Nonnegative matrix factorization (NMF) is a powerful tool for parameter estimation applied in numerous robotics applications, such as path planning, motion trajectory prediction, and motion intention detection. In particular, NMF has been successfully used to extract simplified and organized movement primitives from myoelectric signal (MES) for robust control of multi-degree of freedom humanoid robots. However, MES is typically contaminated by complex noise sources. The system performance often degrades due to the simplified Gaussian assumption of the noise distribution in existing NMF methods. Furthermore, most existing NMF models are unable to automatically determine the rank of the latent matrices. To address these issues, this article presents a hybrid variational Bayesian Gaussian mixture and NMF (GMNMF) model with a finite Gaussian mixture model adopted to fit the mixed noise density function of MES. In addition, the automatic relevant determination criterion is applied to automatically infer the number of movement primitives. The coordinate descent update rules for the proposed model are formulated by mean-field variational Bayesian inference. We assess the model performance on five synthetic noise distribution functions and an experimental MES dataset to perform six wrist movements. The results demonstrate that GMNMF yields low error and high robustness in extracting the movement primitives over four competitive methods for robust cybernetic control.

Extracting low-rank and/or sparse structures using matrix factorization techniques has been extensively studied in the machine learning community. Kernelized matrix factorization (KMF) is a powerful tool to incorporate side information into the low-rank approximation model, which has been applied to solve the problems of data mining, recommender systems, image restoration, and machine vision. However, most existing KMF models rely on specifying the rows and columns of the data matrix through a Gaussian process prior and have to tune manually the rank. There are also computational issues of existing models based on regularization or the Markov chain Monte Carlo. In this article, we develop a hierarchical kernelized sparse Bayesian matrix factorization (KSBMF) model to integrate side information. The KSBMF automatically infers the parameters and latent variables including the reduced rank using the variational Bayesian inference. In addition, the model simultaneously achieves low-rankness through sparse Bayesian learning and columnwise sparsity through an enforced constraint on latent factor matrices. We further connect the KSBMF with the nonlocal image processing framework to develop two algorithms for image denoising and inpainting. Experimental results demonstrate that KSBMF outperforms the state-of-the-art approaches for these image-restoration tasks under various levels of corruption.

Singular value thresholding (SVT)- or nuclear norm minimization (NNM)-based nonlocal image denoising methods often rely on the precise estimation of the noise variance. However, most existing methods either assume that the noise variance is known or require an extra step to estimate it. Under the iterative regularization framework, the error in the noise variance estimate propagates and accumulates with each iteration, ultimately degrading the overall denoising performance. In addition, the essence of these methods is still least squares estimation, which can cause a very high mean-squared error (MSE) and is inadequate for handling missing data or outliers. In order to address these deficiencies, we present a hybrid denoising model based on variational Bayesian inference and Stein's unbiased risk estimator (SURE), which consists of two complementary steps. In the first step, the variational Bayesian SVT performs a low-rank approximation of the nonlocal image patch matrix to simultaneously remove the noise and estimate the noise variance. In the second step, we modify the conventional SURE full-rank SVT and its divergence formulas for rank-reduced eigen-triplets to remove the residual artifacts. The proposed hybrid BSSVT method achieves better performance in recovering the true image compared with state-of-the-art methods.

Fuzzy entropy (FuzzyEn), which employs the fuzzy probability to characterize the similarity between vectors, is a robust nonlinear statistic to quantify the complexity or regularity of nonlinear time series. The aim of this study is to investigate the statistical properties of FuzzyEn and improve the subspace denoising technique using FuzzyEn. We first show the asymptotic normality of FuzzyEn and derive its variance for finite sample behavior. We then analyze the two pending and fundamental issues in subspace denoising, i.e., depending on the so-called “noise floor” and the unaltered noise existing in signal subspace, from the point of view of fuzzy logic. A FuzzyEn-assisted subspace iterative soft threshold (FESIST) denoising method, which can effectively overcome the deficiency in the existing subspace filtering (SSF) techniques, is presented. The effectiveness of the method is first demonstrated on two synthetic chaotic series and then tested on real biological signals. The results demonstrate the superiority of the proposed method over existing SSF techniques, as well as the empirical mode decomposition and wavelet decomposition approaches.