Generalized latent multi-view clustering with tensorized bipartite graph.

Tensor-based multi-view spectral clustering algorithms use tensors to model the structure of multi-dimensional data to take advantage of the complementary information and high-order correlations embedded in the graph, thus achieving impressive clustering performance. However, these algorithms use linear models to obtain consensus, which prevents the learned consensus from adequately representing the nonlinear structure of complex data. In order to address this issue, we propose a method called Generalized Latent Multi-View Clustering with Tensorized Bipartite Graph (GLMC-TBG). Specifically, in this paper we introduce neural networks to learn highly nonlinear mappings that encode nonlinear structures in graphs into latent representations. In addition, multiple views share the same latent consensus through nonlinear interactions. In this way, a more comprehensive common representation from multiple views can be achieved. An Augmented Lagrangian Multiplier with Alternating Direction Minimization (ALM-ADM) framework is designed to optimize the model. Experiments on seven real-world data sets verify that the proposed algorithm is superior to state-of-the-art algorithms.

Bayesian tensor network structure search and its application to tensor completion.

Tensor network (TN) has demonstrated remarkable efficacy in the compact representation of high-order data. In contrast to the TN methods with pre-determined structures, the recently introduced tensor network structure search (TNSS) methods automatically learn a compact TN structure from the data, gaining increasing attention. Nonetheless, TNSS requires time-consuming manual adjustments of the penalty parameters that control the model complexity to achieve better performance, especially in the presence of missing or noisy data. To provide an effective solution to this problem, in this paper, we propose a parameters tuning-free TNSS algorithm based on Bayesian modeling, aiming at conducting TNSS in a fully data-driven manner. Specifically, the uncertainty in the data corruption is well-incorporated in the prior setting of the probabilistic model. For TN structure determination, we reframe it as a rank learning problem of the fully-connected tensor network (FCTN), integrating the generalized inverse Gaussian (GIG) distribution for low-rank promotion. To eliminate the need for hyperparameter tuning, we adopt a fully Bayesian approach and propose an efficient Markov chain Monte Carlo (MCMC) algorithm for posterior distribution sampling. Compared with the previous TNSS method, experiment results demonstrate the proposed algorithm can effectively and efficiently find the latent TN structures of the data under various missing and noise conditions and achieves the best recovery results. Furthermore, our method exhibits superior performance in tensor completion with real-world data compared to other state-of-the-art tensor-decomposition-based completion methods.

Balanced Unfolding Induced Tensor Nuclear Norms for High-Order Tensor Completion.

The recently proposed tensor tubal rank has been witnessed to obtain extraordinary success in real-world tensor data completion. However, existing works usually fix the transform orientation along the third mode and may fail to turn multidimensional low-tubal-rank structure into account. To alleviate these bottlenecks, we introduce two unfolding induced tensor nuclear norms (TNNs) for the tensor completion (TC) problem, which naturally extends tensor tubal rank to high-order data. Specifically, we show how multidimensional low-tubal-rank structure can be captured by utilizing a novel balanced unfolding strategy, upon which two TNNs, namely, overlapped TNN (OTNN) and latent TNN (LTNN), are developed. We also show the immediate relationship between the tubal rank of unfolding tensor and the existing tensor network (TN) rank, e.g., CANDECOMP/PARAFAC (CP) rank, Tucker rank, and tensor ring (TR) rank, to demonstrate its efficiency and practicality. Two efficient TC models are then proposed with theoretical guarantees by analyzing a unified nonasymptotic upper bound. To solve optimization problems, we develop two alternating direction methods of multipliers (ADMM) based algorithms. The proposed models have been demonstrated to exhibit superior performance based on experimental findings involving synthetic and real-world tensors, including facial images, light field images, and video sequences.

Comprehensive Multiview Representation Learning via Deep Autoencoder-Like Nonnegative Matrix Factorization.

Learning a comprehensive representation from multiview data is crucial in many real-world applications. Multiview representation learning (MRL) based on nonnegative matrix factorization (NMF) has been widely adopted by projecting high-dimensional space into a lower order dimensional space with great interpretability. However, most prior NMF-based MRL techniques are shallow models that ignore hierarchical information. Although deep matrix factorization (DMF)-based methods have been proposed recently, most of them only focus on the consistency of multiple views and have cumbersome clustering steps. To address the above issues, in this article, we propose a novel model termed deep autoencoder-like NMF for MRL (DANMF-MRL), which obtains the representation matrix through the deep encoding stage and decodes it back to the original data. In this way, through a DANMF-based framework, we can simultaneously consider the multiview consistency and complementarity, allowing for a more comprehensive representation. We further propose a one-step DANMF-MRL, which learns the latent representation and final clustering labels matrix in a unified framework. In this approach, the two steps can negotiate with each other to fully exploit the latent clustering structure, avoid previous tedious clustering steps, and achieve optimal clustering performance. Furthermore, two efficient iterative optimization algorithms are developed to solve the proposed models both with theoretical convergence analysis. Extensive experiments on five benchmark datasets demonstrate the superiority of our approaches against other state-of-the-art MRL methods.

Classification of the Epileptic Seizure Onset Zone Based on Partial Annotation.

Epilepsy is a chronic disorder caused by excessive electrical discharges. Currently, clinical experts identify the seizure onset zone (SOZ) channel through visual judgment based on long-time intracranial electroencephalogram (iEEG), which is a very time-consuming, difficult and experience-based task. Therefore, there is a need for high-accuracy diagnostic aids to reduce the workload of clinical experts. In this article, we propose a method in which, the iEEG is split into the 20-s segment and for each patient, we ask clinical experts to label a part of the data, which is used to train a model and classify the remaining iEEG data. In recent years, machine learning methods have been successfully applied to solve some medical problems. Filtering, entropy and short-time Fourier transform (STFT) are used for extracting features. We compare them to wavelet transform (WT), empirical mode decomposition (EMD) and other traditional methods with the aim of obtaining the best possible discriminating features. Finally, we look for their medical interpretation, which is important for clinical experts. We achieve high-performance results for SOZ and non-SOZ data classification by using the labeled iEEG data and support vector machine (SVM), fully connected neural network (FCNN) and convolutional neural network (CNN) as classification models. In addition, we introduce the positive unlabeled (PU) learning to further reduce the workload of clinical experts. By using PU learning, we can learn a binary classifier with a small amount of labeled data and a large amount of unlabeled data. This can greatly reduce the amount and difficulty of annotation work by clinical experts. All together, we show that using 105 minutes of labeled data we achieve a classification result of 91.46% on average for multiple patients.

Three-dimensional nickel nanowires modified by amorphous Fe nanosheets as electrocatalysts for the oxygen evolution reaction.

The development of electrode materials with abundant active surface sites is important for large-scale hydrogen production by water electrolysis. In this study, Fe/Ni NWs/NF catalysts were prepared by hydrothermal and electrochemical deposition of iron nanosheets on nickel chain nanowires, initially grown on nickel foam. The synthesized Fe/Ni NWs/NF electrode possessed a 3D layered heterostructure and crystalline-amorphous interfaces, containing amorphous Fe nanosheets, which demonstrated excellent activity in the oxygen evolution reaction (OER). The newly prepared electrode material has a large specific surface area, and its electrocatalytic performance is characterized by a small Tafel slope and an oxygen evolution overpotential of 303 mV at 50 mA cm-2. The electrode was highly stable in alkaline media with no degradation observed after 40 h of continuous OER operation at 50 mA cm-2. The study demonstrates the significant promise of the Fe/Ni NWs/NF electrode material for large-scale hydrogen production by water electrolysis and provides a facile and low-cost approach for the preparation of highly active OER electrocatalysts.

Transferable multi-modal fusion in knee angles and gait phases for their continuous prediction.

Objective.The gait phase and joint angle are two essential and complementary components of kinematics during normal walking, whose accurate prediction is critical for lower-limb rehabilitation, such as controlling the exoskeleton robots. Multi-modal signals have been used to promote the prediction performance of the gait phase or joint angle separately, but it is still few reports to examine how these signals can be used to predict both simultaneously.Approach.To address this problem, we propose a new method named transferable multi-modal fusion (TMMF) to perform a continuous prediction of knee angles and corresponding gait phases by fusing multi-modal signals. Specifically, TMMF consists of a multi-modal signal fusion block, a time series feature extractor, a regressor, and a classifier. The multi-modal signal fusion block leverages the maximum mean discrepancy to reduce the distribution discrepancy across different modals in the latent space, achieving the goal of transferable multi-modal fusion. Subsequently, by using the long short-term memory-based network, we obtain the feature representation from time series data to predict the knee angles and gait phases simultaneously. To validate our proposal, we design an experimental paradigm with random walking and resting to collect data containing multi-modal biomedical signals from electromyography, gyroscopes, and virtual reality.Main results.Comprehensive experiments on our constructed dataset demonstrate the effectiveness of the proposed method. TMMF achieves a root mean square error of0.090±0.022s in knee angle prediction and a precision of83.7±7.7% in gait phase prediction.Significance.We demonstrate the feasibility and validity of using TMMF to predict lower-limb kinematics continuously from multi-modal biomedical signals. This proposed method represents application potential in predicting the motor intent of patients with different pathologies.

Robust to Rank Selection: Low-Rank Sparse Tensor-Ring Completion.

Tensor-ring (TR) decomposition was recently studied and applied for low-rank tensor completion due to its powerful representation ability of high-order tensors. However, most of the existing TR-based methods tend to suffer from deterioration when the selected rank is larger than the true one. To address this issue, this article proposes a new low-rank sparse TR completion method by imposing the Frobenius norm regularization on its latent space. Specifically, we theoretically establish that the proposed method is capable of exploiting the low rankness and Kronecker-basis-representation (KBR)-based sparsity of the target tensor using the Frobenius norm of latent TR-cores. We optimize the proposed TR completion by block coordinate descent (BCD) algorithm and design a modified TR decomposition for the initialization of this algorithm. Extensive experimental results on synthetic data and visual data have demonstrated that the proposed method is able to achieve better results compared to the conventional TR-based completion methods and other state-of-the-art methods and, meanwhile, is quite robust even if the selected TR-rank increases.

Graph-Regularized Non-Negative Tensor-Ring Decomposition for Multiway Representation Learning.

Tensor-ring (TR) decomposition is a powerful tool for exploiting the low-rank property of multiway data and has been demonstrated great potential in a variety of important applications. In this article, non-negative TR (NTR) decomposition and graph-regularized NTR (GNTR) decomposition are proposed. The former equips TR decomposition with the ability to learn the parts-based representation by imposing non-negativity on the core tensors, and the latter additionally introduces a graph regularization to the NTR model to capture manifold geometry information from tensor data. Both of the proposed models extend TR decomposition and can be served as powerful representation learning tools for non-negative multiway data. The optimization algorithms based on an accelerated proximal gradient are derived for NTR and GNTR. We also empirically justified that the proposed methods can provide more interpretable and physically meaningful representations. For example, they are able to extract parts-based components with meaningful color and line patterns from objects. Extensive experimental results demonstrated that the proposed methods have better performance than state-of-the-art tensor-based methods in clustering and classification tasks.

Imbalanced low-rank tensor completion via latent matrix factorization.

Tensor completion has been widely used in computer vision and machine learning. Most existing tensor completion methods empirically assume the intrinsic tensor is simultaneous low-rank in all over modes. However, tensor data recorded from real-world applications may conflict with these assumptions, e.g., face images taken from different subjects often lie in a union of low-rank subspaces, which may result in a quite high rank or even full rank structure in its sample mode. To this aim, in this paper, we propose an imbalanced low-rank tensor completion method, which can flexibly estimate the low-rank incomplete tensor via decomposing it into a mixture of multiple latent tensor ring (TR) rank components. Specifically, each latent component is approximated using low-rank matrix factorization based on TR unfolding matrix. In addition, an effective proximal alternating minimization algorithm is developed and theoretically proved to maintain the global convergence property, that is, the whole sequence of iterates is convergent and converges to a critical point. Extensive experiments on both synthetic and real-world tensor data demonstrate that the proposed method achieves more favorable completion results with less computational cost when compared to the state-of-the-art tensor completion methods.

Noisy Tensor Completion via Low-Rank Tensor Ring.

Tensor completion is a fundamental tool for incomplete data analysis, where the goal is to predict missing entries from partial observations. However, existing methods often make the explicit or implicit assumption that the observed entries are noise-free to provide a theoretical guarantee of exact recovery of missing entries, which is quite restrictive in practice. To remedy such drawback, this article proposes a novel noisy tensor completion model, which complements the incompetence of existing works in handling the degeneration of high-order and noisy observations. Specifically, the tensor ring nuclear norm (TRNN) and least-squares estimator are adopted to regularize the underlying tensor and the observed entries, respectively. In addition, a nonasymptotic upper bound of estimation error is provided to depict the statistical performance of the proposed estimator. Two efficient algorithms are developed to solve the optimization problem with convergence guarantee, one of which is specially tailored to handle large-scale tensors by replacing the minimization of TRNN of the original tensor equivalently with that of a much smaller one in a heterogeneous tensor decomposition framework. Experimental results on both synthetic and real-world data demonstrate the effectiveness and efficiency of the proposed model in recovering noisy incomplete tensor data compared with state-of-the-art tensor completion models.

Online subspace learning and imputation by Tensor-Ring decomposition.

This paper considers the completion problem of a partially observed high-order streaming data, which is cast as an online low-rank tensor completion problem. Though the online low-rank tensor completion problem has drawn lots of attention in recent years, most of them are designed based on the traditional decomposition method, such as CP and Tucker. Inspired by the advantages of Tensor Ring decomposition over the traditional decompositions in expressing high-order data and its superiority in missing values estimation, this paper proposes two online subspace learning and imputation methods based on Tensor Ring decomposition. Specifically, we first propose an online Tensor Ring subspace learning and imputation model by formulating an exponentially weighted least squares with Frobenium norm regularization of TR-cores. Then, two commonly used optimization algorithms, i.e. alternating recursive least squares and stochastic-gradient algorithms, are developed to solve the proposed model. Numerical experiments show that the proposed methods are more effective to exploit the time-varying subspace in comparison with the conventional Tensor Ring completion methods. Besides, the proposed methods are demonstrated to be superior to obtain better results than state-of-the-art online methods in streaming data completion under varying missing ratios and noise.

A Generalized Graph Regularized Non-Negative Tucker Decomposition Framework for Tensor Data Representation.

Non-negative Tucker decomposition (NTD) is one of the most popular techniques for tensor data representation. To enhance the representation ability of NTD by multiple intrinsic cues, that is, manifold structure and supervisory information, in this article, we propose a generalized graph regularized NTD (GNTD) framework for tensor data representation. We first develop the unsupervised GNTD (UGNTD) method by constructing the nearest neighbor graph to maintain the intrinsic manifold structure of tensor data. Then, when limited must-link and cannot-link constraints are given, unlike most existing semisupervised learning methods that only use the pregiven supervisory information, we propagate the constraints through the entire dataset and then build a semisupervised graph weight matrix by which we can formulate the semisupervised GNTD (SGNTD). Moreover, we develop a fast and efficient alternating proximal gradient-based algorithm to solve the optimization problem and show its convergence and correctness. The experimental results on unsupervised and semisupervised clustering tasks using four image datasets demonstrate the effectiveness and high efficiency of the proposed methods.

Accommodating Multiple Tasks' Disparities With Distributed Knowledge-Sharing Mechanism.

Deep multitask learning (MTL) shares beneficial knowledge across participating tasks, alleviating the impacts of extreme learning conditions on their performances such as the data scarcity problem. In practice, participators stemming from different domain sources often have varied complexities and input sizes, for example, in the joint learning of computer vision tasks with RGB and grayscale images. For adapting to these differences, it is appropriate to design networks with proper representational capacities and construct neural layers with corresponding widths. Nevertheless, most of the state-of-the-art methods pay little attention to such situations, and actually fail to handle the disparities. To work with the dissimilitude of tasks' network designs, this article presents a distributed knowledge-sharing framework called tensor ring multitask learning (TRMTL), in which the relationship between knowledge sharing and original weight matrices is cut up. The framework of TRMTL is flexible, which is not only capable of sharing knowledge across heterogenous networks but also able to jointly learn tasks with varied input sizes, significantly improving performances of data-insufficient tasks. Comprehensive experiments on challenging datasets are conducted to empirically validate the effectiveness, efficiency, and flexibility of TRMTL in dealing with the disparities in MTL.

Dynamic Double Classifiers Approximation for Cross-Domain Recognition.

In general, existing cross-domain recognition methods mainly focus on changing the feature representation of data or modifying the classifier parameter and their efficiencies are indicated by the better performance. However, most existing methods do not simultaneously integrate them into a unified optimization objective for further improving the learning efficiency. In this article, we propose a novel cross-domain recognition algorithm framework by integrating both of them. Specifically, we reduce the discrepancies in both the conditional distribution and marginal distribution between different domains in order to learn a new feature representation which pulls the data from different domains closer on the whole. However, the data from different domains but the same class cannot interlace together enough and thus it is not reasonable to mix them for training a single classifier. To this end, we further propose to learn double classifiers on the respective domain and require that they dynamically approximate to each other during learning. This guarantees that we finally learn a suitable classifier from the double classifiers by using the strategy of classifier fusion. The experiments show that the proposed method outperforms over the state-of-the-art methods.

Improving EEG Decoding via Clustering-Based Multitask Feature Learning.

Accurate electroencephalogram (EEG) pattern decoding for specific mental tasks is one of the key steps for the development of brain-computer interface (BCI), which is quite challenging due to the considerably low signal-to-noise ratio of EEG collected at the brain scalp. Machine learning provides a promising technique to optimize EEG patterns toward better decoding accuracy. However, existing algorithms do not effectively explore the underlying data structure capturing the true EEG sample distribution and, hence, can only yield a suboptimal decoding accuracy. To uncover the intrinsic distribution structure of EEG data, we propose a clustering-based multitask feature learning algorithm for improved EEG pattern decoding. Specifically, we perform affinity propagation-based clustering to explore the subclasses (i.e., clusters) in each of the original classes and then assign each subclass a unique label based on a one-versus-all encoding strategy. With the encoded label matrix, we devise a novel multitask learning algorithm by exploiting the subclass relationship to jointly optimize the EEG pattern features from the uncovered subclasses. We then train a linear support vector machine with the optimized features for EEG pattern decoding. Extensive experimental studies are conducted on three EEG data sets to validate the effectiveness of our algorithm in comparison with other state-of-the-art approaches. The improved experimental results demonstrate the outstanding superiority of our algorithm, suggesting its prominent performance for EEG pattern decoding in BCI applications.

Average Approximate Hashing-Based Double Projections Learning for Cross-Modal Retrieval.

Cross-modal retrieval has attracted considerable attention for searching in large-scale multimedia databases because of its efficiency and effectiveness. As a powerful tool of data analysis, matrix factorization is commonly used to learn hash codes for cross-modal retrieval, but there are still many shortcomings. First, most of these methods only focus on preserving locality of data but they ignore other factors such as preserving reconstruction residual of data during matrix factorization. Second, the energy loss of data is not considered when the data of cross-modal are projected into a common semantic space. Third, the data of cross-modal are directly projected into a unified semantic space which is not reasonable since the data from different modalities have different properties. This article proposes a novel method called average approximate hashing (AAH) to address these problems by: 1) integrating the locality and residual preservation into a graph embedding framework by using the label information; 2) projecting data from different modalities into different semantic spaces and then making the two spaces approximate to each other so that a unified hash code can be obtained; and 3) introducing a principal component analysis (PCA)-like projection matrix into the graph embedding framework to guarantee that the projected data can preserve the main energy of data. AAH obtains the final hash codes by using an average approximate strategy, that is, using the mean of projected data of different modalities as the hash codes. Experiments on standard databases show that the proposed AAH outperforms several state-of-the-art cross-modal hashing methods.

Low Tensor-Ring Rank Completion by Parallel Matrix Factorization.

Tensor-ring (TR) decomposition has recently attracted considerable attention in solving the low-rank tensor completion (LRTC) problem. However, due to an unbalanced unfolding scheme used during the update of core tensors, the conventional TR-based completion methods usually require a large TR rank to achieve the optimal performance, which leads to high computational cost in practical applications. To overcome this drawback, we propose a new method to exploit the low TR-rank structure in this article. Specifically, we first introduce a balanced unfolding operation called tensor circular unfolding, by which the relationship between TR rank and the ranks of tensor unfoldings is theoretically established. Using this new unfolding operation, we further propose an algorithm to exploit the low TR-rank structure by performing parallel low-rank matrix factorizations to all circularly unfolded matrices. To tackle the problem of nonuniform missing patterns, we apply a row weighting trick to each circularly unfolded matrix, which significantly improves the adaptive ability to various types of missing patterns. The extensive experiments have demonstrated that the proposed algorithm can achieve outstanding performance using a much smaller TR rank compared with the conventional TR-based completion algorithms; meanwhile, the computational cost is reduced substantially.

Multi-View Multi-Scale Optimization of Feature Representation for EEG Classification Improvement.

Effectively extracting common space pattern (CSP) features from motor imagery (MI) EEG signals is often highly dependent on the filter band selection. At the same time, optimizing the EEG channel combinations is another key issue that substantially affects the SMR feature representations. Although numerous algorithms have been developed to find channels that record important characteristics of MI, most of them select channels in a cumbersome way with low computational efficiency, thereby limiting the practicality of MI-based BCI systems. In this study, we propose the multi-scale optimization (MSO) of spatial patterns, optimizing filter bands over multiple channel sets within CSPs to further improve the performance of MI-based BCI. Specifically, several channel subsets are first heuristically predefined, and then raw EEG data specific to each of these subsets bandpass-filtered at the overlap between a set of filter bands. Further, instead of solving learning problems for each channel subset independently, we propose a multi-view learning based sparse optimization to jointly extract robust CSP features with L2,1 -norm regularization, aiming to capture the shared salient information across multiple related spatial patterns for enhanced classification performance. A support vector machine (SVM) classifier is then trained on these optimized EEG features for accurate recognition of MI tasks. Experimental results on three public EEG datasets validate the effectiveness of MSO compared to several other competing methods and their variants. These superior experimental results demonstrate that the proposed MSO method has promising potential in MI-based BCIs.

Projective Double Reconstructions Based Dictionary Learning Algorithm for Cross-Domain Recognition.

Dictionary learning plays a significant role in the field of machine learning. Existing works mainly focus on learning dictionary from a single domain. In this paper, we propose a novel projective double reconstructions (PDR) based dictionary learning algorithm for cross-domain recognition. Owing the distribution discrepancy between different domains, the label information is hard utilized for improving discriminability of dictionary fully. Thus, we propose a more flexible label consistent term and associate it with each dictionary item, which makes the reconstruction coefficients have more discriminability as much as possible. Due to the intrinsic correlation between cross-domain data, the data should be reconstructed with each other. Based on this consideration, we further propose a projective double reconstructions scheme to guarantee that the learned dictionary has the abilities of data itself reconstruction and data crossreconstruction. This also guarantees that the data from different domains can be boosted mutually for obtaining a good data alignment, making the learned dictionary have more transferability. We integrate the double reconstructions, label consistency constraint and classifier learning into a unified objective and its solution can be obtained by proposed optimization algorithm that is more efficient than the conventional l1 optimization based dictionary learning methods. The experiments show that the proposed PDR not only greatly reduces the time complexity for both training and testing, but also outperforms over the stateof- the-art methods.