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As a powerful coding strategy for superpixels in synthetic aperture radar (SAR) images, Fisher vector (FV) lies in a low-dimensional subspace and can be sparsely represented as a linear combination of training samples. The existing ship detection methods based on FVs often consider the Euclidean distances between target FVs and clutter FVs, where the subspace features of FVs are generally not exploited. In this article, we propose a new ship detection algorithm based on nonnegative sparse locality-representation (NSLR) to exploit the subspace features of FVs. The proposed NSLR method is based on the assumption that FVs of superpixels in SAR images are sparsely represented by the dictionary of background sea clutter only under a null hypothesis. In addition, we propose two FV-based filters to enhance the robustness of our newly developed NSLR to heterogeneous sea clutter environments by further exploiting the intrinsic features of ship targets in terms of intensity and spatiality. The experimental results based on Gaofen-3 SAR images demonstrate that the proposed NSLR detection method provides higher target-to-clutter contrast and achieves better detection performance than other commonly used ship detection algorithms.

This paper will present a model-based methodology for implementing an embedded, data-driven, subspace predictive controller. The control algorithm captures, in real-time, the characteristics of the plant and self-tunes through process modifications. A data-driven subspace approach is used, in which predictors are calculated directly from input and output data projections. Coding and performance aspects are discussed and tested in Model-In-the-Loop, Software-In-the-Loop and real application.

We find an expression for Gateaux derivative of the $C^*$-algebra norm. This gives us alternative proofs or generalizations of various known results on the closely related notions of subdifferential sets, smooth points and Birkhoff-James orthogonality for spaces $\mathscr B(\mathcal H)$ and $C_b(��)$. We also obtain an expression for subdifferential sets of the norm function at $A\in\mathscr B(\mathcal H)$ and a characterization of orthogonality of an operator $A\in\mathscr B(\mathcal H, \mathcal K)$ to a subspace, under the condition $dist(A, \mathscr K(\mathcal H))< \|A\|$ and $dist(A, \mathscr K(\mathcal H, \mathcal K))< \|A\|$ respectively.

Kinship verification using single image of a person is a challenging task for real-world applications. In this paper, we propose a novel robust discriminative feature subspace analysis (RDFSA) method to address single sample per person (SSPP) problem in kinship verification. The proposed RDFSA method takes advantages of facial symmetry and patch-based analysis to extract discriminative features for kinship verification. Each face image is firstly divided into two halves about bilateral symmetry axis, and each halved face is then partitioned into equal sized non-overlapping patches. Multiple image-sets are formed by grouping these patches according to their positions at each halved face. Then, an SSPP is formulated as an RDFSA problem and a feature subspace is learned by maximizing inter-class separation and minimizing intra-class variance for different patches in each image-set. For a given test image pair, similarity is computed for each feature subspace and majority voting strategy is employed to determine if a given image pair is kin related or not. Proposed RDFSA method is extensively evaluated on different publicly available kinship datasets to validate kinship accuracy. Experimental results show that RDFSA achieves competitive accuracy on all kinship datasets while performing kinship verification under unconstrained environment.

Over the past decades, the increasing penetration of distributed energy resources (DERs) has dramatically changed the power load composition in the distribution networks. The traditional static and dynamic load models can hardly capture the dynamic behavior of modern loads especially for fault-induced delayed voltage recovery (FIDVR) events. Thus, a more comprehensive composite load model with combination of static load, different types of induction motors, single-phase A/C motor, electronic load and DERs has been proposed by Western Electricity Coordinating Council (WECC). However, due to the large number of parameters and model complexity, the WECC composite load model (WECC CMLD) raises new challenges to power system studies. To overcome these challenges, in this paper, a cutting-edge parameter reduction (PR) approach for WECC CMLD based on active subspace method (ASM) is proposed. Firstly, the WECC CMLD is parameterized in a discrete-time manner for the application of the proposed method. Then, parameter sensitivities are calculated by discovering the active subspace, which is a lower-dimensional linear subspace of the parameter space of WECC CMLD in which the dynamic response is most sensitive. The interdependency among parameters can be taken into consideration by our approach. Finally, the numerical experiments validate the effectiveness and advantages of the proposed approach for WECC CMLD model.

Superpixel segmentation aims at dividing the input image into some representative regions containing pixels with similar and consistent intrinsic properties, without any prior knowledge about the shape and size of each superpixel. In this paper, to alleviate the limitation of superpixel segmentation applied in practical industrial tasks that detailed boundaries are difficult to be kept, we regard each representative region with independent semantic information as a subspace, and correspondingly formulate superpixel segmentation as a subspace clustering problem to preserve more detailed content boundaries. We show that a simple integration of superpixel segmentation with the conventional subspace clustering does not effectively work due to the spatial correlation of the pixels within a superpixel, which may lead to boundary confusion and segmentation error when the correlation is ignored. Consequently, we devise a spatial regularization and propose a novel convex locality-constrained subspace clustering model that is able to constrain the spatial adjacent pixels with similar attributes to be clustered into a superpixel and generate the content-aware superpixels with more detailed boundaries. Finally, the proposed model is solved by an efficient alternating direction method of multipliers (ADMM) solver. Experiments on different standard datasets demonstrate that the proposed method achieves superior performance both quantitatively and qualitatively compared with some state-of-the-art methods., Accepted by IEEE Transactions on Industrial Informatics, 2020

Cross-scene classification is one of the major challenges for hyperspectral image (HSI) classification, especially for target scenes without label samples. Most traditional domain adaptive methods learn a domain invariant subspace to reduce statistical shift while ignoring the fact that there may not exist a shared subspace when marginal distributions of source and target domains are very different. In addition, it is important for HSI classification to preserve discriminant information in the original space. To solve this issue, discriminative cooperative alignment (DCA) of subspace and distribution is proposed to cooperatively reduce the geometric and statistical shift. In the proposed framework, both geometrical and statistical alignments are considered to learn subspaces of the two domains with preserving discrimination information. Furthermore, a reconstruction constraint is imposed to enhance the robustness of subspace projection. Experimental results on three cross-scene HSI data sets demonstrate that the proposed DCA is significantly better than some state-of-the-art domain-adaptive approaches.

To achieve a better tradeoff between the direction-of-arrival (DOA) estimation resolution and complexity compared to the existing sparse array based estimators, this letter proposes a pseudo noise subspace based DOA estimator for an unfolded coprime linear array (UCLA). On one hand, by unfolding the two subarrays of a general coprime linear array (CLA), the UCLA acquires a larger aperture, giving rise to a higher angular resolution. On the other hand, a mapping relationship is explored to convert the original noise subspace into the pseudo noise subspace (in the Nyquist spatial sampling sense), from which the DOAs can be accurately estimated by root-MUSIC method instead of exhaustive peak searching, thereby reducing the complexity. Numerical results also confirm this superiority over other sparse array based estimators.

In this paper, a novel indoor localization system with channel state information (CSI) fingerprints is proposed, which learns the spatial and frequency features of CSI in the fifth-generation (5G) cellular network by a Siamese convolution neural network. In particular, considering that the CSI continuously collected by a moving target possesses the implicit spatial association, we locate the target by the successive CSI data gathered within a time interval which can be regarded as an information subspace of the fingerprint database. Therefore, the fingerprint localization can be modeled as a subspace matching problem and solved by the Siamese network-based similarity learning. In the proposed system, we design a structure of CSI fingerprint which includes the information from multiple base stations in spatial and frequency domains. Then, the proposed Siamese architecture extracts the CSI feature and estimates the location of the target by feature similarity comparison. Compared with the existing algorithms, it can increase the positioning accuracy significantly by the feature relevance among the CSI data collected at different positions. The field tests indicate that compared to other CSI fingerprint-based positioning methods, our proposed algorithm can effectively reduce the localization error.

This study considers the problem of text-based person search, which aims to find the corresponding person of a given text description in an image gallery. Existing methods usually learn a similarity mapping of local parts between image and text, or embed the whole image and text into a unified embedding space. However, the relevance between local and the whole is largely underexplored. In this paper, we design a Divide-and-Merge Embedding (DME) learning framework for text-based person search. DME explicitly 1) models the relations between local parts and global embedding, 2) incorporates local details into global embedding. Specifically, we design a Feature Dividing Network (FDN) to embed the input into K locally guided semantic representations by self-attentive embedding, each representation depicts a local part of the person. Then, we propose a Relevance based Subspace Projection (RSP) method for merging diverse local representations to a compact global embedding. RSP helps the model to obtain discriminative embedding by jointly minimizing the redundancy of local parts and maximizing the relevance between local parts and global embedding. Extensive experimental results on three challenging benchmarks, i.e., CUHK-PEDES, CUB and Flowers datasets, have demonstrated the effectiveness of the proposed method.

One of the best options for managing energy markets and power system performance optimization is precise Electricity Price Forecasting (EPF). In detecting the prices of energy, some factors are of stochastic behavior which has made an unwieldy task. In this study, carrying out Tensor Canonical Correlation Analysis (TCCA) is the first activity to choose the operative parameters in EPF issues and removing redundant factors with low correlation ranks. The second activity is making use of a Deep Neural Network (DNN) with a novel Stacked Pruning Sparse Denoising Autoencoder (SPSDAE) to decrease the noise of data sets with different sources individually. The third activity is that a novel method which is called the Maximum Separation Subspace (MASES) in Sufficient Dimension Reduction (SDR) with Categorical Response. This method is used to detect the outstanding properties of the input data and removing the uncertainty characteristics. The new multi-modal combined (MMC) method is the final step that needs to be taken to predict the day-ahead (one day in advance) cost of electricity. The proposed method is investigated based on the data that were collected from Australia The combination of various predicting models and suggested methods might develop the function of predicting possibility by supplying divergent types of compactness performance. The combined model comprised of three predicting possibilities called beta circulation fitting, scattered Bayesian learning, core compactness prediction. Predicting data respectively are used as a yardstick to compare the efficiency of forecasted results and consequently assess the proposed method. Results of this study confirmed a decrease of effectual error criterion and accuracy enhancement in EPF field as the advantageous effects of this proposed SDR structure.

A fuzzy compactum in a space X is an upper semi-continuous map f : A → [ 0 , 1 ] from a nonempty compact subspace A ⊂ X to the unit closed interval [ 0 , 1 ] such that { x ∈ A : f ( x ) > 0 } is dense in A. In this paper, we investigate the topological structure of the space K e ( X ) of fuzzy compacta of a separable metric space X with the Hausdorff metric. In particular, we prove that K e ( X ) ≈ l 2 if X is an infinite, locally compact, locally connected, connected and separable metric space.

The Internet was designed to move data worldwide, and to do so in spite of disruptions from natural disasters, nuclear attacks, or other catastrophes. At first the goal was just to increase the volume of data moving over networks. But with the rising importance of real-time applications like videoconferencing and online gaming, what now matters most is reducing latency—the time it takes to move data across the network.

In this letter, the problem of 2-D direction of arrival (DOA) estimation using uniform circular array (UCA) is addressed. The performance of the beamspace transform (BT) based algorithm is degraded when shrinking the quantity of antennas because the BT raises the residual error. To overcome this problem, we propose a 2-D compensation method. Firstly, we estimate the biased 2-D DOAs via UCA-ESPRIT algorithm. Secondly, the eigenvalue decomposition (EVD) of covariance matrix without the BT is conducted to extract the noise subspace in element space. Thereafter, inspired by the relationship that the steering vector is orthogonal to the noise subspace, the first-order Taylor expansion is performed for the direction matrix which is reconstructed by the biased DOA estimates. Finally, the offsets are compensated via least squares (LS). Compared to virtual array transformation methods, the proposed method possesses better estimation performance and needs less computation cost. Multiple simulation experiments are presented to verify the efficiency of the approach.

How to use multi-view data effectively has become one of the challenging problems in the computer vision community. The existing multi-view learning methods are mainly based on common subspace learning which aim to explore the discriminative information between multi-view data and find its potential common subspace. Most of the existing multi-view subspace learning methods rely on the within-class scatter matrix and between-class scatter matrix while capturing the discriminative information of multiple views. However, these methods just roughly minimize the within-class distance and maximize the between-class distance, and do not make full use of the intra-view and inter-view information. To address this problem, we propose a weighted common subspace learning method, which can effectively adjust the contribution ratio of between-class and within-class information through a weighted parameter, so that an optimized common subspace can be obtained. And we use the maximum scatter difference criterion as the metric of inter-view and intra-view after projection. Extensive experiments on the public data sets show the superiority of this method.

Traditional image recognition methods require abundant labelled images to learn robust recognition models, and only the images from the classes that appear in the training set (also called seen classes) can be recognized. Thus, determining how to recognize an image from a novel class (also called unseen class) is very challenging. Zero-Shot Learning (ZSL) is proposed to address the above issue. In this paper, we present a novel ZSL model called ZSL based on class prototype and dual latent subspace learning with reconstruction (ZSL-CPLSR). Aiming at the problems of domain shift and information loss, ZSL-CPLSR integrates generation and embedding into a unified framework in the inductive setting, which takes full advantage of the semantic information of unseen classes to alleviate the domain shift and learns more discriminative information with less effective information loss. We conduct comprehensive experiments on four benchmark datasets widely adopted in ZSL. The experimental results show the superiority of ZSL-CPLSR to the state-of-the-art ZSL methods, validating the effectiveness of ZSL-CPLSR.

This article presents a new approach to construct reduced-order models for large nonlinear circuits excited by periodical or quasi-periodical sources. The key feature in the constructed reduced model is that it enables, through solving a much smaller system, tracing the variations in the periodical steady-state response of the original circuit with regards to variations in selected design parameters. The proposed approach is based on the notion of using discrete empirical interpolation to project the nonlinear operator of the circuit equation onto a smaller subspace. In addition, the original system equations are projected onto the subspace spanned by the first few derivatives of the solution with respect to the selected design parameters. Computational savings are made possible through solving a reduced system of equations instead of the full system. Numerical examples are presented to validate the accuracy and efficiency of the proposed approach.

The problem of off-policy evaluation (OPE) has long been advocated as one of the foremost challenges in reinforcement learning. Gradient-based and emphasis-based temporal-difference (TD) learning algorithms comprise the major part of off-policy TD learning methods. In this work, we investigate the derivation of efficient OPE algorithms from a novel perspective based on the advantages of these two categories. The gradient-based framework is adopted, and the emphatic approach is used to improve convergence performance. We begin by proposing a new analogue of the on-policy objective, called the distribution-correction-based mean square projected Bellman error (DC-MSPBE). The key to the construction of DC-MSPBE is the use of emphatic weightings on the representable subspace of the original MSPBE. Based on this objective function, the emphatic TD with lower-variance gradient correction (ETD-LVC) algorithm is proposed. Under standard off-policy and stochastic approximation conditions, we provide the convergence analysis of the ETD-LVC algorithm in the case of linear function approximation. Further, we generalize the algorithm to nonlinear smooth function approximation. Finally, we empirically demonstrate the improved performance of our ETD-LVC algorithm on off-policy benchmarks. Taken together, we hope that our work can guide the future discovery of a better alternative in the off-policy TD learning algorithm family.

Traditional approaches that represent observations in vector or matrix notation easily lead to structure information losses and dependency destruction between elements. Tensors are the generalizations of matrices, providing a natural representation of rich structure in real-world multiway arrays. Although tensor decomposition has been verified and used in classification tasks, the heterogeneity gap among different orders is often neglected. In this paper, we exploited tensor decomposition framework and presented a heterogeneous tensor decomposition for robust classification (HTDRC) approach, which integrates nuclear and l 2 , 1 -norm for intrinsic representation learning. Specifically, to obtain the lowest-rank intrinsic representations of tensorial data from an underlying low-dimensional subspace, HTDRC simultaneously learns a set of orthogonality constrained factor matrices and a low-rank constrained representation matrix. To better guide the decomposition process, a robust discriminant feature selection scheme is utilized by imposing l 2 , 1 -norm penalty on the constructed classification loss and the regularized terms simultaneously. Experiments on four datasets demonstrated the superior performance of our proposed approach.

Recent studies have confirmed that attention mechanisms with location constraint strategy are helpful to reduce the misrecognition caused by incorrect alignments in attention-based end-to-end automatic speech recognition (E2E ASR) systems. The significant advantage of these mechanisms is that they consider the monotonicity of the alignment by employing a location constraint vector. This vector is directly obtained from historical attention scores for most such attention mechanisms. However, an unreasonable vector may become an additional interference when an inaccurate historical attention score occurs. Moreover, the subsequent process of attention scoring will be affected by the interference continuously. To address the problem, we obtain a reasonable location constraint vector from the matching relationship between the historical output information and the summary information, where the summary information includes content and temporal information about speech sequence. We further propose an enhanced location constrained attention mechanism, i.e., summary constrained (SC) attention mechanism, to generate the vector by a matching relationship-based neural network. We use a summary subspace embedding learned by a linear subspace projection to represent the summary information. Furthermore, considering the complementarity of the SC and typical location constrained attention mechanisms, a fused attention mechanism is used to generate a more reasonable vector by combining the two mechanisms. The SC and fused attention mechanisms-based E2E ASR systems were evaluated on a Switchboard conversational telephone speech recognition. The experimental results show that our mechanisms obtained the relative reductions of 10.6 % and 16.7 % in the word error rate compared with the baseline system.

In this paper, a thermodynamic mechanism-based key performance indicator (KPI) construction is proposed for the diesel engine turbocharging system, upon which the corresponding fault detection scheme is studied. To be specific, the efficiency of the turbocharger is first selected as the KPI and constructed by the thermodynamic mechanism. Based on this, the relation between the KPI and the measurable correlated variables is built as the KPI-related model. Then, the subspace identification approach is applied to identify the established model. By applying T 2 test statistic on the residual of the KPI-related model, a fault detection scheme is presented for system monitoring. Finally, the effectiveness of the proposed scheme is demonstrated on a simulation of the real turbocharger in the large ocean-going bulk carrier.

Linear codes with good parameters have wide applications in secret sharing schemes, authentication codes, association schemes, consumer electronics and communications, etc. During the past four decades, constructions of linear codes with good parameters received much attention and many classes of such codes were presented. In this paper, we obtain a family of linear codes with good parameters over $$\mathbb {F}_p$$ by exploring further properties of constant dimension subspace codes, where p is a prime. The weight distribution of three classes of linear codes presented in this family is determined. Most notably, three classes of linear codes presented in this family are distance-optimal with respect to the Griesmer bound. Also, this paper presents a sufficient and necessary condition for this family of linear codes to have a $$\lambda $$ -dimensional hull. In addition, we show that our linear codes can be used to construct secret sharing schemes with interesting access structures and strongly regular graphs.

We consider the subspace of the Schwartz space of rapidly decreasing infinitely differentiable functions on an unbounded closed convex set in a multidimensional real space equipped with the topology defined by a countable family of norms constructed with the help of a family of convex separately radial functions in ℝn. We describe the strong dual of this subspace in terms of the Fourier–Laplace transform of functionals.

A method for recursive subspace identification of continuous-time systems based on generalized Poisson moment functionals is proposed. Most of the existing subspace identification methods have concentrated mainly on the time-invariant discrete-time systems. The results of subspace identification methods are confined to the discrete-time cases, due to the difference on the construction of Hankel matrices. In addition, the time-invariant identification algorithms are not suitable for online identification cases. In order to solve the problems above, the time derivatives of Hankel matrices can be evaluated by generalized Poisson moment functionals, which provides a simple linear mapping for identification algorithm without the amplification of stochastic noises. The size of the data matrices is fixed a priori to fade the influence of old data to the updated data, which is a key to reduce computational burden and storage cost of recursive algorithms. The efficiency of the presented method is provided by comparing simulation results.

Heterogeneous domain adaptation (HDA) aims to adapt a trained model on a source domain with different input feature space to an unlabeled target domain. In fact, HDA is a challenging issue, since there exists feature and distribution discrepancies across domains. In this paper, we propose a novel approach named as heterogeneous domain adaptation with statistical distribution alignment and progressive pseudo label selection (SDA-PPLS). SDA-PPLS learns two projection matrices for source and target domains to map them into a latent subspace to have a shared feature space. Moreover, to mitigate the distribution gap, SDA-PPLS aligns both first-order and second-order statistical information, simultaneously, to improve the target classification model performance. In addition, to discriminate instances into distinct classes, SDA-PPLS aligns the class conditional distributions by pseudo label refinement of target domain data. Finally, to prevent the propagation of inaccurate pseudo labels to the next iteration, a progressive technique is proposed to select instances with higher probability. Experimental results on several real-word datasets on image to image, text to text and text to image tasks with different feature representations, demonstrate that the proposed method outperforms other state-of-the-art HDA methods.

In this article, we propose a novel deep framework termed local alignment deep network (LADN) for infrared-visible cross-modal person reidentification (IVCM ReID) in 6G-enabled IoT, which could meet the demands of all-day and real-time surveillance. The proposed LADN is designed as a two-stream structure, and it learns shallow interested feature maps and common subspace feature maps to reduce the gap between IR and RGB images. To overcome the challenge of pose and viewpoint variations of pedestrians, we learn the local features in the deep layers. We also propose the local alignment triplet loss (LAT) to align local features, which could capture the consistent local information via comparing noncorresponding local features in a certain range. Furthermore, we learn the global features to provide the global field of vision for the representation. The proposed LADN is optimized in an end-to-end way by combining different cross-modality losses. We evaluate the proposed method on two standard benchmark data sets, i.e., SYSU-MM01 and RegDB, and the results demonstrate the effectiveness of LADN.

This paper proposes an improved co-prime parallel array (CPPA) configuration for two-dimensional direction of arrival (2-D DOA) estimation. Specifically, the proposed array consists of a CPPA and two extra sensors along the vertical axis. The array aperture is extended through two steps. Firstly, a virtual parallel symmetric co-prime array (ViP-SCPA), consisting of two symmetric co-prime arrays(SCPAs), is constructed by using the conjugate augmented processing(CAP). Secondly, a one-dimensional (1-D) virtual co-array of ViP-SCPA is derived by exploiting the difference and sum co-array of the CPPA. Based on the obtained 1-D virtual co-array of ViP-SCPA, the 2-D DOA estimation is cast as a 1-D DOA estimation problem, for which both subspace-based methods and sparse representation algorithms can be adopted. To evaluate the array apertures of the proposed array, analytical expressions are derived to quantify the achievable number of unique lags, and the maximum number of consecutive lags of the resultant 1-D virtual co-array of ViP-SCPA. Simulation results verify the effectiveness of the proposed configuration by using the classical multiple signal classification (MUSIC) and sparse representation(SR) algorithm respectively.

Subspace methods, e.g., multiple signal classification algorithm (MUSIC), show great promise to high-resolution environment sensing in the 6G-enabled mobile Internet of Things (IoT), e.g., the emerging unmanned systems. Existing schemes, aiming to simplify the computational 1-D search of the MUSIC pseudospectrum, unfortunately have still an unaffordable complexity or the compromised accuracy, especially when the millimeter-wave massive multiple-input–multiple-output (MIMO) radar is considered. In this work, we address the fast and accurate estimation of the high-resolution pseudospectrum in massive MIMO radars. To enable real-time automotive sensing, we first formulate this computational procedure as one matrix product problem, which is then solved by leveraging randomized matrix sketching techniques. To be specific, we compute the large matrix product approximately by the product of two small matrices abstracted via random sampling. To minimize the approximation error, we further design another sampling, pruning, and recomputing (SaPRe) algorithm, which refines the approximated results and thus attains the exact pseudospectrum. Finally, the theoretical analysis and numerical simulations are provided to validate the proposed methods. Our fast approaches dramatically reduce the time complexity and simultaneously attain the accurate Direction-of-Arrival (DoA) estimation, which have the great potential to real time and high-resolution automotive sensing with massive MIMO radars.

Red Huajiao was the most important Zanthoxylum species in China, and its quality was highly determined the geographical region. This study was aimed to establish a determination method for the geographical origin recognition of Red Huajiao by using the electronic nose and ensemble recognition algorithm. Six origins of samples were detected by the electronic nose, and two categories of electronic nose sensors characteristic values, named as "optimized characteristic value" and "filtered characteristic value," were obtained by the principal component analysis and discrimination index method and Filter-Wrapper method. Based on the two categories of characteristic values, 22 kinds of model analysis methods, which belonged to five categories of ensemble recognition algorithms were used to recognize the geographical origin. The total recognition accuracy rate of the two categories of characteristic values were 83.9% and 85.7%, respectively. Furthermore, during 22 kinds of model analysis method, the ensemble Subspace KNN and Bagged Trees methods in Ensemble Learning algorithm exhibited the best distinguishing ability with the accuracy rate more than 90%. Therefore, the electronic nose combined with Ensemble Learning would be promising for the geographical origin determination application. PRACTICAL APPLICATION: This work demonstrates that the Red Huajiao can be simply and rapidly determined by using electronic nose combined with ensemble recognition algorithm, allowing to effectively distinguish geographical origin of Red Huajiao, which can provide an important reference for the quality assessment of Huajiao.

In this paper, we study the spectrum and the invariant subspace of compressed shifts on the Beurling type quotient module $${{\cal K}_\theta}$$ of Hardy space H2(ⅅ2). Suppose θ is a rational inner function with degree (1, 1). Firstly, we characterize the spectrum of $${S_{{z_1}}}$$ on $${{\cal K}_\theta}$$ ; secondly, we characterize the Agler type subspace of the compressed shift.

EEG signal classification is a key technology for EEG signal processing and identification systems. Dictionary learning has shown excellent performance due to its sparse representation and learning capability. Usually dictionary learning requires sufficient labeled EEG signals to build classification models, and assumes that the data distribution of training and test signals are the same. However, in new EEG signal domain, often only a small amount of signals are labeled, and more are not labeled. At the same time, data dynamicity, confounding factors and strong interclass similarity also seriously disrupt the performance of EEG signal classifier. To this end, a geometric preserving transfer discriminative dictionary learning method called GPTDDL is developed for cross-domain EEG signal classification. Through projected signals of different domains to the common subspace, a shared discriminative dictionary is obtained, which explores the geometric structure information by graph Laplacian regularization and discriminative information by principal component analysis regularization. Benefiting from the discriminative information transferred from source domain, the discriminability of the learned sparse coding of target domain is strengthened. GPTDDL integrates this idea into the framework of LC-KSVD, and learns the subspace and dictionary learning parameters in an iterative strategy. The experimental results on Bonn EEG signal dataset demonstrate the validity of the GPTDDL method.

A family of irreducible holomorphic symplectic (ihs) manifolds over the complex projective line has unobstructed deformations if its period map is an embedding. This applies in particular to twistor spaces of ihs manifolds. Moreover, a family of ihs manifolds over a subspace of the period domain extends to a universal family over an open neighborhood in the period domain.

Aiming at the problem of "dimension disaster" in hyperspectral image classification, a method of dimension reduction based on manifold data analysis and sparse subspace projection (MDASSP) is proposed. The sparse coefficient matrix is established by the new method, and the sparse subspace projection is carried out by the optimization method. To keep the geometric structure of the manifold, the objective function is regularized by the manifold learning method. The new method combines sparse coding and manifold learning to generate features with better classification ability. The experimental results show that the new method is better than other methods in the case of small samples.

Let K ( X , Y ) be the space of compact operators. For a proximinal subspace Z ⊂ Y , this paper deals with the question, when does every Y-valued compact operator admit a Z-valued compact best approximation? For any reflexive Banach space X and for a L 1 -predual space Y, if Z ⊂ Y is a strongly proximinal subspace of finite codimension, we show that K ( X , Z ) is a proximinal subspace of K ( X , Y ) under an additional condition on the position of K ( X , Z ) . When Y is a c 0 -direct sum of finite dimensional spaces we achieve a strong transitivity result by showing that for any proximinal subspace of finite codimension Z ⊂ Y , every Y-valued bounded operator admits a best Z-valued compact approximation.

Exploring the data-driven prediction strategy of dielectric constant (e) is attractive for the rational design of polymer dielectrics with targeted property, especially for the design of high e and low loss dielectric energy storage. To accelerate the design and discovery of novel polymer-based dielectric energy storage, the machine learning-based predictor, interval support vector regression with optimized genetic algorithm (OGA-ISVR), is proposed to predict e values, which could improve prediction accuracy and reduce time consumption via splitting the overall data space into subspaces, then adaptively choosing the kernel function and obtaining optimal hyper-parameters by genetic algorithm in each subspace. Here, the developed model is sufficiently trained and tested from the experimentally measured data and density functional theory-based computational data at various frequencies (spanning from 60 Hz to 1015 Hz). The mapping relationships between features and property and influencing factor of e values are identified by this machine learning-based model. Furthermore, compared with common support vector regression method, the proposed model has lower computing overhead and higher prediction accuracy. The proposed model is successfully demonstrated here for the instant property predictions of polymer dielectrics.

Hashing methods have been extensively applied to efficient multimedia data indexing and retrieval on account of the explosion of multimedia data. Cross-modal hashing usually learns binary codes by mapping multi-modal data into a common Hamming space. Most supervised methods utilize relation information like class labels as pairwise similarities of cross-modal data pair to narrow intra-modal and inter-modal gap. In this paper, we propose a novel supervised cross-modal hashing method dubbed Subspace Relation Learning for Cross-modal Hashing (SRLCH), which exploits relation information of labels in semantic space to make similar data from different modalities closer in the low-dimension Hamming subspace. SRLCH preserves the modality relationships, the discrete constraints and nonlinear structures, while admitting a closed-form binary codes solution, which effectively enhances the training efficiency. An iterative alternative optimization algorithm is developed to simultaneously learn both hash functions and unified binary codes. With these binary codes and hash functions, we can index multimedia data and search them in an efficient way. Evaluations in two cross-modal retrieval tasks on several widely-used datasets show that the proposed SRLCH outperforms most cross-modal hashing methods. Theoretical analysis also illustrates reasons for our method’s promotion in subspace relation learning.

The performance of model predictive control mainly depends on the accuracy of model and parameters, such as the back electromotive force (EMF) harmonics in dual three-phase permanent magnet synchronous motors (PMSMs). However, the back EMF harmonics would vary with the operation conditions. Thus, the parameter mismatches in the harmonic subspace would be inevitable. In this article, a direct harmonic current control scheme is proposed to provide further harmonic current suppression under parameter mismatches in the xy subspace. First, deadbeat control concept is applied to calculate the reference voltage in the αβ subspace. This reference voltage vector is utilized to generate a group of control sets with different voltage vectors in the xy subspace. Then, a slide mode control scheme is provided to deal with the inaccurate parameters in the xy subspace. The reference voltage vector in the xy subspace is obtained with this slide mode control scheme without the remaining inductance parameters. Third, a two-step modulation method and cost function are discussed to further suppress the harmonic currents. The control sets generated by deadbeat control are optimized with the cost function. Moreover, a switching pattern with fixed switching frequency is proposed in this section. Finally, experimental results verify that proposed control scheme could further suppress the harmonic currents.

This letter investigates the disturbance decoupling problem (DDP) for Boolean control networks (BCNs), and proposes some new perspectives on the solvability of DDP. The DDP of BCNs is generalized in the sense that the output-friendly subspace is a subset of the invariant subspace, based on which, a new criterion is presented to design state feedback DDP controllers for a given output-friendly coordinate frame. The study of an illustrative example shows that additional state feedback DDP controllers can be obtained with respect to those that can be obtained with the method proposed in the existing literature.

Facial expression recognition has drawn increasing attention because of its great potential in human behavior analysis. Traditional recognition models usually assume that the training set is sufficient, and the training and testing data sets have the same distribution. However, these two factors are not satisfied in some cases. In this study, a transfer model collaborating metric learning and dictionary learning called TMMLDL is proposed to address the transfer facial expression recognition problem. To reduce the impact of cross-domain distribution variation, the information of global structure and pairwise constraints are utilized among training images in different domains. In particular, a discriminative metric space is learned into dictionary learning procedure such that the dictionary items can well present the discriminative information of different facial expression classes in the metric subspace. The proposed model tunes dictionary and metric space in an alternative optimization algorithm, which is guaranteed to obtain the optimal model parameters simultaneously. The experimental results on nine cross-domain facial expression classification tasks show that the proposed model achieves the satisfactory recognition performance.

It is shown that the set of finite multisets can be identified with the space of symmetric polynomials on a linear space of finite sequences whose completion in a suitable metric gives a topologization of the set of multisets as a subspace of the space of symmetric analytic functions on l1. As one of possible topologizations, we can mention the topology of Hilbert space. Moreover, we consider some algebraic operations on the set of multisets, in particular, the analogs of fractional mappings.

This paper proposed a novel Robust Multi-View Continuous Subspace Clustering (RMVCSC) algorithm, which can untangle heavily mixed clusters by optimizing a single continuous objective. The proposed objective uses robust estimators to automatically clip specious inter-cluster connections while maintaining convincing intra-cluster correspondences in the common representation subspace learned from multiple views. The common representation subspace can reveal the underlying cluster structure in data. RMVCSC is optimized in an alternating minimization scheme, in which the clustering result and the common representation subspace are simultaneously optimized. Since different views can describe distinct perspectives of input data, the proposed algorithm has more accurate clustering performance than conventional algorithms by exploring information among multi-view data. In other words, the proposed algorithm optimizes a novel continuous objective in the simultaneously learned common representation subspace across multiple views. By using robust redescending estimators, the proposed algorithm is not prone to stick into bad local minima even with outliers in data. This kind of robust continuous clustering methods has never been used for multi-view clustering before. Moreover, the convergence of the proposed algorithm is theoretically proved, and the experimental results show that the proposed RMVCSC can outperform several very recent proposed algorithms in terms of clustering accuracy.

Recently, many scenarios, such as affective disorders treatment, have sparked rising needs for establishment of personalized emotion recognition (PER) models. Unfortunately, the data sparsity issue violates the basic i.i.d. assumption of supervised learning (i.e., training data and test data are independently and identically distributed). In this paper, we present a semi-supervised joint domain adaption (SSJDA) solution, aiming to inject the hidden domain knowledge from ample labeled data of multiple source individuals into the target subject’s customized model. Specifically, we put forward a novel Progressive Low-Rank Subspace Alignment (PLRSA) approach, which unifies a semi-supervised instance-transfer paradigm and an unsupervised mapping-transfer learning paradigm in a single optimization framework. We leverage the boosting-based TrAdaBoost algorithm and the Transfer Component Analysis (TCA) algorithm for the implementation of instance reweighting and feature matching, respectively. Then we introduce the l 2 , 1 - norm to pass feedback and make the joint learning feasible. The central idea is to progressively minimize the cross-domain distribution discrepancies to finally construct the optimal domain-invariant features. We systematically compare the PLRSA method with five state-of-the-art techniques using two public EEG datasets (DEAP and SEED). Both many-to-one and one-to-one evaluations are performed. The experimental results have confirmed the efficacy of the proposed method.

The recent years have witnessed significant advances in deep video action recognition. However, the performances of deep learning-based video action recognition methods are limited in the case of relatively small samples or no labeled samples. Therefore, trying to use unlabeled video data to generate clustering label is essential for small sample learning and zero sample learning. In this paper, we propose a novel deep video action clustering network, which aims to learn the similarity relationship among the unlabeled video samples, and generate the clustering label for each video sample. Specifically, the proposed method simultaneously learns the spatio-temporal features and subspace representations under a jointly optimized framework. It consists of a 3D U-Net self-representation generator, a video-clip reconstruction discriminator, and a confidence-based feedback mechanism. The 3D U-Net self-representation generator learns the spatio-temporal features of the video clips and produces subspace representation matrix. Then, the similarity graph is constructed based on this subspace representation matrix, and the clustering result is obtained. In the learning procedure, a confidence-based feedback mechanism is designed to feed the high-confidence labels of partial samples back to further guide the subspace structure learning, so that the optimal result can be obtained. During training, the video-clip reconstruction discriminator is introduced to evaluate the reconstructed video clips, which is beneficial for capturing the discriminative spatio-temporal features. Experimental results on a video benchmark dataset demonstrate the effectiveness of the proposed method.

The spatial covariance matrix, as the core of subspace direction of arrival (DOA) estimation, is unavailable in the hybrid analog-digital structure, which is widely used in large-scale transceivers to reduce the number of radio frequency chains. In previous studies, the beam sweeping algorithm (BSA) has been used for effectively reconstructing the spatial covariance matrix. However, the BSA is not practical owning to the intractable computational cost due to the high-dimensional matrix operations. To address this problem, a high-efficiency BSA (HeBSA) is proposed. The main motivation behind the HeBSA is to avoid the high-dimensional matrix multiplication and inversion. By appropriately adjusting weights connected to antennas, the real-valued spatial covariance matrix can be reconstructed according to low-dimensional matrix multiplication. Then the classical U-root multiple signal classification can be adopted to estimate the DOA angle of each signal. Finally, simulation experiments are conducted to verify the performance of the HeBSA. The results indicate that the HeBSA can achieve DOA estimation performance comparable with that of BSA even at considerably lower computational cost.

We propose new repair schemes for Reed-Solomon codes that use subspace polynomials and hence generalize previous works in the literature that employ trace polynomials. The Reed-Solomon codes are over $\mathbb {F}_{{q}^{\ell }}$ and have redundancy ${{r}} = {{n}}-{{k}} \geq {{q}}^{{m}}$ , $1\leq {{m}}\leq \ell $ , where ${{n}}$ and ${{k}}$ are the code length and dimension, respectively. In particular, for one erasure, we show that our schemes can achieve optimal repair bandwidths whenever ${{n}}={{q}}^\ell $ and ${{r}} = {{q}}^{{m}}$ , for all $1 \leq {{m}} \leq \ell $ . For two erasures, our schemes use the same bandwidth per erasure as the single erasure schemes, for $\ell /{{m}}$ is a power of ${{q}}$ , and for $\ell ={{q}}^{{a}}$ , ${{m}}={{q}}^{{b}}-1>1$ ( ${{a}} \geq {{b}} \geq 1$ ), and for ${{m}}\geq \ell /2$ when $\ell $ is even and ${{q}}$ is a power of two.

In this article, a gray-box parsimonious subspace identification method using sampled dynamical and steady-state data is proposed for block-oriented Hammerstein-type systems. Compared with the conventional subspace identification methods based on over-parameterized models, the proposed method assumes parsimonious models, where the number of parameters is as minimal as possible to ensure the model accuracy, especially for highly nonlinear models. Generally, the available dynamical data do not contain adequate information on the low-frequency characteristics of the system. To improve the accuracy of model identification, the steady-state information of the system is taken into account, and a multiregularization method is developed, where the whole model parameters are estimated in a hierarchical, iterative manner from two sets of data: the dynamical input–output data and the steady-state input–output data. The use of parsimonious models and hierarchical estimation can significantly reduce the size of the associated parameter estimation error covariance matrix, thus improving the model accuracy and decreasing the variance of the estimated parameters, compared with the over-parametrization methods only using dynamical data. The effectiveness and merits are demonstrated by a simulation example and a real-world example.

Deep brain stimulation (DBS) of the Basal Ganglia (BG) is an effective treatment to suppress the symptoms of Parkinson’s disease (PD). Using a closed-loop scheme in DBS can not only improve its therapeutic effects but it can also reduce its energy consumption and possible side effects. In this paper, a predictive closed loop control strategy is employed to suppress the PD in real-time. A linear multi-input multi-output (MIMO) state-delayed system is considered as a simplified model of the BG neuronal network relating the stimulation signals as inputs to the beta power of local field potentials as PD biomarkers. The effect of time delay in different areas of the BG is incorporated into this model and a real-time subspace-based identification is implemented to continuously model the state of the BG neuronal network and drive the predictive control strategy. Simulation results show that the proposed MIMO subspace based predictive controller can suppress PD symptoms more effectively and with less power consumption compared to the conventional open-loop DBS and a recently proposed single-input single-output closed loop controller.

We consider a one-dimensional chain of N equidistantly spaced noninteracting qubits embedded in an open waveguide. In the frame of single-excitation subspace, we systematically study the evolution of qubits amplitudes if the only qubit in the chain was initially excited. We show that the temporal dynamics of qubits amplitudes crucially depend on the value of kd, where k is the wave vector, d is a distance between neighbor qubits. If kd is equal to an integer multiple of $\pi$, then the qubits are excited to a stationary level which scales as SN^{-1}S. We show that in this case, it is the dark states which prevent qubits from decaying to zero even though they do not contribute to the output spectrum of photon emission. For other values of kd the excitations of qubits have the form of damping oscillations, which represent the vacuum Rabi oscillations in a multi-qubit system. In this case, the output spectrum of photon radiation is defined by a subradiant state with the smallest width., Comment: 22 pages, 12 figures, 17 references