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.

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.

Tensor Robust Kernel PCA for Multidimensional Data.

Recently, the tensor nuclear norm (TNN)-based tensor robust principle component analysis (TRPCA) has achieved impressive performance in multidimensional data processing. The underlying assumption in TNN is the low-rankness of frontal slices of the tensor in the transformed domain (e.g., Fourier domain). However, the low-rankness assumption is usually violative for real-world multidimensional data (e.g., video and image) due to their intrinsically nonlinear structure. How to effectively and efficiently exploit the intrinsic structure of multidimensional data remains a challenge. In this article, we first suggest a kernelized TNN (KTNN) by leveraging the nonlinear kernel mapping in the transform domain, which faithfully captures the intrinsic structure (i.e., implicit low-rankness) of multidimensional data and is computed at a lower cost by introducing kernel trick. Armed with KTNN, we propose a tensor robust kernel PCA (TRKPCA) model for handling multidimensional data, which decomposes the observed tensor into an implicit low-rank component and a sparse component. To tackle the nonlinear and nonconvex model, we develop an efficient alternating direction method of multipliers (ADMM)-based algorithm. Extensive experiments on real-world applications collectively verify that TRKPCA achieves superiority over the state-of-the-art RPCA methods.

Experimental study on the effect of quaternary ammonium salt + monoethylene glycol compound to methane hydrate agglomeration in oil-water system.

Natural gas hydrate has been a critical risk to the safety of offshore oil and gas well test and subsea transportation. Herein, the effect of three quaternary ammonium salt (QAS) surfactants with monoethylene glycol (MEG) to methane hydrate agglomeration in water-oil system was experimentally studied by a rocking cell. Based on the hydrate volume fraction and the slider trajectory, a classification method of the gas hydrate anti-agglomerants was established. All the QASs in this work show the capability of reducing hydrate agglomeration, among which N1,N3-didodecyl-N1,N1,N3,N3-tetramethylpropane-1,3-diaminium chloride (AA-2) has the best anti-agglomerating performance, and the slider moved at a large trajectory of 61-174 mm. The three QASs were compounded with 5, 10, and 15 wt% (based on water) MEG, respectively. Experimental results showed that AA-2 compounded with MEG (10 wt%) can effectively prevent hydrate agglomeration. The slider moved in the cell at the full trajectory range, showing the compound of grade A performance. The compound of QAS and MEG shows a synergistic effect. The addition of QAS can significantly reduce the required MEG dosage for the hydrate blockage prevention than the MEG only situation. Considering the economic factors of the filed hydrate management, the combination application of QAS + MEG may provide a promising option.

A Novel Tensor Ring Sparsity Measurement for Image Completion.

As a promising data analysis technique, sparse modeling has gained widespread traction in the field of image processing, particularly for image recovery. The matrix rank, served as a measure of data sparsity, quantifies the sparsity within the Kronecker basis representation of a given piece of data in the matrix format. Nevertheless, in practical scenarios, much of the data are intrinsically multi-dimensional, and thus, using a matrix format for data representation will inevitably yield sub-optimal outcomes. Tensor decomposition (TD), as a high-order generalization of matrix decomposition, has been widely used to analyze multi-dimensional data. In a direct generalization to the matrix rank, low-rank tensor modeling has been developed for multi-dimensional data analysis and achieved great success. Despite its efficacy, the connection between TD rank and the sparsity of the tensor data is not direct. In this work, we introduce a novel tensor ring sparsity measurement (TRSM) for measuring the sparsity of the tensor. This metric relies on the tensor ring (TR) Kronecker basis representation of the tensor, providing a unified interpretation akin to matrix sparsity measurements, wherein the Kronecker basis serves as the foundational representation component. Moreover, TRSM can be efficiently computed by the product of the ranks of the mode-2 unfolded TR-cores. To enhance the practical performance of TRSM, the folded-concave penalty of the minimax concave penalty is introduced as a nonconvex relaxation. Lastly, we extend the TRSM to the tensor completion problem and use the alternating direction method of the multipliers scheme to solve it. Experiments on image and video data completion demonstrate the effectiveness of the proposed method.

Nonparametric tensor ring decomposition with scalable amortized inference.

Multi-dimensional data are common in many applications, such as videos and multi-variate time series. While tensor decomposition (TD) provides promising tools for analyzing such data, there still remains several limitations. First, traditional TDs assume multi-linear structures of the latent embeddings, which greatly limits their expressive power. Second, TDs cannot be straightforwardly applied to datasets with massive samples. To address these issues, we propose a nonparametric TD with amortized inference networks. Specifically, we establish a non-linear extension of tensor ring decomposition, using neural networks, to model complex latent structures. To jointly model the cross-sample correlations and physical structures, a matrix Gaussian process (GP) prior is imposed over the core tensors. From learning perspective, we develop a VAE-like amortized inference network to infer the posterior of core tensors corresponding to new tensor data, which enables TDs to be applied to large datasets. Our model can be also viewed as a kind of decomposition of VAE, which can additionally capture hidden tensor structure and enhance the expressiveness power. Finally, we derive an evidence lower bound such that a scalable optimization algorithm is developed. The advantages of our method have been evaluated extensively by data imputation on the Healing MNIST dataset and four multi-variate time series data.

Fractional Tensor Recurrent Unit (fTRU): A Stable Forecasting Model With Long Memory.

The tensor recurrent model is a family of nonlinear dynamical systems, of which the recurrence relation consists of a p -fold (called degree- p ) tensor product. Despite such models frequently appearing in advanced recurrent neural networks (RNNs), to this date, there are limited studies on their long memory properties and stability in sequence tasks. In this article, we propose a fractional tensor recurrent model, where the tensor degree p is extended from the discrete domain to the continuous domain, so it is effectively learnable from various datasets. Theoretically, we prove that a large degree p is essential to achieve the long memory effect in a tensor recurrent model, yet it could lead to unstable dynamical behaviors. Hence, our new model, named fractional tensor recurrent unit (fTRU), is expected to seek the saddle point between long memory property and model stability during the training. We experimentally show that the proposed model achieves competitive performance with a long memory and stable manners in several forecasting tasks compared to various advanced RNNs.

Construction and application of flow pressure drop model of perforated well considering pressure loss of perforation hole.

Perforating well is one of the main production wells in reservoir development. Perforating effect directly affects well production, so the optimization of perforating parameters has attracted wide attention. Because pressure difference serves as the driving force for fluid flowing from formation to wellbore, it is important to understand the composition of production pressure difference in perforating well, which can guide the optimization of perforating parameters and the evaluation of perforating effect. In order to clarify the composition of production pressure difference during the production process of perforated wells, a pressure drop model pressure drop model is established based on fluid mechanics theory, which includes a pressure drop model of formation and a pressure drop model of perforation hole. The pressure drop model of formation is firstly constructed based on the Darcy's law and the equivalent resistance method, and the pressure drop model of perforation hole is built by the fluid tube-flow theory. Secondly, the numerical calculation method is adopted to realize the coupling solution of models, and the accuracy of this model is verified by comparison of the Karakas-Tariq model. Finally, the effects of formation physical properties and perforating parameters on flow pressure drop are discussed. The results show that there is a difference of more than 2 orders of magnitude between the pressure drop generated in perforation hole and flow pressure difference, and pressure drop of perforation hole can be neglected in practical applications. Comparing with medium-high permeability reservoirs, optimizing perforation parameters in low permeability reservoirs has a more significant impact on flow pressure drop. Among perforating parameters, perforation length and perforation density have great influence on flow pressure difference, while perforation diameter and phase angle have relatively little influence. These results have certain guiding significance for optimizing perforating parameters in different permeability reservoirs.

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.

TT-Net: Tensorized Transformer Network for 3D medical image segmentation.

Accurate segmentation of organs, tissues and lesions is essential for computer-assisted diagnosis. Previous works have achieved success in the field of automatic segmentation. However, there exists two limitations. (1) They are remain challenged by complex conditions, such as segmentation target is variable in location, size and shape, especially for different imaging modalities. (2) Existing transformer-based networks suffer from a high parametric complexity. To solve these limitations, we propose a new Tensorized Transformer Network (TT-Net). In this paper, (1) Multi-scale transformer with layers-fusion is proposed to faithfully capture context interaction information. (2) Cross Shared Attention (CSA) module that based on pHash similarity fusion (pSF) is well-designed to extract the global multi-variate dependency features. (3) Tensorized Self-Attention (TSA) module is proposed to deal with the large number of parameters, which can also be easily embedded into other models. In addition, TT-Net gains a good explainability through visualizing the transformer layers. The proposed method is evaluated on three widely accepted public datasets and one clinical dataset, which contains different imaging modalities. Comprehensive results show that TT-Net outperforms other state-of-the-art methods for the four different segmentation tasks. Besides, the compression module which can be easily embedded into other transformer-based methods achieves lower computation with comparable segmentation performance.

Light diffraction by sarcomeres produces iridescence in transmission in the transparent ghost catfish.

Despite the elaborate varieties of iridescent colors in biological species, most of them are reflective. Here we show the rainbow-like structural colors found in the ghost catfish (Kryptopterus vitreolus), which exist only in transmission. The fish shows flickering iridescence throughout the transparent body. The iridescence originates from the collective diffraction of light after passing through the periodic band structures of the sarcomeres inside the tightly stacked myofibril sheets, and the muscle fibers thus work as transmission gratings. The length of the sarcomeres varies from ~1 µm from the body neutral plane near the skeleton to ~2 µm next to the skin, and the iridescence of a live fish mainly results from the longer sarcomeres. The length of the sarcomere changes by ~80 nm as it relaxes and contracts, and the fish shows a quickly blinking dynamic diffraction pattern as it swims. While similar diffraction colors are also observed in thin slices of muscles from non-transparent species such as the white crucian carps, a transparent skin is required indeed to have such iridescence in live species. The ghost catfish skin is of a plywood structure of collagen fibrils, which allows more than 90% of the incident light to pass directly into the muscles and the diffracted light to exit the body. Our findings could also potentially explain the iridescence in other transparent aquatic species, including the eel larvae (Leptocephalus) and the icefishes (Salangidae).

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.

Subject adaptation convolutional neural network for EEG-based motor imagery classification.

Objective.Deep transfer learning has been widely used to address the nonstationarity of electroencephalogram (EEG) data during motor imagery (MI) classification. However, previous deep learning approaches suffer from limited classification accuracy because the temporal and spatial features cannot be effectively extracted.Approach.Here, we propose a novel end-to-end deep subject adaptation convolutional neural network (SACNN) to handle the problem of EEG-based MI classification. Our proposed model jointly optimizes three modules, i.e. a feature extractor, a classifier, and a subject adapter. Specifically, the feature extractor simultaneously extracts the temporal and spatial features from the raw EEG data using a parallel multiscale convolution network. In addition, we design a subject adapter to reduce the feature distribution shift between the source and target subjects by using the maximum mean discrepancy. By minimizing the classification loss and the distribution discrepancy, the model is able to extract the temporal-spatial features to the prediction of a new subject.Main results.Extensive experiments are carried out on three EEG-based MI datasets, i.e. brain-computer interface (BCI) competition IV dataset IIb, BCI competition III dataset IVa, and BCI competition IV dataset I, and the average accuracy reaches to 86.42%, 81.71% and 79.35% on the three datasets respectively. Furthermore, the statistical analysis also indicates the significant performance improvement of SACNN.Significance.This paper reveals the importance of the temporal-spatial features on EEG-based MI classification task. Our proposed SACNN model can make fully use of the temporal-spatial information to achieve the purpose.

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.

Non-Local Meets Global: An Iterative Paradigm for Hyperspectral Image Restoration.

Non-local low-rank tensor approximation has been developed as a state-of-the-art method for hyperspectral image (HSI) restoration, which includes the tasks of denoising, compressed HSI reconstruction and inpainting. Unfortunately, while its restoration performance benefits from more spectral bands, its runtime also substantially increases. In this paper, we claim that the HSI lies in a global spectral low-rank subspace, and the spectral subspaces of each full band patch group should lie in this global low-rank subspace. This motivates us to propose a unified paradigm combining the spatial and spectral properties for HSI restoration. The proposed paradigm enjoys performance superiority from the non-local spatial denoising and light computation complexity from the low-rank orthogonal basis exploration. An efficient alternating minimization algorithm with rank adaptation is developed. It is done by first solving a fidelity term-related problem for the update of a latent input image, and then learning a low-dimensional orthogonal basis and the related reduced image from the latent input image. Subsequently, non-local low-rank denoising is developed to refine the reduced image and orthogonal basis iteratively. Finally, the experiments on HSI denoising, compressed reconstruction, and inpainting tasks, with both simulated and real datasets, demonstrate its superiority with respect to state-of-the-art HSI restoration 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.

Manifold Modeling in Embedded Space: An Interpretable Alternative to Deep Image Prior.

Deep image prior (DIP), which uses a deep convolutional network (ConvNet) structure as an image prior, has attracted wide attention in computer vision and machine learning. DIP empirically shows the effectiveness of the ConvNet structures for various image restoration applications. However, why the DIP works so well is still unknown. In addition, the reason why the convolution operation is useful in image reconstruction, or image enhancement is not very clear. This study tackles this ambiguity of ConvNet/DIP by proposing an interpretable approach that divides the convolution into "delay embedding" and "transformation" (i.e., encoder-decoder). Our approach is a simple, but essential, image/tensor modeling method that is closely related to self-similarity. The proposed method is called manifold modeling in embedded space (MMES) since it is implemented using a denoising autoencoder in combination with a multiway delay-embedding transform. In spite of its simplicity, MMES can obtain quite similar results to DIP on image/tensor completion, super-resolution, deconvolution, and denoising. In addition, MMES is proven to be competitive with DIP, as shown in our experiments. These results can also facilitate interpretation/characterization of DIP from the perspective of a "low-dimensional patch-manifold prior."