An Overdispersed Black-Box Variational Bayesian–Kalman Filter with Inaccurate Noise Second-Order Statistics

Aimed at the problems in which the performance of filters derived from a hypothetical model will decline or the cost of time of the filters derived from a posterior model will increase when prior knowledge and second-order statistics of noise are uncertain, a new filter is proposed. In this paper, a Bayesian robust Kalman filter based on posterior noise statistics (KFPNS) is derived, and the recursive equations of this filter are very similar to that of the classical algorithm. Note that the posterior noise distributions are approximated by overdispersed black-box variational inference (O-BBVI). More precisely, we introduce an overdispersed distribution to push more probability density to the tails of variational distribution and incorporated the idea of importance sampling into two strategies of control variates and Rao–Blackwellization in order to reduce the variance of estimators. As a result, the convergence process will speed up. From the simulations, we can observe that the proposed filter has good performance for the model with uncertain noise. Moreover, we verify the proposed algorithm by using a practical multiple-input multiple-output (MIMO) radar system.

Minimum Distribution Support Vector Clustering

Support vector clustering (SVC) is a boundary-based algorithm, which has several advantages over other clustering methods, including identifying clusters of arbitrary shapes and numbers. Leveraged by the high generalization ability of the large margin distribution machine (LDM) and the optimal margin distribution clustering (ODMC), we propose a new clustering method: minimum distribution for support vector clustering (MDSVC), for improving the robustness of boundary point recognition, which characterizes the optimal hypersphere by the first-order and second-order statistics and tries to minimize the mean and variance simultaneously. In addition, we further prove, theoretically, that our algorithm can obtain better generalization performance. Some instructive insights for adjusting the number of support vector points are gained. For the optimization problem of MDSVC, we propose a double coordinate descent algorithm for small and medium samples. The experimental results on both artificial and real datasets indicate that our MDSVC has a significant improvement in generalization performance compared to SVC.

Functional brain–heart interplay extends to the multifractal domain

The study of functional brain–heart interplay has provided meaningful insights in cardiology and neuroscience. Regarding biosignal processing, this interplay involves predominantly neural and heartbeat linear dynamics expressed via time and frequency domain-related features. However, the dynamics of central and autonomous nervous systems show nonlinear and multifractal behaviours, and the extent to which this behaviour influences brain–heart interactions is currently unknown. Here, we report a novel signal processing framework aimed at quantifying nonlinear functional brain–heart interplay in the non-Gaussian and multifractal domains that combines electroencephalography (EEG) and heart rate variability series. This framework relies on a maximal information coefficient analysis between nonlinear multiscale features derived from EEG spectra and from an inhomogeneous point-process model for heartbeat dynamics. Experimental results were gathered from 24 healthy volunteers during a resting state and a cold pressor test, revealing that synchronous changes between brain and heartbeat multifractal spectra occur at higher EEG frequency bands and through nonlinear/complex cardiovascular control. We conclude that significant bodily, sympathovagal changes such as those elicited by cold-pressure stimuli affect the functional brain–heart interplay beyond second-order statistics, thus extending it to multifractal dynamics. These results provide a platform to define novel nervous-system-targeted biomarkers. This article is part of the theme issue ‘Advanced computation in cardiovascular physiology: new challenges and opportunities’.

Fundamentals of Narrowband Array Signal Processing

Array signal processing is an actively developing research area connected to the progress in optimization theory, and remains the key technological development that attracts prevalent attention in signal processing. This chapter provides an overview of the fundamental concepts and essential terminologies employed in narrowband array signal processing. We first develop a general signal model for narrowband adaptive arrays and discuss the beamforming operation. We next introduce the basic performance parameters of adaptive arrays and the second order statistics of the array data. We then formulate various optimal weigh vector solution criteria. Finally, we discuss various types of adaptive filtering algorithms. Besides, this chapter emphasizes the theory of narrowband array signal processing employed in narrowband beamforming and direction-of-arrival (DOA) estimation algorithms.

Spatial Hurst–Kolmogorov Clustering

The stochastic analysis in the scale domain (instead of the traditional lag or frequency domains) is introduced as a robust means to identify, model and simulate the Hurst–Kolmogorov (HK) dynamics, ranging from small (fractal) to large scales exhibiting the clustering behavior (else known as the Hurst phenomenon or long-range dependence). The HK clustering is an attribute of a multidimensional (1D, 2D, etc.) spatio-temporal stationary stochastic process with an arbitrary marginal distribution function, and a fractal behavior on small spatio-temporal scales of the dependence structure and a power-type on large scales, yielding a high probability of low- or high-magnitude events to group together in space and time. This behavior is preferably analyzed through the second-order statistics, and in the scale domain, by the stochastic metric of the climacogram, i.e., the variance of the averaged spatio-temporal process vs. spatio-temporal scale.

Intelligent Fault Diagnosis Based on Dynamic Convolutional Depth Domain Adaptive Network

Deep learning-based mechanical fault diagnosis method has made great achievements. A high-performance neural network model requires sufficient labelled data for training to obtain accurate classification results. Desired results mainly depends on assumption that training and testing data are collected under the same working conditions, environment and operating conditions, where the data have the same probability distribution. However, in the practical scenarios, training data and the testing data follow different distributions to some degree, and the newly collected testing data are usually unlabeled. In order to solve the problems above, a model based on transfer learning and domain adaptation is proposed to achieve efficient fault diagnosis under different data distributions. The proposed framework adapts the features extracted by multiple dynamic convolutional layers, and creatively utilizes correlation alignment(CORAL) to perform a non-linear transformation to align the second-order statistics of the two distributions for fault diagnosis, which greatly improves the accuracy of fault classification in the target domain under unlabeled data. Finally, experimental verifications have been carried out among two different datasets.

Structured random receptive fields enable informative sensory encodings

The brain must represent the outside world in a way that enables an animal to survive and thrive. In early sensory systems, populations of neurons have a variety of receptive fields that are structured to detect features in input statistics. Alongside this structure, experimental recordings consistently show that these receptive fields also have a great deal of unexplained variability, which has often been ignored in classical models of sensory neurons. In this work, we model neuronal receptive fields as random samples from probability distributions in two sensory modalities, using data from insect mechanosensors and from neurons of mammalian primary visual cortex (V1). In particular, we build generative receptive field models where our random distributions are Gaussian processes with covariance functions that match the second-order statistics of experimental receptive data. We show theoretical results that these random feature neurons effectively perform randomized wavelet transform on the inputs in the temporal domain for mechanosensory neurons and spatial domain for V1 neurons. Such a transformation removes irrelevant components in the inputs, such as high-frequency noise, and boosts the signal. We demonstrate that these random feature neurons produce better learning from fewer training samples and with smaller networks in a variety of artificial tasks. The random feature model of receptive fields provides a unifying, mathematically tractable framework to understand sensory encodings across both spatial and temporal domains.

Brain Function Network: Higher Order vs. More Discrimination

Brain functional network (BFN) has become an increasingly important tool to explore individual differences and identify neurological/mental diseases. For estimating a “good” BFN (with more discriminative information for example), researchers have developed various methods, in which the most popular and simplest is Pearson's correlation (PC). Despite its empirical effectiveness, PC only encodes the low-order (second-order) statistics between brain regions. To model high-order statistics, researchers recently proposed to estimate BFN by conducting two sequential PCs (denoted as PC2 in this paper), and found that PC2-based BFN can provide additional information for group difference analysis. This inspires us to think about (1) what will happen if continuing the correlation operation to construct much higher-order BFN by PCn (n>2), and (2) whether the higher-order correlation will result in stronger discriminative ability. To answer these questions, we use PCn-based BFNs to predict individual differences (Female vs. Male) as well as identify subjects with mild cognitive impairment (MCI) from healthy controls (HCs). Through experiments, we have the following findings: (1) with the increase of n, the discriminative ability of PCn-based BFNs tends to decrease; (2) fusing the PCn-based BFNs (n>1) with the PC1-based BFN can generally improve the sensitivity for MCI identification, but fail to help the classification accuracy. In addition, we empirically find that the sequence of BFN adjacency matrices estimated by PCn (n = 1,2,3,⋯ ) will converge to a binary matrix with elements of ± 1.