlation induced between voxels in the reconstructed images, and these artificial correlations are shown to reside in the low temporal frequency spectrum commonly associated with functional connectivity. Through a real-valued isomorphism, such as the one outlined in this manuscript, the exact artificial correlations induced by the GRAPPA model are not simply estimated, as they would be with simulations, but are precisely quantified. If these correlations are unaccounted for, they can incur an increase in false positives in functional connectivity studies

A Winner-Take-All Approach to Emotional Neural Networks with Universal Approximation Property

Here, we propose a brain-inspired winner-take-all emotional neural network (WTAENN) and prove the universal approximation property for the novel architecture. WTAENN is a single layered feedforward neural network that benefits from the excitatory, inhibitory, and expandatory neural connections as well as the winner-take-all (WTA) competitions in the human brain s nervous system. The WTA competition increases the information capacity of the model without adding hidden neurons. The universal approximation capability of the proposed architecture is illustrated on two example functions, trained by a genetic algorithm, and then applied to several competing recent and benchmark problems such as in curve fitting, pattern recognition, classification and prediction. In particular, it is tested on twelve UCI classification datasets, a facial recognition problem, three real world prediction problems (2 chaotic time series of geomagnetic activity indices and wind farm power generation data), two synthetic case studies with constant and nonconstant noise variance as well as k-selector and linear programming problems. Results indicate the general applicability and often superiority of the approach in terms of higher accuracy and lower model complexity, especially where low computational complexity is imperative.Comment: Information Sciences (2015), Elsevier Publishe

Harnessing machine learning for fiber-induced nonlinearity mitigation in long-haul coherent optical OFDM

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).Coherent optical orthogonal frequency division multiplexing (CO-OFDM) has attracted a lot of interest in optical fiber communications due to its simplified digital signal processing (DSP) units, high spectral-efficiency, flexibility, and tolerance to linear impairments. However, CO-OFDM’s high peak-to-average power ratio imposes high vulnerability to fiber-induced non-linearities. DSP-based machine learning has been considered as a promising approach for fiber non-linearity compensation without sacrificing computational complexity. In this paper, we review the existing machine learning approaches for CO-OFDM in a common framework and review the progress in this area with a focus on practical aspects and comparison with benchmark DSP solutions.Peer reviewe

Predicting and Explaining Behavioral Data with Structured Feature Space Decomposition

Modeling human behavioral data is challenging due to its scale, sparseness (few observations per individual), heterogeneity (differently behaving individuals), and class imbalance (few observations of the outcome of interest). An additional challenge is learning an interpretable model that not only accurately predicts outcomes, but also identifies important factors associated with a given behavior. To address these challenges, we describe a statistical approach to modeling behavioral data called the structured sum-of-squares decomposition (S3D). The algorithm, which is inspired by decision trees, selects important features that collectively explain the variation of the outcome, quantifies correlations between the features, and partitions the subspace of important features into smaller, more homogeneous blocks that correspond to similarly-behaving subgroups within the population. This partitioned subspace allows us to predict and analyze the behavior of the outcome variable both statistically and visually, giving a medium to examine the effect of various features and to create explainable predictions. We apply S3D to learn models of online activity from large-scale data collected from diverse sites, such as Stack Exchange, Khan Academy, Twitter, Duolingo, and Digg. We show that S3D creates parsimonious models that can predict outcomes in the held-out data at levels comparable to state-of-the-art approaches, but in addition, produces interpretable models that provide insights into behaviors. This is important for informing strategies aimed at changing behavior, designing social systems, but also for explaining predictions, a critical step towards minimizing algorithmic bias.Comment: Code and replication data available at https://github.com/peterfennell/S3

A Data Analytics Perspective of the Clarke and Related Transforms in Power Grid Analysis

Affordable and reliable electric power is fundamental to modern society and economy, with the Smart Grid becoming an increasingly important factor in power generation and distribution. In order to fully exploit it advantages, the analysis of modern Smart Grid requires close collaboration and convergence between power engineers and signal processing and machine learning experts. Current analysis techniques are typically derived from a Circuit Theory perspective; such an approach is adequate for only fully balanced systems operating at nominal conditions and non-obvious for data scientists - this is prohibitive for the analysis of dynamically unbalanced smart grids, where Data Analytics is not only well suited but also necessary. A common language that bridges the gap between Circuit Theory and Data Analytics, and the respective community of experts, would be a natural step forward. To this end, we revisit the Clarke and related transforms from a subspace, latent component, and spatial frequency analysis frameworks, to establish fundamental relationships between the standard three-phase transforms and modern Data Analytics. We show that the Clarke transform admits a physical interpretation as a "spatial dimensionality" reduction technique which is equivalent to Principal Component Analysis (PCA) for balanced systems, but is sub-optimal for dynamically unbalanced systems, such as the Smart Grid, while the related Park transform performs further "temporal" dimensionality reduction. Such a perspective opens numerous new avenues for the use Signal Processing and Machine Learning in power grid research, and paves the way for innovative optimisation, transformation, and analysis techniques that are not accessible to arrive at from the standard Circuit Theory principles, as demonstrated in this work through the possibility of simultaneous frequency estimation and fault detection.Comment: 20 pages, 11 figure

Tensor Analysis and Fusion of Multimodal Brain Images

Current high-throughput data acquisition technologies probe dynamical systems with different imaging modalities, generating massive data sets at different spatial and temporal resolutions posing challenging problems in multimodal data fusion. A case in point is the attempt to parse out the brain structures and networks that underpin human cognitive processes by analysis of different neuroimaging modalities (functional MRI, EEG, NIRS etc.). We emphasize that the multimodal, multi-scale nature of neuroimaging data is well reflected by a multi-way (tensor) structure where the underlying processes can be summarized by a relatively small number of components or "atoms". We introduce Markov-Penrose diagrams - an integration of Bayesian DAG and tensor network notation in order to analyze these models. These diagrams not only clarify matrix and tensor EEG and fMRI time/frequency analysis and inverse problems, but also help understand multimodal fusion via Multiway Partial Least Squares and Coupled Matrix-Tensor Factorization. We show here, for the first time, that Granger causal analysis of brain networks is a tensor regression problem, thus allowing the atomic decomposition of brain networks. Analysis of EEG and fMRI recordings shows the potential of the methods and suggests their use in other scientific domains.Comment: 23 pages, 15 figures, submitted to Proceedings of the IEE

An Efficient Deep Learning Technique for the Navier-Stokes Equations: Application to Unsteady Wake Flow Dynamics

We present an efficient deep learning technique for the model reduction of the Navier-Stokes equations for unsteady flow problems. The proposed technique relies on the Convolutional Neural Network (CNN) and the stochastic gradient descent method. Of particular interest is to predict the unsteady fluid forces for different bluff body shapes at low Reynolds number. The discrete convolution process with a nonlinear rectification is employed to approximate the mapping between the bluff-body shape and the fluid forces. The deep neural network is fed by the Euclidean distance function as the input and the target data generated by the full-order Navier-Stokes computations for primitive bluff body shapes. The convolutional networks are iteratively trained using the stochastic gradient descent method with the momentum term to predict the fluid force coefficients of different geometries and the results are compared with the full-order computations. We attempt to provide a physical analogy of the stochastic gradient method with the momentum term with the simplified form of the incompressible Navier-Stokes momentum equation. We also construct a direct relationship between the CNN-based deep learning and the Mori-Zwanzig formalism for the model reduction of a fluid dynamical system. A systematic convergence and sensitivity study is performed to identify the effective dimensions of the deep-learned CNN process such as the convolution kernel size, the number of kernels and the convolution layers. Within the error threshold, the prediction based on our deep convolutional network has a speed-up nearly four orders of magnitude compared to the full-order results and consumes an insignificant fraction of computational resources. The proposed CNN-based approximation procedure has a profound impact on the parametric design of bluff bodies and the feedback control of separated flows.Comment: 49 pages, 12 figure

Linked Component Analysis from Matrices to High Order Tensors: Applications to Biomedical Data

With the increasing availability of various sensor technologies, we now have access to large amounts of multi-block (also called multi-set, multi-relational, or multi-view) data that need to be jointly analyzed to explore their latent connections. Various component analysis methods have played an increasingly important role for the analysis of such coupled data. In this paper, we first provide a brief review of existing matrix-based (two-way) component analysis methods for the joint analysis of such data with a focus on biomedical applications. Then, we discuss their important extensions and generalization to multi-block multiway (tensor) data. We show how constrained multi-block tensor decomposition methods are able to extract similar or statistically dependent common features that are shared by all blocks, by incorporating the multiway nature of data. Special emphasis is given to the flexible common and individual feature analysis of multi-block data with the aim to simultaneously extract common and individual latent components with desired properties and types of diversity. Illustrative examples are given to demonstrate their effectiveness for biomedical data analysis.Comment: 20 pages, 11 figures, Proceedings of the IEEE, 201

Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives

Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost functions, while providing an outline of their applications in machine learning and data analytics. A particular emphasis is on the tensor train (TT) and Hierarchical Tucker (HT) decompositions, and their physically meaningful interpretations which reflect the scalability of the tensor network approach. Through a graphical approach, we also elucidate how, by virtue of the underlying low-rank tensor approximations and sophisticated contractions of core tensors, tensor networks have the ability to perform distributed computations on otherwise prohibitively large volumes of data/parameters, thereby alleviating or even eliminating the curse of dimensionality. The usefulness of this concept is illustrated over a number of applied areas, including generalized regression and classification (support tensor machines, canonical correlation analysis, higher order partial least squares), generalized eigenvalue decomposition, Riemannian optimization, and in the optimization of deep neural networks. Part 1 and Part 2 of this work can be used either as stand-alone separate texts, or indeed as a conjoint comprehensive review of the exciting field of low-rank tensor networks and tensor decompositions.Comment: 232 page

A Spectral Series Approach to High-Dimensional Nonparametric Regression

A key question in modern statistics is how to make fast and reliable inferences for complex, high-dimensional data. While there has been much interest in sparse techniques, current methods do not generalize well to data with nonlinear structure. In this work, we present an orthogonal series estimator for predictors that are complex aggregate objects, such as natural images, galaxy spectra, trajectories, and movies. Our series approach ties together ideas from kernel machine learning, and Fourier methods. We expand the unknown regression on the data in terms of the eigenfunctions of a kernel-based operator, and we take advantage of orthogonality of the basis with respect to the underlying data distribution, P, to speed up computations and tuning of parameters. If the kernel is appropriately chosen, then the eigenfunctions adapt to the intrinsic geometry and dimension of the data. We provide theoretical guarantees for a radial kernel with varying bandwidth, and we relate smoothness of the regression function with respect to P to sparsity in the eigenbasis. Finally, using simulated and real-world data, we systematically compare the performance of the spectral series approach with classical kernel smoothing, k-nearest neighbors regression, kernel ridge regression, and state-of-the-art manifold and local regression methods