Tensor Subspace Research Articles

Enhancing plant disease detection: a novel CNN-based approach with tensor subspace learning and HOWSVD-MDA

Enhancing plant disease detection: a novel CNN-based approach with tensor subspace learning and HOWSVD-MDA

Irreducible Cartesian tensor decomposition: A computational approach

Cartesian tensors are widely used in physics and chemistry, especially for the formulation of linear and nonlinear spectroscopies as well as for molecular response properties. In this work, we review the problem of irreducible Cartesian tensor (ICT) decomposition of a generic Cartesian tensor of rank n into its irreducible parts, each characterized by a specific symmetry. The matrix formulation of the ICT decomposition is structurally similar to the problem of rotational averaging using isotropic Cartesian tensors. Analogously to the latter, the ICT decomposition can be considered as a problem of selecting a set of permutations of n indices that provides a linearly independent set of mappings between Cartesian tensor subspaces. This selection can be performed using a simple computational approach based on the reduced row echelon form (rref) algorithm. This protocol has been implemented in a computer code used to re-derive the already known ICT decomposition for 2 ≤ n ≤ 4. Finally, for the first time, we performed the explicit ICT decomposition of a Cartesian tensor of rank n = 5.

Modeling and Learning on High-Dimensional Matrix-Variate Sequences

We propose a new matrix factor model, named RaDFaM, which is strictly derived from the general rank decomposition and assumes a high-dimensional vector factor model structure for each basis vector. RaDFaM contributes a novel class of low-rank latent structures that trade off between signal intensity and dimension reduction from a tensor subspace perspective. Based on the intrinsic separable covariance structure of RaDFaM, for a collection of matrix-valued observations, we derive a new class of PCA variants for estimating loading matrices, and sequentially the latent factor matrices. The peak signal-to-noise ratio of RaDFaM is proved to be superior in the category of PCA-type estimators. We also establish an asymptotic theory including the consistency, convergence rates, and asymptotic distributions for components in the signal part. Numerically, we demonstrate the performance of RaDFaM in applications such as matrix reconstruction, supervised learning, and clustering, on uncorrelated and correlated data, respectively. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

Novel Knowledge Pre-trained CNN based Tensor Subspace Learning for Tomato Leaf Diseases Detection

Novel Knowledge Pre-trained CNN based Tensor Subspace Learning for Tomato Leaf Diseases Detection

Multichannel Image Completion With Mixture Noise: Adaptive Sparse Low-Rank Tensor Subspace Meets Nonlocal Self-Similarity.

Multichannel image completion with mixture noise is a common but complex problem in the fields of machine learning, image processing, and computer vision. Most existing algorithms devote to explore global low-rank information and fail to optimize local and joint-mode structures, which may lead to oversmooth restoration results or lower quality restoration details. In this study, we propose a novel model to deal with multichannel image completion with mixture noise based on adaptive sparse low-rank tensor subspace and nonlocal self-similarity (ASLTS-NS). In the proposed model, a nonlocal similar patch matching framework cooperating with Tucker decomposition is used to explore information of global and joint modes and optimize the local structure for improving restoration quality. In order to enhance the robustness of low-rank decomposition to data missing and mixture noise, we present an adaptive sparse low-rank regularization to construct robust tensor subspace for self-weighing importance of different modes and capturing a stable inherent structure. In addition, joint tensor Frobenius and l1 regularizations are exploited to control two different types of noise. Based on alternating directions method of multipliers (ADMM), a convergent learning algorithm is designed to solve this model. Experimental results on three different types of multichannel image sets demonstrate the advantages of ASLTS-NS under five complex scenarios.

Convex Robust Recovery of Corrupted Tensors via Tensor Singular Value Decomposition and Local Low-Rank Approximation

This paper discusses the recovery of tensor data corrupted by random noise. Our approach assumes that the potential structure of data is a linear combination of several low-rank tensor subspaces. The goal is to recover exactly these local low-rank tensors and remove random noise as much as possible. Non-parametric kernel smoothing technique is employed to establish an effective mathematical notion of local models. After that, each local model can be robustly separated into a low-rank tensor and a sparse tensor. The low-rank tensor can be recovered by minimizing a weighted combination of the norm and the tensor nuclear norm (TNN) obtained as the tightest convex relaxation of tensor multi-linear rank defined in Tensor Singular Value Decomposition (TSVD). Numerical simulation experiments verify that our proposed approach can effectively denoise the tensor data such as color images with random noise and has superior performance compared to the existing methods.

Pure kernel graph fusion tensor subspace clustering under non-negative matrix factorization framework

Currently, graph-based multi-kernel subspace clustering methods have achieved rich research results in dealing with nonlinear data structures. However, most of the methods still have the following two limitations: (1) the model optimization goal is finding the optimal consensus kernel rather than the optimal affinity graph, which leads to kernel noise always interfering with the learning of the target affinity graph in the optimization process; (2) in the process of finding the optimal affinity graph, only the correlation between different kernel views is exploited, ignoring the higher-order correlation between multiple kernel views. In light of this, we propose a pure kernel graph fusion tensor (PKGT) subspace clustering under non-negative matrix factorization (NMF) framework. Specifically, we first use NMF to construct local affinity feature graphs with standard block diagonal structure for each base kernel matrix, and then achieve adaptive weight assignment by optimizing the inconsistencies among multiple local affinity feature graphs. Finally, we use tensor to capture the higher-order correlation between multiple local affinity feature graphs to provide more feature information for the learning of optimal target affinity graph, which enhances the model clustering performance. Extensive experiments on nine real datasets demonstrate that PKGT has superior clustering performance. The code is available at https://github.com/ZS0124/PKGT.

High-order knowledge-based Discriminant features for kinship verification

This research work aims to propose an effective and robust face kinship verification system by leveraging several axes, including advanced learning techniques, deep learning, and CNN networks. The contributions of this work include the use of a preprocessing method known as Multiscale Retinex with Chromaticity Preservation (MSRCP) and the Gradientfaces technique (GRF) to improve image quality and contrast enhancement. Additionally, a novel discriminative handcrafted descriptor called Histograms of dual-tree complex wavelet transform (Hist-DTCWT) is proposed. Moreover, a logistic regression for score-level fusion is used to enhance the matching process. Furthermore, a high-order knowledge-based feature using a tensor subspace model was proposed to combine multiple discriminative features. Tests were conducted out using three datasets, where the proposed method has outperformed the state the art. Typically, verification accuracies of 96.62%, 95.54% and 92.94% have been reached under Cornell KinFace, UB KinFace and TS KinFace datasets, respectively.

Spectral computation with third-order tensors using the t-product

The tensor t-product is a powerful tool for the analysis of and computation with third-order tensors. This paper discusses properties and the computation of eigentubes and eigenslices of third-order tensors under the t-product; the eigentubes and eigenslices are analogues of eigenvalues and eigenvectors for matrices. The computational methods considered and analysed include the tensor power method, tensor subspace iteration, and the tensor QR algorithm. Computed examples illustrate the performance of these methods.

Double pulsed field gradient diffusion MRI to assess skeletal muscle microstructure.

Preliminary study to determine whether double pulsed field gradient (PFG) diffusion MRI is sensitive to key features of muscle microstructure related to function. The restricted diffusion profile of molecules in models of muscle microstructure derived from histology were systematically simulated using a numerical simulation approach. Diffusion tensor subspace imaging analysis of the diffusion signal was performed, and spherical anisotropy (SA) was calculated for each model. Linear regression was used to determine the predictive capacity of SA on the fiber area, fiber diameter, and surface area to volume ratio of the models. Additionally, a rat model of muscle hypertrophy was scanned using a single PFG and a double PFG pulse sequence, and the restricted diffusion measurements were compared with histological measurements of microstructure. Excellent agreement between SA and muscle fiber area (r2 = 0.71; p < 0.0001), fiber diameter (r2 = 0.83; p < 0.0001), and surface area to volume ratio (r2 = 0.97; p < 0.0001) in simulated models was found. In a scanned rat leg, the distribution of these microstructural features measured from histology was broad and demonstrated that there is a wide variance in the microstructural features observed, similar to the SA distributions. However, the distribution of fractional anisotropy measurements in the same tissue was narrow. This study demonstrates that SA-a scalar value from diffusion tensor subspace imaging analysis-is highly sensitive to muscle microstructural features predictive of function. Furthermore, these techniques and analysis tools can be translated to real experiments in skeletal muscle. The increased dynamic range of SA compared with fractional anisotropy in the same tissue suggests increased sensitivity to detecting changes in tissue microstructure.

Age invariant face recognition using discriminative tensor subspace learning with fuzzy based classification

AbstractAging is a complex process that affects both the shape and texture of a face. In the aging domain, various methods have been proposed for age estimation or simulation of the face based on an image at a given age. Face recognition methods that are designed for automatic face recognition are still a challenging issue. We present a novel age invariant face recognition method using tensor subspace learning with fuzzy synthetic classification. Local Binary Pattern (LBP) processed face images are used to learn the tensor sub‐space, which converts high dimensional feature space to age‐invariants while retaining key elements of the local geometrical structure of the face. Tensor sub‐space is better in terms of sub‐space learning and feature extraction than Principal Component Analysis (PCA)/Linear Discriminant Analysis (LDA) that been used in many techniques in the literature. Tensor Normalized Face images are generated which exhibit maximum inter‐class distances and minimum intra‐class distances. Further local patches are used for synthesizing global Fuzzy membership scores to classify the test face images. Experiments performed on standard face‐aging datasets, namely FG‐NET, AGEDB, and MORPH‐Album‐II, and received accuracy of 99.15%, 99.20%, and 99.8%, respectively. Experimental results outperform the current state‐of‐the‐art techniques, and results show the promise of the proposed system for personal identification despite the aging process. It also proved that the local descriptor gives better performance over the global descriptor like PCA for the aging process. The method also demonstrated improved performance as compared with compute‐intensive methods that required training on deep networks.

A Tensor-based domain alignment method for intelligent fault diagnosis of rolling bearing in rotating machinery

Fault diagnosis of rolling bearings plays a pivotal role in modern industry. Most existing methods have two disadvantages: 1) The assumption that the training and test data obey the same distribution; and 2) They are designed for vector representation which is unable to characterize the important structure of the rolling bearings data of interest. To overcome these drawbacks, this paper proposes a novel tensor based domain adaptation method. Firstly, this method uses the time domain signals, the frequency domain signals, and the Hilbert marginal spectrum and integrates them into a third-order tensor model. Secondly, these three types of signals are split into two parts: the source and target domain data; all the representative features are identified in the source domain. Thirdly, a tensor decomposition method is used to decompose the features into a series of third-order tensors, and several alignment matrices are defined to align the representation of the two domains to the tensor invariant subspace. Then, the alignment matrices and the tensor subspace are jointly optimized to realize the adaptive learning. Finally, the feature tensor is reconstructed into a matrix form to realize the fault diagnosis through the classifier. Extensive experiments are conducted on a public dataset and a dataset collected from our own laboratory; experimental results show the satisfactory performance of the proposed method.

Online Tensor Low-Rank Representation for Streaming Data Clustering

Tensor low-rank representation (TLRR) has attracted increasing attention in recent years due to its effectiveness in capturing the intrinsic low-rank structure of tensor data. However, it is known that TLRR suffers from high computational complexity for large-scale data because it minimizes the tensor rank of the representation tensor whose size is proportional to the sample size. This paper develops a streaming algorithm—termed online low-rank tensor subspace clustering (OLRTSC)—for low-rank tensor data recovery and clustering based on the tensor singular value decomposition (t-SVD) algebraic framework. The key idea of OLRTSC is the non-convex reformulation of the objective function of TLRR by decomposing the tensor nuclear norm into an explicit tensor product of two low-rank tensors, which can be solved by leveraging the stochastic optimization technique. Compared to batch TLRR, OLRTSC is online by nature, can handle dynamic data, avoids computing t-SVD of the representation tensor, and reduces the storage cost significantly. This paper provides the theoretical guarantee that the sequence of the solutions produced by OLRTSC converges almost surely to a stationary point of the objective function. Moreover, an extension of OLRTSC is also proposed to handle the case when parts of the data are missing. Finally, experimental results on both synthetic and real data demonstrate the efficiency and robustness of the proposed approaches.

Low-Rank Tensor Subspace Decomposition With Weighted Group Sparsity for the Acceleration of Non-Cartesian Dynamic MRI.

Dynamic MR imaging often requires long scan time, and acceleration of data acquisition is highly desirable in clinical applications. We proposed a Low-rank Tensor subspace decomposition with Weighted Group Sparsity (LTWGS) algorithm for non-Cartesian dynamic MRI. The proposed algorithm introduces the weighted group sparse constraints together with the subspace decomposition technique into the framework of low-rank tensor and sparse decomposition to better utilize the sparsity in the data. LTWGS increases the PSNR values by 1.97 dB, 2.03 dB, and 2.83 dB compared with PROST (patch-based reconstruction), SRTPCA (smooth robust tensor principal component analysis), and LRTES (low-rank tensor with "explicit subspace") in the dynamic abdominal imaging at an acceleration rate R = 25. LTWGS increases the PSNR values by 2.42 dB and 3.57 dB compared with PROST and LRTES in DCE liver imaging at R = 25. LTWGS increases the PSNR values by 1.40 dB and 1.96 dB compared with PROST and SRTPCA in cardiac cine imaging at R = 25. Jointly using group sparsity and sparsity can obtain better results than that using group sparsity alone, and weighted regularization can achieve better results than that without weighted regularization. The proposed algorithm results in reduced reconstruction error and improved image structural similarity in comparison with several state-of-the-art methods at relatively high acceleration factors. The proposed algorithm has the potential in various dynamic MRI application scenarios.

Tensor Cascaded-Rank Minimization in Subspace: A Unified Regime for Hyperspectral Image Low-Level Vision.

Low-rank tensor representation philosophy has enjoyed a reputation in many hyperspectral image (HSI) low-level vision applications, but previous studies often failed to comprehensively exploit the low-rank nature of HSI along different modes in low-dimensional subspace, and unsurprisingly handled only one specific task. To address these challenges, in this paper, we figured out that in addition to the spatial correlation, the spectral dependency of HSI also implicitly exists in the coefficient tensor of its subspace, this crucial dependency that was not fully utilized by previous studies yet can be effectively exploited in a cascaded manner. This led us to propose a unified subspace low-rank learning regime with a new tensor cascaded rank minimization, named STCR, to fully couple the low-rankness of HSI in different domains for various low-level vision tasks. Technically, the high-dimensional HSI was first projected into a low-dimensional tensor subspace, then a novel tensor low-cascaded-rank decomposition was designed to collapse the constructed tensor into three core tensors in succession to more thoroughly exploit the correlations in spatial, nonlocal, and spectral modes of the coefficient tensor. Next, difference continuity-regularization was introduced to learn a basis that more closely approximates the HSI's endmembers. The proposed regime realizes a comprehensive delineation of the self-portrait of HSI tensor. Extensive evaluations conducted with dozens of state-of-the-art (SOTA) baselines on eight datasets verified that the proposed regime is highly effective and robust to typical HSI low-level vision tasks, including denoising, compressive sensing reconstruction, inpainting, and destriping. The source code of our method is released at https://github.com/CX-He/STCR.git.

T-Linear Tensor Subspace Learning for Robust Feature Extraction of Hyperspectral Images

Subspace learning has been widely applied for feature extraction of hyperspectral images (HSIs) and achieved great success. However, the current methods still leave two problems that need to be further investigated. First, those methods mainly focus on finding one or multiple projection matrices for mapping the high-dimensional data into a low-dimensional subspace, which can only capture the information from each direction of high-order hyperspectral data separately. Second, the performance of feature extraction is barely satisfactory when the hyperspectral data is severely corrupted by noise. To address these issues, this article presents a t-linear tensor subspace learning (tLTSL) model for robust feature extraction of HSIs based on t-product projection. In the model, t-product projection is a new defined tensor transformation way similar to linear transformation in vector space, which can maximally capture the intrinsic structure of tensor data. The integrated tensor low-rank and sparse decomposition can effectively remove the noise corruption and the learned t-product projection can directly transform the high-order hyperspectral data into a subspace with information from all modes comprehensively considered. Moreover, a proposition related to tensor rank is proofed for interpreting the meaning of the tLTSL model. Extensive experiments are conducted on two different kinds of noise (i.e., simulated and real noise) corrupted HSI data, which validate the effectiveness of tLTSL.

Patch Tracking-Based Streaming Tensor Ring Completion for Visual Data Recovery

Tensor completion aims to recover the missing entries of a partially observed tensor by exploiting its low-rank structure, and has been applied to visual data recovery. In applications where the data arrives sequentially such as streaming video completion, the missing entries of the tensor need to be dynamically recovered in a streaming fashion. Traditional streaming tensor completion algorithms treat the entire visual data as a tensor, which may not work satisfactorily when there is a big change in the tensor subspace along the temporal dimension, such as due to strong motion across the video frames. In this paper, we develop a novel patch tracking-based streaming tensor ring completion framework for visual data recovery. Given a newly incoming frame, small patches are tracked from the previous frame. Meanwhile, for each tracked patch, a patch tensor is constructed by stacking similar patches from the new frame. Patch tensors are then completed using a streaming tensor ring completion algorithm, and the incoming frame is recovered using the completed patch tensors. We propose a new patch tracking strategy that can accurately and efficiently track the patches with missing data. Further, a new streaming tensor ring completion algorithm is proposed which can efficiently and accurately update the latent core tensors and complete the missing entries of the patch tensors. Extensive experimental results demonstrate the superior performance of the proposed algorithms compared with both batch and streaming state-of-the-art tensor completion methods.

Facial age estimation using tensor based subspace learning and deep random forests

Recently, the estimation of facial age has attracted much attention. This letter extends and improves a recently developed method (Guehairia et al., 2020) for fusing multiple deep facial features for age estimation. This method was based on deep random forests. We propose a new pipeline that integrates tensor-based subspace learning before applying DRFs. Deep face features of a training set are represented as a 3D tensor. Multi-linear Whitened Principal Component (MWPCA) and Tensor Exponential Discriminant (TEDA) are used to extract the most discriminative information. The tensor subspace features are then fed into DRFs to predict age. Experiments conducted on five public face databases show that our method can compete with many state-of-the-art methods.

Tensor subspace clustering using consensus tensor low-rank representation

Recently, subspace clustering (SC) has received an increasing amount of attention. Generally, SC methods are implemented on sample data in matrix form. Even for multiway or tensor data, which is prevalent in reality, traditional SC methods should convert each sample to a vector and then form a data matrix. However, the vectorization process will damage the underlying inherent spatial structure of the data. To address this problem, in this paper, we propose a novel consensus tensor low-rank representation (CTLRR) method, which is directly implemented on tensor data. First, the tensor nuclear norm (TNN) and t-product, which is defined as the multiplication of two tensors, are employed to model the data and obtain the low-rank representation tensor. Second, spectral clustering is unified into CTLRR to explore the consensus information among the low-rank representation tensor, which helps obtain the final fusion similarity matrix with the k connected components, where k is the number of clusters. Third, the cluster structure is characterized, and the clustering performance is substantially improved. Last, an optimization procedure for CTLRR is presented. Experimental results on certain challenging datasets show that the proposed CTLRR method outperforms the state-of-the-art methods.

Unsupervised Domain-Adaptation-Based Tensor Feature Learning With Structure Preservation

Domain adaptation (DA) is widely used in computer vision and pattern recognition applications. It is an effective process where a model is trained on objects from the source domain to predict the categories of the objects in the target domain. The aim of feature extraction in domain adaptation is to learn the best representation of the data in a certain domain and use it in other domains. However, the main challenge here is the difference between the data distributions of the source and target domains. Also, in computer vision, the data are represented as tensor objects such as 3-D images and video sequences. Most of the existing methods in DA apply vectorization to the data, which leads to information loss due to failure to preserve the natural tensor structure in a low-dimensional space. Thus, in this article, we propose <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">unsupervised DA-based tensor feature learning (UDA-TFL)</i> as a novel adapted feature extraction method that aims to avoid vectorization during transfer knowledge simultaneously; retain the structure of the tensor objects; reduce the data discrepancy between source and target domains; and represent the original tensor object in a lower dimensional space that is resistant to noise. Therefore, multilinear projections are determined to learn the tensor subspace without vectorizing the original tensor objects via an alternating optimization strategy. We integrate maximum mean discrepancy in the objective function to reduce the difference between source and target distributions. Extensive experiments are conducted on 39 cross-domain datasets from different fields, including images and videos. The promising results indicate that UDA-TFL significantly outperforms the state-of-the-art.