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To generate a high-spatial-resolution hyperspectral (HHS) image from a high-spatial-resolution multispectral (HMS) image, both spatial information and spectral information should be considered simultaneously if we want to build a more accurate mapping from HMS to HHS. To this end, a spectral and spatial jointed spectral super-resolution method is proposed in this letter using an end-to-end learning strategy for each subspace with the cluster-based multibranch backpropagation neural network (BPNN). More specifically, in addition to the spectra similarity, a modified superpixel segmentation is introduced to jointly take spatial contextual information into account, and a new framework with it is given. Comparisons on the Columbia University Automated Vision Environment (CAVE) data set show that our proposed method outperforms other relative state-of-the-art methods more than 0.3 in the root mean squared error (RMSE) and more than 1.0 in the spectral angle mapper (SAM) index. Especially, an exemplary application is demonstrated using the synchronized observation data collected by the multispectral and hyperspectral sensors mounted on the HJ-1A satellite at the same time.

In a post-COVID-19 world, extensive study of deep learning-based biometric authentication techniques prompts the need to secure them. Further, the biometric data is assumed to be largely immutable; thus, if it is compromised, it is lost forever. Hence, reliable and secure biometric authentication is of utmost importance. In this paper, we address the security and privacy concerns of biometric templates generated via deep networks. We propose a cancelable biometric authentication approach. The framework consists of a lightweight Convolutional Neural Network (CNN) with a few-shot enrollment for generating biometric templates. Further, to enhance biometric templates’ discriminative power and to provide revocability, biometric templates are projected onto a random subspace (based on the user-specific key). Later projected biometric templates are mapped onto robust n - bit unique codes (using a KNN classifier) and protected via. SHA-3 hash digest. Moreover, a real-world biometric authentication system is always dynamic (users keep on changing). Thus we have also integrated phase-wise incremental learning within a deep learning-based cancelable biometric authentication framework. This is the first work in which deep cancelable templates are generated incrementally to the best of our knowledge. We analyze the proposed scheme for its performance and privacy preservation on three benchmarks constrained iris data-sets and over one unconstrained iris data-set along with one publicly available knuckle data-set. Furthermore, it has been demonstrated that the proposed cancelable incremental framework strictly follows the four fundamental properties of cancelability viz. non-invertibility, unlinkability, revocability, and usability.

We study the forecasting of the power consumptions of a population of households and of subpopulations thereof. These subpopulations are built according to location, to exogenous information and/or to profiles we determined from historical households consumption time series. Thus, we aim to forecast the electricity consumption time series at several levels of households aggregation. These time series are linked through some summation constraints which induce a hierarchy. Our approach consists in three steps: feature generation, aggregation and projection. Firstly (feature generation step), we build, for each considering group for households, a benchmark forecast (called features), using random forests or generalized additive models. Secondly (aggregation step), aggregation algorithms, run in parallel, aggregate these forecasts and provide new predictions. Finally (projection step), we use the summation constraints induced by the time series underlying hierarchy to re-conciliate the forecasts by projecting them in a well-chosen linear subspace. We provide some theoretical guaranties on the average prediction error of this methodology, through the minimization of a quantity called regret. We also test our approach on households power consumption data collected in Great Britain by multiple energy providers in the Energy Demand Research Project context. We build and compare various population segmentations for the evaluation of our approach performance.

We consider detection of a source by a vertical line array (VLA) in shallow water: the source position is unknown and the environmental parameters (such as water depth) are known only in that they are within certain limits. The performances of familiar correlation detectors, e.g., generalized likelihood ratio, Bayesian, robust matched field processing detectors, can deteriorate markedly in some environment/source-position pairs. Previous work proposed a robust mode space detector, robust in the sense that the performance only depends on the signal-to-noise ratio and is insensitive to the unknown environmental and source-position specifics, with the mode space being spanned by VLA sampled modes (modal depth functions). However, only complete mode sampling was considered. Given that modes are generally incompletely sampled due to insufficient array aperture, robustness absent complete mode sampling is here investigated. We propose to use the physically supported greatest dimensional effective mode space to implement a robust subspace detector, as opposed to the original greatest dimensional one as before: the former is exactly the latter, but with nuisance modes rejected, thus leading to a better robust performance. The resulting greatest dimensional effective mode space detector (GE-MSD) suffers only light performance decreases relative to the correlation detectors’ performance peaks, and is much more computationally efficient. The effect of surface-generated noise on the GE-MSD’s robustness is numerically investigated. The results suggest that surface noise indeed degrades the GE-MSD’s robustness, but that incomplete mode sampling, which causes an approximate collinearity among sampled modes, can mitigate this.

Mutual interference in automotive radar will reduce the signal-to-noise ratio (SNR) of the received signals. It is difficult to accurately distinguish the signal subspace and the noise subspace for low SNR signals, which will degrade the direction of arrival (DOA) estimation performance of the multiple signal classification (MUSIC) algorithm. To solve this problem, this letter proposes a DOA estimation method for automotive radar based on empirical mode decomposition (EMD) and MUSIC in the case of interference. In our method, the interference signals are suppressed before the DOA estimation. The received signals of the receiving antennas affected by the interference are decomposed into several components by using EMD, and then the interference signals in the interference components are suppressed. Finally, all the received signals are used for the DOA estimation. The results of the simulation and field experiments show that the proposed method can obtain an accurate DOA estimation when the received signals contain the interference signals, and the performance of the proposed method is better than the existing DOA estimation algorithms.

For the purpose of locating the orthogonal frequency division multiplexing (OFDM) signal emitter efficiently and accurately in multipath environment, an innovative direction position determination (DPD) algorithm based on the multiple carrier characteristic of OFDM signals is proposed in this paper. The time of the arrival (TOA), angle of arrival (AOA) and Doppler frequency shift information contained in the observed data are jointly employed to locate the emitter. High-dimensional search can be avoided by decoupling unknown parameters and the estimation performance is improved due to the expansion of the subspace. The compact closed-form expressions of the Cramer-Rao lower bound (CRLB) corresponding to the parameters of interest are also derived. Simulation results show that compared with the traditional DPD based on MUSIC algorithm, the localization performance of the proposed algorithm can attain the CRLB at higher noise levels.

High resolution and wide-swath imaging always suffer channel errors of the multiple azimuth channels (MACs) SAR. This paper presents an image-domain channel error estimation algorithm based on image subspace least square (ISPLS) method, and a post-imaging reconstruction algorithm for MACs SAR. The proposed method mainly consists of three parts: firstly, preprocessing and SAR imaging; secondly, the ISP-LSbased channel error estimation and calibration algorithm; thirdly, post-imaging reconstruction and ambiguity suppression. The channel phase and baseline errors are joint-estimated based on image subspace after SAR imaging, providing advantages that the higher SNR regions SAR images and the subspace method can be used to achieve a more accurate estimate with a relatively low computational load. We also propose a post-imaging reconstruction method for ambiguity suppression, which can realize imaging each channel data and then combining the multichannel SAR images. Simulated and acquired airborne SAR data are processed to demonstrate the effectiveness of the proposed method.

Hyperspectral images (HSIs) are often contaminated by several types of noise, which significantly limits the accuracy of subsequent applications. Recently, low-rank modeling based on tensor singular value decomposition (T-SVD) has achieved great success in HSI restoration. Most of them use the convex and nonconvex surrogates of the tensor rank, which cannot well approximate the tensor singular values and obtain suboptimal restored results. We suggest a novel HSI restoration model by introducing a fibered rank constrained tensor restoration framework with an embedded plug-and-play (PnP)-based regularization (FRCTR-PnP). More precisely, instead of using the convex and nonconvex surrogates to approximate the fibered rank, the proposed model directly constrains the tensor fibered rank of the solution, leading to a better approximation to the original image. Since exploiting the low-fibered-rankness of HSI is mainly to capture the global structure, we further employ an implicit PnP-based regularization to preserve the image details. Particularly, the above two building blocks are complementary to each other, rather than isolated and uncorrelated. Based on the alternating direction multiplier method (ADMM), we propose an efficient algorithm to tackle the proposed model. For robustness, we develop a three-directional randomized T-SVD (3DRT-SVD), which preserves the intrinsic structure of the clean HSI and removes partial noise by projecting the HSI onto a low-dimensional essential subspace. Extensive experimental results including simulated and real data demonstrate that the proposed method achieves superior performance over compared methods in terms of quantitative evaluation and visual inspection.

Multinomial logistic regression (MLR) is a useful tool for solving multi-classification problems. The l q , 0 ( q ⩾ 1 ) norm is an ideal regularization term for characterizing group sparsity in multinomial logistic regression and selecting important features in the high dimensional data. However, l q , 0 regularized multinomial logistic regression ( l q , 0 -MLR) is nonconvex, discontinuous, and NP-hard. Thus, most prior studies adopted a continuous approximation of the l q , 0 norm. In this paper, we present a novel l q , 0 -proximal Newton algorithm ( l q , 0 - PNA ) to solve the l q , 0 -MLR. We first define a strong α -stationary point and prove that this point is a local minimizer of l q , 0 -MLR. We then convert such a point into a stationary equation and solve it by l q , 0 - PNA , which is a Newton-type method running on a group sparse subspace with a low computational cost. Furthermore, we establish a locally quadratic convergence of l q , 0 - PNA . Finally, numerical experiments on simulated and real data show the superiority of l q , 0 - PNA in terms of computational time and accuracy, when compared with six state-of-the-art solvers, especially for high dimensional data.

Multiple kernel subspace clustering (MKSC), as an important extension for handling multi-view non-linear subspace data, has shown notable success in a wide variety of machine learning tasks. The key objective of MKSC is to build a flexible and appropriate graph for clustering from the kernel space. However, existing MKSC methods apply a mechanism utilizing the kernel trick to the traditional self-expressive principle, where the similarity graphs are built on the respective high-dimensional (or even infinite) reproducing kernel Hilbert space (RKHS). Regarding this strategy, we argue that the original high-dimensional spaces usually include noise and unreliable similarity measures and, therefore, output a low-quality graph matrix, which degrades clustering performance. In this paper, inspired by projective clustering, we propose the utilization of a complementary similarity graph by fusing the multiple kernel graphs constructed in the low-dimensional partition space, termed projective multiple kernel subspace clustering (PMKSC). By incorporating intrinsic structures with multi-view data, PMKSC alleviates the noise and redundancy in the original kernel space and obtains high-quality similarity to uncover the underlying clustering structures. Furthermore, we design a three-step alternate algorithm with proven convergence to solve the proposed optimization problem. The experimental results on ten multiple kernel benchmark datasets validate the effectiveness of our proposed PMKSC, compared to the state-of-the-art multiple kernel and kernel subspace clustering methods, by a large margin. Our code is available at \url{https://github.com/MengjingSun/PMKSC-code}.

With the rapid advancement of spectrometers, the imaging range of the electromagnetic spectrum starts growing narrower. The reduction of electromagnetic wave energy received in a single wavelength range leads more complex noise into the generated hyperspectral image (HSI), thus causing a severe cripple in the accuracy of subsequent applications. The requirement for the HSI mixed denoising algorithm's accuracy is further lifted. To address this challenge, in this letter, we propose a novel difference continuity-regularized nonlocal tensor subspace low-rank learning (named DNTSLR) method for HSI mixed denoising. Technically, the original high-dimensional HSI data was first projected into a low-dimensional subspace spanned by a spectral difference continuous basis instead of an orthogonal basis, so the data continuity of the restored HSI spectrum and tensor low-rankness was guaranteed. Then, a cube matching strategy was employed to stack the nonlocal tensor patches from the projected coefficient tensor, and a shrinkage algorithm was used to approximate the low-rank coefficient tensor. Eventually, the subspace low-rank learning algorithm was designed to alternately separate the noise tensor and restore the latent clean low-rank HSI tensor. Extensive experiments on multiple open datasets validate that the proposed method realizes the state-of-the-art denoising accuracy for HSI.

Spectrum mapping has emerged as an important problem in wireless communications, which generates a spectrum map for the spectrum resource analysis and management. Given the constrained transceiver volume and the limited energy consumption, how to effectively reconstruct the spectrum situation by the limited sampling data is a pressing challenge for spectrum mapping. In this paper, by exploiting the sparse nature of spectrum situation, we firstly attempt to solve the three-dimensional (3D) compressed spectrum mapping problem in the way of compressed sensing. Then, we develop a quadrature and right-triangular (QR) pivoting based measurement matrix optimization algorithm. By iteratively selecting new dominant sampling locations, it promotes the recovery accuracy compared to random measurement. After that, we propose a 3D spatial subspace based orthogonal matching pursuit (OMP) algorithm to recover spectrum situation for 3D compressed spectrum mapping. Finally, simulations are presented to show the comparisons in terms of localization, source signal strength recovery, recovery success rate and situation recovery. Results show our proposed 3D spectrum mapping scheme not only effectively reduces the sampling number, but also achieves a high level of spectrum mapping accuracy.

High-resolution wide-swath (HRWS) multichannel synthetic aperture radar (SAR) system possesses a number of receiving channels along the azimuth direction, so it has the capacity of moving target indication and imaging. However, due to the radial velocity of the moving target, false targets occur in the focused image. By estimating the radial velocity and combining it with moving target imaging, false targets can be effectively suppressed. In this letter, a method of radial velocity estimation of a moving target is proposed based on the theory of subspace projection. This method does not need to estimate the real azimuth position of the moving target and can predict the processing time. Simulation and airborne measured data show the effectiveness of the proposed method.

Deep multiview clustering methods have achieved remarkable performance. However, all of them failed to consider the difficulty labels (uncertainty of ground truth for training samples) over multiview samples, which may result in a nonideal clustering network for getting stuck into poor local optima during the training process; worse still, the difficulty labels from the multiview samples are always inconsistent, and such a fact makes it even more challenging to handle. In this article, we propose a novel deep adversarial inconsistent cognitive sampling (DAICS) method for multiview progressive subspace clustering. A multiview binary classification (easy or difficult) loss and a feature similarity loss are proposed to jointly learn a binary classifier and a deep consistent feature embedding network, throughout an adversarial minimax game over difficulty labels of multiview consistent samples. We develop a multiview cognitive sampling strategy to select the input samples from easy to difficult for multiview clustering network training. However, the distributions of easy and difficult samples are mixed together, hence not trivial to achieve the goal. To resolve it, we define a sampling probability with a theoretical guarantee. Based on that, a golden section mechanism is further designed to generate a sample set boundary to progressively select the samples with varied difficulty labels via a gate unit, which is utilized to jointly learn a multiview common progressive subspace and clustering network for more efficient clustering. Experimental results on four real-world datasets demonstrate the superiority of DAICS over state-of-the-art methods.

Various palmprint recognition methods have been proposed and applied in security, particularly authentication. However, improving the performance of palmprint recognition with insufficient training samples per person is still a challenging task. The undersampling problem limits the application and popularization of palmprint recognition. In this article, by regularly sampling different local regions of the palmprint image, we learn complete and discriminative convolution features by using deep convolutional neural networks (DCNNs). With this powerful palmprint description, a joint constrained least-square regression (JCLSR) framework, which performs representation for each local region of the same palmprint image requiring all regular local regions of the palmprint image to have similar projected target matrices, is presented to exploit the commonality of different patches. The proposed method can well solve the undersampling classification problem in palmprint recognition. Experiments were conducted on the IITD, CASIA, noisy IITD, and PolyU multispectral palmprint databases. It can be seen from the experimental results that the proposed JCLSR consistently outperformed the classical palmprint recognition methods and some subspace learning-based methods for palmprint recognition.

In multi-label learning, feature selection is a topical issue for addressing high-dimension data. However, most of existing methods adopt imperfect labels to perform feature selection. Although some graph-based multi-label feature selection methods are proposed to deal with the problem, they adopt the fixed graph Laplacian matrix so that the performances of these models are under-performing. To this end, this paper proposes a Dynamic Subspace dual-graph regularized Multi-label Feature Selection method named DSMFS. DSMFS decomposes the original label space into a low-dimensional subspace, and then both the dynamic label-level subspace graph and the feature-level graph are used to obtain a high-quality label subspace to conduct feature selection process. Seven state-of-the-art methods are compared to the proposed method on twelve multi-label benchmark data sets in the experiments. Experimental results demonstrate the superiority of DSMFS.

Due to the difficulty and time-consuming of labeling ground truth map in practical situations, unsupervised multiple change detection (MCD) for multispectral images (MSIs) have attracted much attention in recent years. One possible strategy to obtain multiple changes is to assign labels to the binary change result. However, some methods are difficult to obtain the accurate binary result because of the complexity of backgrounds; moreover, assigning labels is also a challenge owing to the limitation of the number of spectral channels in MSIs. Therefore, we propose a novel unsupervised MCD framework based on auto-updating multitemporal matrix factorization (AMMF) and spatiospectral channel augmentation (SSCA). In AMMF, the accurate binary change result can be detected based on joint matrix factorization, during which the distribution and subspace information of each temporal image are regularized to encode the spatiotemporal correlation. In SSCA, some novel augmentation strategies are introduced to increase the number of channels in MSIs to form the normalized high-dimensional maps for each temporal image based on nonlinear operations and convolutional sparse analysis, respectively. MCD can be achieved by integrating the binary change result and directional information that can be calculated by high-dimensional maps of different temporal images. Experiments are conducted on two real MSIs, indicating that the proposed framework performs well in detecting multiple changes.

Factors such as insufficient training samples, high-dimensional data features, and unbalanced data classes can degrade the accuracy of hyperspectral classification. To this end, this paper proposes an iterative spatial-spectral training sample augmentation (ITSA) algorithm and a new classification model incorporating maximum marginal projection (ITSA-MMP). First, ITSA iteratively augments samples by a similar region clustering strategy (SRCS) integrating spatial-spectral metric. Then, box-plot for representative sample selection (BPRSS) is adopted to screen optimal samples for the final augmented sample set (ASS). Next, based on the ASS, MMP projects the hyperspectral image into a low-dimensional subspace to explore the local structure of the data manifold and improve the inter-class separability of the data. Finally, the MMP-reduced data is classified by support vector machine. Experiments on two real hyperspectral datasets validate that ITSA-MMP can effectively increase the training sample set especially for small initial sample set and unbalanced dataset, and obtain a higher classification accuracy.

The Random Subspace Method (RSM) is an ensemble procedure in which each constituent learner is constructed using a randomly chosen subset of the data features. Regression trees are ideal candidate learners in RSM ensembles. By constructing trees upon different feature subsets, RSM reduces correlation between trees resulting in a stronger ensemble. Furthermore, it lessens computational burden by only considering a subset of the features when building each tree. Despite its apparent advantages, RSM has a notable drawback. In some instances a randomly chosen subspace may lack informative features. This is especially true in situations in which the number of truly informative variables is small relative to the total number of variables. Trees that are constructed using feature subsets lacking informative features can be damaging to the ensemble. Here we present Grafted Random Subspaces (GRS) and Vanishing Random Subspaces (VRS), two novel ensemble procedures designed to remedy the aforementioned drawback by reusing information across trees. Both techniques borrow from RSM by growing individual trees on randomly selected feature subsets. For each tree in a GRS ensemble, the most important variable is identified and guaranteed inclusion into the next q feature subsets. This allows GRS to recycle a promising feature from one tree across several successive trees, effectively grafting the variable into the next q active subsets. In the VRS procedure the least important feature is guaranteed exclusion from the next q feature subsets. This creates a more enriched pool of candidate variables from which the successive feature subsets are drawn.

In the context of constant--dimension subspace codes, an important problem is to determine the largest possible size $A_q(n, d; k)$ of codes whose codewords are $k$-subspaces of $\mathbb{F}_q^n$ with minimum subspace distance $d$. Here in order to obtain improved constructions, we investigate several approaches to combine subspace codes. This allow us to present improvements on the lower bounds for constant--dimension subspace codes for many parameters, including $A_q(10, 4; 5)$, $A_q(12, 4; 4)$, $A_q(12, 6, 6)$ and $A_q(16, 4; 4)$., 17 pages; construction for A_(10,4;5) was flawed

Artifact Subspace Reconstruction (ASR) is a machine learning technique widely used to remove non-brain signals (referred to as “artifacts”) from electroencephalograms (EEGs). The ASR algorithm can, however, be constrained by the limited memory available on portable devices. To address this challenge, we propose a Hardware-Oriented Memory-Limited Online ASR (HMO-ASR) algorithm. The proposed HMO-ASR algorithm consists of (1) two-level window-based preprocessing including PCA-based and z-score-based preprocessing to clean the data in each window, (2) iterative mean, standard deviation, and covariance update using a parallel algorithm to achieve window-based processing, and (3) early eigenvector matrix determination to save the computation. With the three schemes, the HMO-ASR method can be implemented on mobile devices, application-specific integrated circuits (ASICs) or field programmable gate arrays (FPGAs) with limited memory. The study results showed that the proposed HMO-ASR algorithm can achieve comparable performance to those obtained by the offline ASR algorithm with a 98.64% reduction in memory size. An FPGA implementation is used for silicon proof of the proposed HMO-ASR algorithm.

In this article, a data-driven design scheme of undetectable false data-injection attacks against cyber-physical systems is proposed first, with the aid of the subspace identification technique. Then, the impacts of undetectable false data-injection attacks are evaluated by solving a constrained optimization problem, with the constraints of undetectability and energy limitation considered. Moreover, the detection of designed data-driven false data-injection attacks is investigated via the coding theory. Finally, the simulations on the model of a flight vehicle are illustrated to verify the effectiveness of the proposed methods.

Noise in hyperspectral images (HSIs) may degrade the HSI classification result. Robust principal component analysis (RPCA) is an excellent method to obtain low-rank (LR) representation of data and is widely used in image denoising and also in HSI classification. However, data are drawn as a union from multiple subspaces in HSIs, so LR subspace estimation (LRSE) is necessary when using RPCA, which is complicated and time-consuming. To solve this problem, this letter proposes a novel LR-based method for HSI classification called two-branch network combined with RPCA, which combines RPCA with a neural network. Specifically, both the LR component and the sparse component are preserved and used for feature extraction in two independent convolutional branches. This way, we can avoid information loss without using accurate LRSE. A concatenate operation and a pointwise convolution are then adopted to realize the feature fusion. Finally, fused features are constructed to indicate the ground truth of each pixel in the classification process. The proposed method constructs a convenient model for HSI classification by discarding the LRSE and combining denoising, feature extraction, feature fusion, and classification into an end-to-end network. The experimental results on three data sets demonstrate that the proposed method outperforms many state-of-the-art methods including ones based on LR representation and ones based on deep learning. In addition, it maintains good classification performance for the cases of small samples and class imbalance.

This article proposes a hybrid signal injection-based maximum torque per ampere (MTPA) control for dual three-phase permanent magnet synchronous machines (PMSMs). The proposed method consists of a real dc current injection in the harmonic subspace and a virtual ac current injection in the fundamental subspace. The real dc current injection in the harmonic subspace does not impact the average torque production, and induced losses are small enough to be neglected. In the meantime, to guarantee the accuracy of the proposed MTPA method, a novel machine parameter estimation scheme considering voltage source inverter nonlinearity effects is proposed in this article, which can track the variation of $q_{1}$ -axis inductance and resistance accurately. Therefore, the proposed method only requires command voltages and currents in the torque model, and the variations of machine parameters are compensated by the proposed parameter estimation scheme. As the command voltages have correspondence with the variations of machine parameters, the magnetic saturation and temperature effects have been taken into account. The proposed method is validated by simulations and experimental results under various torque, speed, and temperature conditions. Additionally, the accuracy of the proposed method is validated, and its performance is proven to be superior through comparison of the derived results with those obtained from various existing methods.

In this letter, a convolutional sparsity regularization (CSR) is introduced into the framework of nonlinear iterative methods for solving inverse scattering problems (ISPs). The permittivity image of scatterers is sparsely represented in a convolutional form with pre-learned dictionary filters. The CSR is then incorporated with the subspace-based optimization method (SOM), termed as (SOM-CSR), to reconstruct the target image as a sparse coding by dictionary filters. The whole optimization function of SOM-CSR is solved using an alternative iteration method. Both synthetic and experimental data are employed to validate the effectiveness of the proposed SOM-CSR method. The results demonstrate that the CSR, as a structural constraint, is beneficial to nonlinear iterative reconstruction methods for solving ISP in contrast to pixel-based inversion.

The ever-increasing spectral resolution of hyperspectral images (HSIs) is often obtained at the cost of a decrease in the signal-to-noise ratio of the measurements, thus calling for effective denoising techniques. HSIs from the real world lie in low-dimensional subspaces and are self-similar. The low dimensionality stems from the high correlation existing among the reflectance vectors, and self-similarity is common in real-world images. In this article, we exploit the above two properties. The low dimensionality is a global property that enables the denoising to be formulated just with respect to the subspace representation coefficients, thus greatly improving the denoising performance and reducing the computational complexity during processing. The self-similarity is exploited via a low-rank tensor factorization of nonlocal similar 3-D patches. The proposed factorization hinges on the optimal shrinkage/thresholding of the singular value decomposition (SVD) singular values of low-rank tensor unfoldings. As a result, the proposed method is user friendly and insensitive to its parameters. Its effectiveness is illustrated in a comparison with state-of-the-art competitors. A MATLAB demo of this work is available at https://github.com/LinaZhuang for the sake of reproducibility.

Transient electromagnetic method (TEM) is one of the major tools to image the subsurface resistivity. The gradient-based inversion of TEM data only provides a unique solution using a subjectively defined regularization penalty, leaving the uncertainty of the solution unaddressed. The Bayesian method can be used to estimate the model parameters, as well as quantify their uncertainty. However, it requires far higher computational costs than gradient-based inversion, which limits the Bayesian inversion of TEM data to 1-D assumptions. We propose an accelerated Bayesian method based on Markov chain Monte Carlo (MCMC) subposteriors to perform full 2-D inversion of TEM data. A robust scheme is designed to divide the model space of a TEM profile into subspaces so that independent MCMC chains can be used to update the parameters in each subspace in parallel. The division is based on the coverage of the source loops using a cumulative sensitivity matrix. Then, the subposteriors obtained at each subspace are merged to approximate the full posterior of the model space using a weighting strategy. A numerical test of a 2-D valley model is used to validate the proposed method. The Bayesian inversion successfully obtained posterior that converges to the true model. The median model makes a good inference of the model parameters, while the probability density function gives their uncertainty estimates. The statistical model of interest can be further extracted from the model ensemble. The proposed method provides an effective framework for Bayesian inversion of TEM data with a multidimensional forward operator.

We present a parallel data-driven strategy to identify finite-dimensional functional spaces invariant under the Koopman operator associated to an unknown dynamical system. We build on the Symmetric Subspace Decomposition (SSD) algorithm, a centralized method that under mild conditions on data sampling provably finds the maximal Koopman-invariant subspace and all Koopman eigenfunctions in an arbitrary finite-dimensional functional space. A network of processors, each aware of a common dictionary of functions and equipped with a local set of data snapshots, repeatedly interact over a directed communication graph. Each processor receives its neighbors' estimates of the invariant dictionary and refines its estimate by applying SSD with its local data on the intersection of the subspaces spanned by its own dictionary and the neighbors' dictionaries. We identify conditions on the network topology to ensure the algorithm identifies the maximal Koopman-invariant subspace in the span of the original dictionary, characterize its time, computational, and communication complexity, and establish its robustness against communication failures.

This paper studies the Schatten-q error of low-rank matrix estimation by singular value decomposition under perturbation. We specifically establish a perturbation bound on the low-rank matrix estimation via a perturbation projection error bound. Then, we establish lower bounds to justify the tightness of the upper bound on the low-rank matrix estimation error. We further develop a user-friendly sinΘ bound for singular subspace perturbation based on the matrix perturbation projection error bound. Finally, we demonstrate the advantage of our results over the ones in the literature by simulation.

Semi-supervised learning is dedicated to solving the problem of poor model performance caused by the scarcity of labeled samples. Co-training algorithm, as a representative of semi-supervised learning algorithms, through constructing the diversity of classifiers, is used to solve the shortage of label samples that leads to low classifier accuracy. However, traditional Co-training style algorithms have strong constraints: (1) there are multiple views of data, and (2) the randomness of data views is relatively large, which leads to the low stability of the Co-training style algorithms. To optimize and solve the shortcomings of traditional Co-training style algorithms, a novel Co-training method based on sub-Kmeans named Op-FSCO is proposed. The proposed approach uses an optimal subspace construct method to extend Co-training to single-view data, greatly improving the application field of Co-training style algorithm. The clustering subspace is generated by plotting the probability of the correlation between the feature and the mutual information measure between the feature and the class label. For the resulting cluster subspace, the top two are selected to construct different views. Finally, experiments on a synthetic dataset, UCI dataset, and real-world dataset demonstrate that the proposed approach is more effective than other Co-training style algorithms. On the UCI benchmark dataset, the performance of the Op-FSCO algorithm on 15 UCI datasets is significantly better than the traditional Co-training algorithm. And on the cere bral stroke dataset, our approach is 2%–5% higher than that of traditional Co-training style algorithms.

Effectively recognizing different sceneries with complex backgrounds and varied lighting conditions plays an important role in modern AI systems. Competitive performance has recently been achieved by the deep scene categorization models. However, these models implicitly hypothesize that the image-level labels are 100% correct, which is too restrictive. Practically, the image-level labels for massive-scale scenery sets are usually calculated by external predictors such as ImageNet-CN. These labels can easily become contaminated because no predictors are completely accurate. This article proposes a new deep architecture that calculates scene categories by hierarchically deriving stable templates, which are discovered using a generative model. Specifically, we first construct a semantic space by incorporating image-level labels using subspace embedding. Afterward, it is noticeable that in the semantic space, the superpixel distributions from identically labeled images remain unchanged, regardless of the image-level label noises. On the basis of this observation, a probabilistic generative model learns the stable templates for each scene category. To deeply represent each scenery category, a novel aggregation network is developed to statistically concatenate the CNN features learned from scene annotations predicted by HSA. Finally, the learned deep representations are integrated into an image kernel, which is subsequently incorporated into a multiclass SVM for distinguishing scene categories. Thorough experiments have shown the performance of our method. As a byproduct, an empirical study of 33 SIFT-flow categories shows that the learned stable templates remain almost unchanged under a nearly 36% image label contamination rate.

This letter is on observability of discrete-time LTI systems under unknown piece-wise constant inputs with sufficiently slow, but arbitrary update times. Assuming knowledge of the update times, we characterize the unobservable subspace and show that with sufficiently many measurements in each inter-update interval of the input, the unobservable subspace remains fixed. We explore the implications of the result for privacy in event-triggered control through an illustrative example.

Data classification is usually challenged by the difficulty and/or high cost in collecting sufficient labeled data, and unavoidability of data missing. Besides, most of the existing algorithms belong to centralized processing, in which all of the training data must be stored and processed at a fusion center. But in many real applications, data are distributed over multiple nodes, and cannot be centralized to one node for processing due to various reasons. Considering this, in this article, we focus on the problem of distributed classification of missing data with a small proportion of labeled data samples, and develop a distributed semi-supervised missing-data classification (dS²MDC) algorithm. The proposed algorithm is a distributed joint subspace/classifier learning, that is, a latent subspace representation for missing feature imputation is learned jointly with the training of nonlinear classifiers modeled by the χ² kernel using a semi-supervised learning strategy. Theoretical performance analysis and simulations on several datasets clearly validate the effectiveness of the proposed dS²MDC algorithm from different perspectives.

In the practical applications of supervised learning methods, the high cost of obtaining labeled data for learning tasks is a critical problem. One promising research area for solving the problem is transfer learning, which aims to learn a task in target domain by utilizing the training data in a different but related source domain. In this paper, we propose a novel heterogeneous transfer learning algorithm called Heterogeneous Daily Living Activity Learning (HDLAL) which derives domain invariant feature representation space from cross-domain data distributions by projecting both domain data into the derived space in the close proximity of each other using Maximum Mean Discrepancy. Within the new feature space, we utilize ensemble classification algorithm to train multi-label classifier using the projected data to predict the labels in the target domain. We show the effectiveness of our approach by experimenting on real-world smart home datasets. The results shows that our HDLAL algorithm outperforms the common direct learning approaches in the context of predicting labels of activities of daily living (ADL.

Recent years have witnessed the rapid development of face image hallucination techniques. However, the previous face hallucination methods are unsupervised and ignore the label information of training samples, leading to undesirable results. This article proposes a locality-constrained and category embedding representation (LCER) method to super-resolve face image in a supervised manner by embedding the label information in data representation. The proposed LCER incorporates the locality prior and category information into one unified framework, which aims to learn both the advantages of locality in preserving the true typologic structure of data manifold and the discriminability in exposing the class subspace information. Such strategy allows the LCER not only to preserve more sharpen image details but also to guarantee the face structure pattern be transferred mainly from the same subject in super-resolution reconstruction. Extensive experiments were conducted to evaluate the proposed LCER, and the comparative results demonstrate that it achieved superior face hallucination performance in both the quantitative measurements and visual impressions compared to several state-of-the-art.

In this paper, we address the issues of the trade-off between QoS and QoE with an analytical analysis based on mathematical modeling under a unified normalization measurement. We model through computation the awareness of QoS and QoE with a strategy of quality-aware QoE-QoS coordination. A balanced coordination is proposed using modeling correlations between user experience and service performance. The main contributions of this paper include three main parts. First, a comprehensive mapping is modeled in a close form to illustrate the analytic correlations between QoS, QoE, and data communication. Second, an analytical method to analyze and coordinate the nonlinear trade-off between QoE and QoS is proposed based on the theoretical proof with discussions on necessary-sufficient conditions. Third, an algorithmic framework is provided to perform QoE-QoS coordination based on quality-awareness computing with a test proof. An assessment model for user experience quantification is built with the mean opinion score (MOS) test. Quality-aware QoE and QoS models are built based on the subspace learning strategy. Simulations are given to prove the feasibility and effectiveness of the proposed method. The results show that the operations with the proposed solution can be obtained analytically with balanced efficiency in both user experience performance and network performance.

Polarons play a vital role for many energy-conversion and storage processes; it is accordingly imperative to understand their system-specific formation and reactivity. In first-principles simulatio...

As we all know, the model mismatch, primarily when the desired signal exists in the training data, or when the sample data is used for training, will seriously affect algorithm performance. This paper combines the subspace algorithm based on direction of arrival (DOA) estimation with the adaptive beamforming. It proposes a reconstruction algorithm based on the interference plus noise covariance matrix (INCM). Firstly, the eigenvector of the desired signal is obtained according to the eigenvalue decomposition of the subspace algorithm, and the eigenvector is used as the estimated value of the desired signal steering vector (SV). Then the INCM is reconstructed according to the estimated parameters to remove the adverse effect of the desired signal component on the beamformer. Finally, the estimated desired signal SV and the reconstructed INCM are used to calculate the weight. Compared with the previous work, the proposed algorithm not only improves the performance of the adaptive beamformer but also dramatically reduces the complexity. Simulation experiment results show the effectiveness and robustness of the proposed beamforming algorithm.

Anomaly or outlier detection is consider as one of the vital application of data mining, which deals with anomalies or outliers. Anomalies are considered as data points that are dramatically different from the rest of the data points. In this survey, we comprehensively present anomaly detection algorithms in an organized manner. We begin this survey with the definition of anomaly, then provide essential elements of anomaly detection, such as different types of anomaly, different application domains, and evaluation measures. Such anomaly detection algorithms are categorized in seven categories based on their working mechanisms, which includes total of 52 algorithms. The categories are anomaly detection algorithms based on statistics, density, distance, clustering, isolation, ensemble and subspace. For each category, we provide the time complexity of each algorithm and their general advantages and disadvantages. In the end, we compared all discussed anomaly detection algorithms in detail.

Chemometric multivariate analysis based on low-dimensional linear and bilinear data modelling is presented as a fast and interpretable alternative to more fancy “AI” for practical use of Big Data streams from hyperspectral “video” cameras. The purpose of the present illustration is to find, quantify and understand the various known and unknown factors affecting the process of drying moist wood. It involves an “interpretable machine learning” that analyses more than 350 million absorbance spectra, requiring 418 GB of data storage, without the use of black box operations. The 159-channel high-resolution hyperspectral wood “video” in the 500–1005 nm range was reduced to five known and four unknown variation components of physical and chemical nature, each with its spectral, spatial and temporal parameters quantified. Together, this 9-dimensional linear model explained more than 99.98% of the total input variance.

In this paper, we devise a unitary noise subspace fitting method for monostatic multiple-input multiple-output radar, which can obtain high-resolution direction-of-arrival (DOA) estimation with non-orthogonal waveforms. Firstly, the cross-covariance matrix without spatially colored noise can be obtained by the spatial cross-correlation technique of two transmit subarrays. Secondly, unitary transformation is introduced to convert the singular value decomposition from the complex-valued matrix to the real-valued matrix. Finally, DOAs are achieved by solving the optimization problem. Some numerical simulation results confirm the effectiveness and superiority of the proposed approach, which can provide higher angular resolution, more accurate estimation performance and low computational cost.

Purpose: To develop a cardiac T1 mapping method for free-breathing 3D T1 mapping of the whole heart at 3T with transmit B1 (B1+) correction Methods: A free-breathing, ECG-gated inversion recovery sequence with spoiled gradient-echo readout was developed and optimized for cardiac T1 mapping at 3T. High-frame rate dynamic images were reconstructed from sparse (k,t)-space data acquired along a stack-of-stars trajectory using a subspace-based method for accelerated imaging. Joint T1 and flip-angle (FA) estimation was performed in T1 mapping to improve its robustness to B1+ inhomogeneity. Subject-specific timing of data acquisition was utilized in the estimation to account for natural heart-rate variations during the imaging experiment. Results: Simulations showed that accuracy and precision of T1 mapping can be improved with joint T1 and FA estimation and optimized ECG-gated SPGR-based IR acquisition scheme. The phantom study showed good agreement between the T1 maps from the proposed method and the reference method. 3D cardiac T1 maps (40 slices) were obtained at a 1.9 mm in-plane and 4.5 mm through-plane spatial resolution from healthy subjects (n=6) with an average imaging time of 14.2 +- 1.6 min (heartbeat rate: 64.2 +- 7.1 bpm), showing myocardial T1 values comparable to those obtained from MOLLI. The proposed method generated B1+ maps with spatially smooth variation showing 21-32% and 11-15% variations across the septal-lateral and inferior-anterior regions of the myocardium in the left ventricle. Conclusion: The proposed method allows free-breathing 3D T1 mapping of the whole-heart with transmit B1 correction in a practical imaging time., Comment: 33 pages, 10 figures, 3 supplementary figures, 1 supplementary table

[EN[ In this work, a new mathematical algorithm for sparse and orthogonal constrained biplots, called CenetBiplots, is proposed. Biplots provide a joint representation of observations and variables of a multidimensional matrix in the same reference system. In this subspace the relationships between them can be interpreted in terms of geometric elements. CenetBiplots projects a matrix onto a low-dimensional space generated simultaneously by sparse and orthogonal principal components. Sparsity is desired to select variables automatically, and orthogonality is necessary to keep the geometrical properties that ensure the biplots graphical interpretation. To this purpose, the present study focuses on two different objectives: 1) the extension of constrained singular value decomposition to incorporate an elastic net sparse constraint (CenetSVD), and 2) the implementation of CenetBiplots using CenetSVD. The usefulness of the proposed methodologies for analysing high-dimensional and low-dimensional matrices is shown. Our method is implemented in R software and available for download from https://github.com/ananieto/SparseCenetMA., Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. This work was not supported by any grant., Publicación en abierto financiada por el Consorcio de Bibliotecas Universitarias de Castilla y León (BUCLE), con cargo al Programa Operativo 2014ES16RFOP009 FEDER 2014-2020 DE CASTILLA Y LEÓN, Actuación:20007-CL - Apoyo Consorcio BUCLE

The article focuses on the dynamic identification and finite element (FE) modelling of a butterfly-arch stress-ribbon pedestrian bridge in Fuzhou, Fujian, China. The Stochastic Subspace Identificat...

Due to sensor drift, instrumental variation, or change of measurement object, the distributions of the datasets (domains) acquired by the sensors are often different. A domain adaptive framework called MCSP-SSS is proposed to reduce the distribution discrepancy across domains for high-accuracy sensor data classification. The framework consists of two key parts: Multi-Constraint Subspace Projection (MCSP) and Source Sample Selection (SSS). MCSP is a subspace-projection-based approach, which introduces four constraints to get an optimized projection matrix: Principal Component Analysis (PCA) is used to reduce the redundancy of features; Mean Distribution Discrepancy (MDD) is applied to minimize the difference between source and target data; Hilbert-Schmidt Independence Criterion (HSIC) is adopted to maximizing the dependence between features and labels; A so-called weighted-within-class scatter matrix is introduced to minimize the within-class variance to avoid samples with different labels to overlap in the subspace. SSS is designed to remove the outliers in projected source samples so as to reduce distribution discrepancy between the source and target samples projected by MCSP. Experimental results show that our framework can achieve the best accuracies in all classification tasks in comparison with other state-of-the-art approaches. The accuracy of MCSP-SSS is 3.57 percentage points (pps) higher on average than that of the second best approach for single-source domain adaptation, and 7.00 pps for multi-source domain adaptation. Source code is available at https://github.com/threedteam/tsc_subspace_projection .

This paper analyzes the subspace trail of Midori-64 and uses the propagation law and mutual relationship of the subspaces of Midori-64 to provide a 6-round Midori-64 subspace trail-based impossible differential key recovery attack. The data complexity of the attack is 2 54.6 chosen plaintexts, and the computational complexity is 2 58.2 lookup operations. Its overall complexity is less than that of the known 6-round truncated impossible differential distinguisher. This distinguisher is also applicable to Midori-128 with a secret S -box. Additionally, utilizing the properties of subspaces, we prove that a subspace trail-based impossible differential distinguisher of Midori-64 contains at most 7 rounds. This is 1 more than the upper bound of Midori-64’s truncated impossible differential distinguisher which is 6. According to the Hamming weights of the starting and ending subspaces, we classify all 7-round Midori-64 subspace trail-based impossible differential distinguishers into two types and they need 2 59.6 and 2 51.4 chosen plaintexts, respectively.

Multi-label transfer learning aiming to learn robust classifiers for the target domain by leveraging knowledge from a source domain has been received considerable attention recently. The core part of such research is similarity measurement. Nevertheless, the existing similarity measurement functions of probability distributions are still too simple to fully describe the similarity of probability distributions.. In order to address this problem, we propose a Multi-label Transfer Learning Via Latent Graph Alignment (G-MLTL). G-MLTL uses subspace learning to make the feature distribution of the target domain consistent with the source domain. At the same time, G-MLTL decomposes the label matrix to ensure data points sharing the same labels to have identical latent semantic representation in the new reconstruction space. The proposed G-MLTL also focuses on directly utilizing Latent Graph Alignment to guide the knowledge transfer process. Extensive experiments demonstrate that G-MLTL significantly outperforms the existing multi-label transfer learning methods. Especially when the number of labels is more than four, the mean Average Precision of G-MLTL is higher than the baseline algorithm by 2.1-10.5%.

PurposeThe present study aims to construct ensemble machine learning (EML) algorithms for groundwater potentiality mapping (GPM) in the Teesta River basin of Bangladesh, including random forest (RF) and random subspace (RSS).Design/methodology/approachThe RF and RSS models have been implemented for integrating 14 selected groundwater condition parametres with groundwater inventories for generating GPMs. The GPM were then validated using the empirical and bionormal receiver operating characteristics (ROC) curve.FindingsThe very high (831–1200 km2) and high groundwater potential areas (521–680 km2) were predicted using EML algorithms. The RSS (AUC-0.892) model outperformed RF model based on ROC's area under curve (AUC).Originality/valueTwo new EML models have been constructed for GPM. These findings will aid in proposing sustainable water resource management plans.