Neural networks in geophysical applications

Neural networks are increasingly popular in geophysics. Because they are universal approximators, these tools can approximate any continuous function with an arbitrary precision. Hence, they may yield important contributions to finding solutions to a variety of geophysical applications. However, knowledge of many methods and techniques recently developed to increase the performance and to facilitate the use of neural networks does not seem to be widespread in the geophysical community. Therefore, the power of these tools has not yet been explored to their full extent. In this paper, techniques are described for faster training, better overall performance, i.e., generalization,and the automatic estimation of network size and architecture

Metaheuristic design of feedforward neural networks: a review of two decades of research

Over the past two decades, the feedforward neural network (FNN) optimization has been a key interest among the researchers and practitioners of multiple disciplines. The FNN optimization is often viewed from the various perspectives: the optimization of weights, network architecture, activation nodes, learning parameters, learning environment, etc. Researchers adopted such different viewpoints mainly to improve the FNN's generalization ability. The gradient-descent algorithm such as backpropagation has been widely applied to optimize the FNNs. Its success is evident from the FNN's application to numerous real-world problems. However, due to the limitations of the gradient-based optimization methods, the metaheuristic algorithms including the evolutionary algorithms, swarm intelligence, etc., are still being widely explored by the researchers aiming to obtain generalized FNN for a given problem. This article attempts to summarize a broad spectrum of FNN optimization methodologies including conventional and metaheuristic approaches. This article also tries to connect various research directions emerged out of the FNN optimization practices, such as evolving neural network (NN), cooperative coevolution NN, complex-valued NN, deep learning, extreme learning machine, quantum NN, etc. Additionally, it provides interesting research challenges for future research to cope-up with the present information processing era

Deep attractor network for single-microphone speaker separation

Despite the overwhelming success of deep learning in various speech processing tasks, the problem of separating simultaneous speakers in a mixture remains challenging. Two major difficulties in such systems are the arbitrary source permutation and unknown number of sources in the mixture. We propose a novel deep learning framework for single channel speech separation by creating attractor points in high dimensional embedding space of the acoustic signals which pull together the time-frequency bins corresponding to each source. Attractor points in this study are created by finding the centroids of the sources in the embedding space, which are subsequently used to determine the similarity of each bin in the mixture to each source. The network is then trained to minimize the reconstruction error of each source by optimizing the embeddings. The proposed model is different from prior works in that it implements an end-to-end training, and it does not depend on the number of sources in the mixture. Two strategies are explored in the test time, K-means and fixed attractor points, where the latter requires no post-processing and can be implemented in real-time. We evaluated our system on Wall Street Journal dataset and show 5.49\% improvement over the previous state-of-the-art methods.Comment: 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP

Region-Referenced Spectral Power Dynamics of EEG Signals: A Hierarchical Modeling Approach

Functional brain imaging through electroencephalography (EEG) relies upon the analysis and interpretation of high-dimensional, spatially organized time series. We propose to represent time-localized frequency domain characterizations of EEG data as region-referenced functional data. This representation is coupled with a hierarchical modeling approach to multivariate functional observations. Within this familiar setting, we discuss how several prior models relate to structural assumptions about multivariate covariance operators. An overarching modeling framework, based on infinite factorial decompositions, is finally proposed to balance flexibility and efficiency in estimation. The motivating application stems from a study of implicit auditory learning, in which typically developing (TD) children, and children with autism spectrum disorder (ASD) were exposed to a continuous speech stream. Using the proposed model, we examine differential band power dynamics as brain function is interrogated throughout the duration of a computer-controlled experiment. Our work offers a novel look at previous findings in psychiatry, and provides further insights into the understanding of ASD. Our approach to inference is fully Bayesian and implemented in a highly optimized Rcpp package

Wavelet Neural Networks: A Practical Guide

Wavelet networks (WNs) are a new class of networks which have been used with great success in a wide range of application. However a general accepted framework for applying WNs is missing from the literature. In this study, we present a complete statistical model identification framework in order to apply WNs in various applications. The following subjects were thorough examined: the structure of a WN, training methods, initialization algorithms, variable significance and variable selection algorithms, model selection methods and finally methods to construct confidence and prediction intervals. In addition the complexity of each algorithm is discussed. Our proposed framework was tested in two simulated cases, in one chaotic time series described by the Mackey-Glass equation and in three real datasets described by daily temperatures in Berlin, daily wind speeds in New York and breast cancer classification. Our results have shown that the proposed algorithms produce stable and robust results indicating that our proposed framework can be applied in various applications

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

The Incomplete Rosetta Stone Problem: Identifiability Results for Multi-View Nonlinear ICA

We consider the problem of recovering a common latent source with independent components from multiple views. This applies to settings in which a variable is measured with multiple experimental modalities, and where the goal is to synthesize the disparate measurements into a single unified representation. We consider the case that the observed views are a nonlinear mixing of component-wise corruptions of the sources. When the views are considered separately, this reduces to nonlinear Independent Component Analysis (ICA) for which it is provably impossible to undo the mixing. We present novel identifiability proofs that this is possible when the multiple views are considered jointly, showing that the mixing can theoretically be undone using function approximators such as deep neural networks. In contrast to known identifiability results for nonlinear ICA, we prove that independent latent sources with arbitrary mixing can be recovered as long as multiple, sufficiently different noisy views are available