Journal articles: 'Tensor PCA'

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Zare, Ali, Alp Ozdemir, Mark A. Iwen, and Selin Aviyente. "Extension of PCA to Higher Order Data Structures: An Introduction to Tensors, Tensor Decompositions, and Tensor PCA." Proceedings of the IEEE 106, no. 8 (August 2018): 1341–58. http://dx.doi.org/10.1109/jproc.2018.2848209.

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Wang, An-Dong, Zhong Jin, and Jing-Yu Yang. "A faster tensor robust PCA via tensor factorization." International Journal of Machine Learning and Cybernetics 11, no. 12 (June 24, 2020): 2771–91. http://dx.doi.org/10.1007/s13042-020-01150-2.

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Jagannath, Aukosh, Patrick Lopatto, and Léo Miolane. "Statistical thresholds for tensor PCA." Annals of Applied Probability 30, no. 4 (August 2020): 1910–33. http://dx.doi.org/10.1214/19-aap1547.

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Ben Arous, Gérard, Reza Gheissari, and Aukosh Jagannath. "Algorithmic thresholds for tensor PCA." Annals of Probability 48, no. 4 (July 2020): 2052–87. http://dx.doi.org/10.1214/19-aop1415.

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Jiang, Bo, Shiqian Ma, and Shuzhong Zhang. "Low-M-Rank Tensor Completion and Robust Tensor PCA." IEEE Journal of Selected Topics in Signal Processing 12, no. 6 (December 2018): 1390–404. http://dx.doi.org/10.1109/jstsp.2018.2873144.

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Liu, Cong, Xu Wei-sheng, and Wu Qi-di. "Tensorial Kernel Principal Component Analysis for Action Recognition." Mathematical Problems in Engineering 2013 (2013): 1–16. http://dx.doi.org/10.1155/2013/816836.

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We propose the Tensorial Kernel Principal Component Analysis (TKPCA) for dimensionality reduction and feature extraction from tensor objects, which extends the conventional Principal Component Analysis (PCA) in two perspectives: working directly with multidimensional data (tensors) in their native state and generalizing an existing linear technique to its nonlinear version by applying the kernel trick. Our method aims to remedy the shortcomings of multilinear subspace learning (tensorial PCA) developed recently in modelling the nonlinear manifold of tensor objects and brings together the desirable properties of kernel methods and tensor decompositions for significant performance gain when the data are multidimensional and nonlinear dependencies do exist. Our approach begins by formulating TKPCA as an optimization problem. Then, we develop a kernel function based on Grassmann Manifold that can directly take tensorial representation as parameters instead of traditional vectorized representation. Furthermore, a TKPCA-based tensor object recognition is also proposed for application of the action recognition. Experiments with real action datasets show that the proposed method is insensitive to both noise and occlusion and performs well compared with state-of-the-art algorithms.

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Ouerfelli, Mohamed, Mohamed Tamaazousti, and Vincent Rivasseau. "Random Tensor Theory for Tensor Decomposition." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 7 (June 28, 2022): 7913–21. http://dx.doi.org/10.1609/aaai.v36i7.20761.

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We propose a new framework for tensor decomposition based on trace invariants, which are particular cases of tensor networks. In general, tensor networks are diagrams/graphs that specify a way to "multiply" a collection of tensors together to produce another tensor, matrix or scalar. The particularity of trace invariants is that the operation of multiplying copies of a certain input tensor that produces a scalar obeys specific symmetry constraints. In other words, the scalar resulting from this multiplication is invariant under some specific transformations of the involved tensor. We focus our study on the O(N)-invariant graphs, i.e. invariant under orthogonal transformations of the input tensor. The proposed approach is novel and versatile since it allows to address different theoretical and practical aspects of both CANDECOMP/PARAFAC (CP) and Tucker decomposition models. In particular we obtain several results: (i) we generalize the computational limit of Tensor PCA (a rank-one tensor decomposition) to the case of a tensor with axes of different dimensions (ii) we introduce new algorithms for both decomposition models (iii) we obtain theoretical guarantees for these algorithms and (iv) we show improvements with respect to state of the art on synthetic and real data which also highlights a promising potential for practical applications.

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Zhang, Hongjun, Peng Li, Weibei Fan, Zhuangzhuang Xue, and Fanshuo Meng. "Tensor Multi-Clustering Parallel Intelligent Computing Method Based on Tensor Chain Decomposition." Computational Intelligence and Neuroscience 2022 (September 6, 2022): 1–12. http://dx.doi.org/10.1155/2022/7396185.

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Adaptable methods for representing higher-order data with various features and high dimensionality have been demanded by the increasing usage of multi-sensor technologies and the emergence of large data sets. Arrays of multi-dimensional data, known as tensors, can be found in a variety of applications. Standard data that depicts things from a single point of view lacks the semantic richness, utility, and complexity of multi-dimensional data. Research into multi-clustering has taken off since traditional clustering methods are unable to handle large datasets. There are three main kinds of multi-clustering algorithms: Self-weighted Multiview Clustering (SwMC), Latent Multi-view Subspace Clustering (LMSC), and Multi-view Subspace Clustering with Intactness-Aware Similarity (MSC IAS) that are explored in this paper. To evaluate their performance, we do in-depth tests on seven real-world datasets. The three most important metrics Accuracy (ACC), normalized mutual information (NMI), and purity are grouped. Furthermore, traditional Principal Component Analysis (PCA) cannot uncover hidden components within multi-dimensional data. For this purpose, tensor decomposition algorithms have been presented that are flexible in terms of constraint selection and extract more broad latent components. In this examination, we also go through the various tensor decomposition methods, with an emphasis on the issues that classical PCA is designed to solve. Various tensor models are also tested for dimensionality reduction and supervised learning applications in the experiments presented here.

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Qiu, Yuning, Guoxu Zhou, Zhenhao Huang, Qibin Zhao, and Shengli Xie. "Efficient Tensor Robust PCA Under Hybrid Model of Tucker and Tensor Train." IEEE Signal Processing Letters 29 (2022): 627–31. http://dx.doi.org/10.1109/lsp.2022.3143721.

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Yang, Sihai, Xian-Hua Han, and Yen-Wei Chen. "GND-PCA Method for Identification of Gene Functions Involved in Asymmetric Division of C. elegans." Mathematics 11, no. 9 (April 25, 2023): 2039. http://dx.doi.org/10.3390/math11092039.

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Due to the rapid development of imaging technology, a large number of biological images have been obtained with three-dimensional (3D) spatial information, time information, and spectral information. Compared with the case of two-dimensional images, the framework for analyzing multidimensional bioimages has not been completely established yet. WDDD is an open biological image database. It dynamically records 3D developmental images of 186 samples of nematodes C. elegans. In this study, based on WDDD, we constructed a framework to analyze the multidimensional dataset, which includes image segmentation, image registration, size registration by the length of main axes, time registration by extracting key time points, and finally, using generalized N-dimensional principal component analysis (GND-PCA) to analyze the phenotypes of bioimages. As a data-driven technique, GND-PCA can automatically extract the important factors involved in the development of P1 and AB in C. elegans. A 3D bioimage can be regarded as a third-order tensor. Therefore, GND-PCA was applied to the set of third-order tensors, and a set of third-order tensor bases was iteratively learned to linearly approximate the set. For each tensor base, a corresponding characteristic image is built to reveal its geometric meaning. The results show that different bases can be used to express different vital factors in development, such as the asymmetric division within the two-cell stage of C. elegans. Based on selected bases, statistical models were built by 50 wild-type (WT) embryos in WDDD, and were applied to RNA interference (RNAi) embryos. The results of statistical testing demonstrated the effectiveness of this method.

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Hached, Mustapha, Khalide Jbilou, Christos Koukouvinos, and Marilena Mitrouli. "A Multidimensional Principal Component Analysis via the C-Product Golub–Kahan–SVD for Classification and Face Recognition." Mathematics 9, no. 11 (May 29, 2021): 1249. http://dx.doi.org/10.3390/math9111249.

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Face recognition and identification are very important applications in machine learning. Due to the increasing amount of available data, traditional approaches based on matricization and matrix PCA methods can be difficult to implement. Moreover, the tensorial approaches are a natural choice, due to the mere structure of the databases, for example in the case of color images. Nevertheless, even though various authors proposed factorization strategies for tensors, the size of the considered tensors can pose some serious issues. Indeed, the most demanding part of the computational effort in recognition or identification problems resides in the training process. When only a few features are needed to construct the projection space, there is no need to compute a SVD on the whole data. Two versions of the tensor Golub–Kahan algorithm are considered in this manuscript, as an alternative to the classical use of the tensor SVD which is based on truncated strategies. In this paper, we consider the Tensor Tubal Golub–Kahan Principal Component Analysis method which purpose it to extract the main features of images using the tensor singular value decomposition (SVD) based on the tensor cosine product that uses the discrete cosine transform. This approach is applied for classification and face recognition and numerical tests show its effectiveness.

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Lee, Kwanyong, and Hyeyoung Park. "Probabilistic learning of similarity measures for tensor PCA." Pattern Recognition Letters 33, no. 10 (July 2012): 1364–72. http://dx.doi.org/10.1016/j.patrec.2012.03.019.

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Reddy, G. Vijendar, B. Siva Manga Raju, K. Varshith, S. Sahil, and L. Harsha Vardhan. "Alzheimer’s Disease Recognition Applying Non-Negative Matrix Factorization Characteristics from Brain Magnetic Resonance Images (MRI)." E3S Web of Conferences 391 (2023): 01047. http://dx.doi.org/10.1051/e3sconf/202339101047.

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To more accurately depict Alzheimer’s disease (AD) and projecting clinical outcomes while taking into account advancements in clinical imaging and substantial learning, several experts are gradually using ConvNet (CNNs) to remove deep intensity features from gathering images. A small deep learning algorithm called the principal component analysis network (PCA-Net) creates multi-faceted channel banks to verify the accuracy of voluminous head part assessments. After binarization, block wise histograms are constructed to obtain picture properties. PCANet is less adaptable because multi-facet channel banks are built with test data, resulting in PCA-Net features with thousands or even millions of aspects. The non-negative matrix factorization tensor decomposition network, or NMF-TD-Net, is an information-free organization based on PCA-Net that we present in this study to address these issues. Instead of PCA, staggered channel banks are made to test nonnegative matrix factorization (NMF). By applying tensor decomposition (TD) to a higher-demand tensor derived from the learning results, the input’s dimensionality is reduced, resulting in the final image features. The support vector machine (SVM) in our technique uses these properties as input to diagnose, predict clinical score, and categorize AD.

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Yang, Ben Juan, and Ben Yong Liu. "Improvement and Kernelization of T-2DPCA with Application to Face Recognition." Applied Mechanics and Materials 713-715 (January 2015): 2177–80. http://dx.doi.org/10.4028/www.scientific.net/amm.713-715.2177.

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T-2DPCA, a novel approach considering the third-order tensors as linear operators on the space of oriented matrices, benefits from treating a 2D image as an inherently integrated object, has been proposed recently and showed better performance than traditional matrix PCA in image analysis and recognition. In T-2DPCA, a reconstructing tubal coefficient is obtained from the defined tensor product, called T-product, of a 2D image and a 2D basis element. In this study, by assuming that an eigenvector of the covariance tensor of the 2D training images is the tensor linear combination, called T-linear combination, of the training images, the T-2DPCA is improved to a new version with better performance. The improved method is further extended to a nonlinear version by using the general kernel trick in machine learning field, but with a new inner product called inside product defined with the T-product in the third-order tensor spaces, and simultaneously the general inner product defended in vector spaces. The effectiveness of the proposed algorithms is tested by face recognition experiment results.

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Shenhar, Chen, Hadassa Degani, Yaara Ber, Jack Baniel, Shlomit Tamir, Ofer Benjaminov, Philip Rosen, Edna Furman-Haran, and David Margel. "Diffusion Is Directional: Innovative Diffusion Tensor Imaging to Improve Prostate Cancer Detection." Diagnostics 11, no. 3 (March 20, 2021): 563. http://dx.doi.org/10.3390/diagnostics11030563.

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In the prostate, water diffusion is faster when moving parallel to duct and gland walls than when moving perpendicular to them, but these data are not currently utilized in multiparametric magnetic resonance imaging (mpMRI) for prostate cancer (PCa) detection. Diffusion tensor imaging (DTI) can quantify the directional diffusion of water in tissue and is applied in brain and breast imaging. Our aim was to determine whether DTI may improve PCa detection. We scanned patients undergoing mpMRI for suspected PCa with a DTI sequence. We calculated diffusion metrics from DTI and diffusion weighted imaging (DWI) for suspected lesions and normal-appearing prostate tissue, using specialized software for DTI analysis, and compared predictive values for PCa in targeted biopsies, performed when clinically indicated. DTI scans were performed on 78 patients, 42 underwent biopsy and 16 were diagnosed with PCa. The median age was 62 (IQR 54.4–68.4), and PSA 4.8 (IQR 1.3–10.7) ng/mL. DTI metrics distinguished PCa lesions from normal tissue. The prime diffusion coefficient (λ1) was lower in both peripheral-zone (p < 0.0001) and central-gland (p < 0.0001) cancers, compared to normal tissue. DTI had higher negative and positive predictive values than mpMRI to predict PCa (positive predictive value (PPV) 77.8% (58.6–97.0%), negative predictive value (NPV) 91.7% (80.6–100%) vs. PPV 46.7% (28.8–64.5%), NPV 83.3% (62.3–100%)). We conclude from this pilot study that DTI combined with T2-weighted imaging may have the potential to improve PCa detection without requiring contrast injection.

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Byeon, Yeong-Hyeon, Jae-Neung Lee, Sung-Bum Pan, and Keun-Chang Kwak. "Multilinear EigenECGs and FisherECGs for Individual Identification from Information Obtained by an Electrocardiogram Sensor." Symmetry 10, no. 10 (October 12, 2018): 487. http://dx.doi.org/10.3390/sym10100487.

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In this study, we present a third-order tensor-based multilinear eigenECG (MEECG) and multilinear Fisher ECG (MFECG) for individual identification based on the information obtained by an electrocardiogram (ECG) sensor. MEECG and MFECG are based on multilinear principal component analysis (MPCA) and multilinear linear discriminant analysis (MLDA) in the field of multilinear subspace learning (MSL), respectively. MSL directly extracts features without the vectorization of input data, while MSL extracts features without vectorizing the input data while maintaining most of the correlations shown in the original structure. In contrast with unsupervised linear subspace learning (LSL) techniques such as PCA (Principal Component Analysis) and LDA (Linear Discriminant Analysis), it is less susceptible to small-data problems because it learns more compact and potentially useful representations, and it can efficiently handle large tensors. Here, the third-order tensor is formed by reordering the one-dimensional ECG signal into a two-dimensional matrix, considering the time frame. The MSL consists of four steps. The first step is preprocessing, in which input samples are centered. The second step is initialization, in which eigen decomposition is performed and the most significant eigenvectors are selected. The third step is local optimization, in which input data is applied by eigenvectors from the second step, and new eigenvectors are calculated using the applied input data. The final step is projection, in which the resultant feature tensors after projection are obtained. The experiments are performed on two databases for performance evaluation. The Physikalisch-Technische Bundesanstalt (PTB)-ECG is a well-known database, and Chosun University (CU)-ECG is directly built for this study using the developed ECG sensor. The experimental results revealed that the tensor-based MEECG and MFECG showed good identification performance in comparison to PCA and LDA of LSL.

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Huang, Jun, Kehua Su, Jamal El-Den, Tao Hu, and Junlong Li. "An MPCA/LDA Based Dimensionality Reduction Algorithm for Face Recognition." Mathematical Problems in Engineering 2014 (2014): 1–12. http://dx.doi.org/10.1155/2014/393265.

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We proposed a face recognition algorithm based on both the multilinear principal component analysis (MPCA) and linear discriminant analysis (LDA). Compared with current traditional existing face recognition methods, our approach treats face images as multidimensional tensor in order to find the optimal tensor subspace for accomplishing dimension reduction. The LDA is used to project samples to a new discriminant feature space, while theKnearest neighbor (KNN) is adopted for sample set classification. The results of our study and the developed algorithm are validated with face databases ORL, FERET, and YALE and compared with PCA, MPCA, and PCA + LDA methods, which demonstrates an improvement in face recognition accuracy.

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Reddy, K. Shirisha, N. Arjun, and Kowkuri Hrushikesh Mudiraj. "Regression and Classification of Alzheimer’s Disease Diagnosis Using NMF-TDNet Features From 3D Brain MR Image." International Journal on Recent and Innovation Trends in Computing and Communication 11, no. 7s (July 13, 2023): 210–16. http://dx.doi.org/10.17762/ijritcc.v11i7s.6993.

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Because of headways in deep learning and clinical imaging innovation, a few specialists are presently utilizing convolutional neural networks (CNNs) to extricate profound level properties from clinical pictures to all the more exactly classify Alzheimer's disease (AD) and expect clinical scores. A limited scale profound learning network called PCANet utilizes principal component analysis (PCA) to make multi-facet channel banks for the incorporated learning of information. Blockwise histograms are made after binarization to get picture ascribes. PCANet is less versatile than different frameworks since the multi-facet channel banks are made involving test information and the produced highlights have aspects during the many thousands or even many thousands. To conquer these issues, we present in this study a PCANet-based, information free organization called the nonnegative matrix factorization tensor decomposition network (NMF-TDNet). To deliver the last picture highlights, we first form higher-request tensors and utilize tensor decomposition (TD) to achieve information dimensionality decrease. Specifically, we foster staggered channel banks for test getting the hang of utilizing nonnegative matrix factorization(NMF) as opposed to PCA. These properties serve as input to the support vector machine (SVM) that our technique employs to diagnose AD, forecast clinical score, and categorise AD.

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Mudiraj, Kowkuri Hrushikesh, N. Arjun, and K. Shirisha Reddy. "Hybrid Approach for Alzheimer’s Disease Diagnosis For 3D Brain MR Image." International Journal on Recent and Innovation Trends in Computing and Communication 11, no. 5s (May 26, 2023): 330–35. http://dx.doi.org/10.17762/ijritcc.v11i5s.6755.

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Because of headways in deep learning and clinical imaging innovation, a few specialists are presently utilizing convolutional neural networks (CNNs) to extricate profound level properties from clinical pictures to all the more exactly classify Alzheimer's disease (AD) and expect clinical scores. A limited scale profound learning network called PCANet utilizes principal component analysis (PCA) to make multi-facet channel banks for the incorporated learning of information. Blockwise histograms are made after binarization to get picture ascribes. PCANet is less versatile than different frameworks since the multi-facet channel banks are made involving test information and the produced highlights have aspects during the many thousands or even many thousands. To conquer these issues, we present in this study a PCANet-based, information free organization called the nonnegative matrix factorization tensor decomposition network (NMF-TDNet). To deliver the last picture highlights, we first form higher-request tensors and utilize tensor decomposition (TD) to achieve information dimensionality decrease. Specifically, we foster staggered channel banks for test getting the hang of utilizing nonnegative matrix factorization(NMF) as opposed to PCA. These properties serve as input to the support vector machine (SVM) that our technique employs to diagnose AD, forecast clinical score, and categorise AD.

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Meng, Shushu, Long-Ting Huang, and Wen-Qin Wang. "Tensor Decomposition and PCA Jointed Algorithm for Hyperspectral Image Denoising." IEEE Geoscience and Remote Sensing Letters 13, no. 7 (July 2016): 897–901. http://dx.doi.org/10.1109/lgrs.2016.2552403.

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Liu, Chang, Tao Yan, WeiDong Zhao, YongHong Liu, Dan Li, Feng Lin, and JiLiu Zhou. "Incremental Tensor Principal Component Analysis for Handwritten Digit Recognition." Mathematical Problems in Engineering 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/819758.

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To overcome the shortcomings of traditional dimensionality reduction algorithms, incremental tensor principal component analysis (ITPCA) based on updated-SVD technique algorithm is proposed in this paper. This paper proves the relationship between PCA, 2DPCA, MPCA, and the graph embedding framework theoretically and derives the incremental learning procedure to add single sample and multiple samples in detail. The experiments on handwritten digit recognition have demonstrated that ITPCA has achieved better recognition performance than that of vector-based principal component analysis (PCA), incremental principal component analysis (IPCA), and multilinear principal component analysis (MPCA) algorithms. At the same time, ITPCA also has lower time and space complexity.

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Wu, Hao, Ruihan Yue, Ruixue Gao, Rui Wen, Jun Feng, and Youhua Wei. "Hyperspectral denoising based on the principal component low-rank tensor decomposition." Open Geosciences 14, no. 1 (January 1, 2022): 518–29. http://dx.doi.org/10.1515/geo-2022-0379.

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Abstract Due to the characteristics of hyperspectral images (HSIs), such as their high spectral resolution and multiple continuous narrow bands, HSI technology has become widely used in fields such as target recognition, environmental detection, and agroforestry detection. HSIs are subject, for various reasons, to noise in the processes of data acquisition and transmission. Therefore, the denoising of HSIs is very necessary and important. In this article, according to the characteristics of HSIs, an HSI denoising model combining principal component analysis (PCA) and CANDECOMP/PARAFAC decomposition (CP decomposition) is proposed, which is called PCA-TensorDecomp. First, we use PCA to reduce the dimension of HSI signals by obtaining the first K principal components and get the principal composite components. The low-rank part corresponding to the first K principal components is considered the characteristic signal. Then, low-rank CP decomposition is carried out, to denoise the first principal components and the remaining minor components, the secondary composite components, which contain a large amount of noise. Finally, the inverse PCA is then used to restore the HSIs denoised, such that the effect of comprehensive denoising is achieved. To test the effectiveness of the improved algorithm introduced in this article, we compare it with several methods on simulated and real hyperspectral data. The results of the analysis herein indicate that the proposed algorithm possesses a good denoising effect.

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YU, HONGCHUAN, JIAN J. ZHANG, and XIAOSONG YANG. "TENSOR-BASED FEATURE REPRESENTATION WITH APPLICATION TO MULTIMODAL FACE RECOGNITION." International Journal of Pattern Recognition and Artificial Intelligence 25, no. 08 (December 2011): 1197–217. http://dx.doi.org/10.1142/s0218001411009081.

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In this paper, a novel feature representation to multimodal face recognition is proposed, which possesses three properties: completeness, robustness and compactness. This feature descriptor allows all information of an object to be reproduced and its representation is invariant to rigid motion. In order to effectively take advantage of the proposed feature descriptor, we amend our previous ND-PCA scheme with multidirectional decomposition technique, and provide the estimation of the upper bound error of the amended classifier. It is proved to be linear optimal compared to other linear classifiers. To investigate the numerical performance of the presented feature descriptor, we apply it to both multiple modal and single modal samples, and the revised ND-PCA classifier is performed on the resulting feature representations. The experiments of verification and identification are carried out on two different gallery-probe face databases in order for the results to be evaluated by ROC and CMC curves independently.

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Sun, Tianyu, Lang He, Xi Fang, and Liang Xie. "Enhanced Multilinear PCA for Efficient Image Analysis and Dimensionality Reduction: Unlocking the Potential of Complex Image Data." Mathematics 13, no. 3 (February 5, 2025): 531. https://doi.org/10.3390/math13030531.

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This paper presents an Enhanced Multilinear Principal Component Analysis (EMPCA) algorithm, an improved variant of the traditional Multilinear Principal Component Analysis (MPCA) tailored for efficient dimensionality reduction in high-dimensional data, particularly in image analysis tasks. EMPCA integrates random singular value decomposition to reduce computational complexity while maintaining data integrity. Additionally, it innovatively combines the dimensionality reduction method with the Mask R-CNN algorithm, enhancing the accuracy of image segmentation. Leveraging tensors, EMPCA achieves dimensionality reduction that specifically benefits image classification, face recognition, and image segmentation. The experimental results demonstrate a 17.7% reduction in computation time compared to conventional methods, without compromising accuracy. In image classification and face recognition experiments, EMPCA significantly enhances classifier efficiency, achieving comparable or superior accuracy to algorithms such as Support Vector Machines (SVMs). Additionally, EMPCA preprocessing exploits latent information within tensor structures, leading to improved segmentation performance. The proposed EMPCA algorithm holds promise for reducing image analysis runtimes and advancing rapid image processing techniques.

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Miyoshi, Tasuku, Yasuhisa Kamada, and Yoshiyuki Kobayashi. "Differences in Simulated EMG Activities between a Non-Rotational Shot and an Ordinary Instep Kick Identified by Principal Component Analysis." Proceedings 49, no. 1 (June 15, 2020): 154. http://dx.doi.org/10.3390/proceedings2020049154.

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The aim of this study was to clarify the major differences in the electromyographic (EMG) activities in the hip joint required to achieve a non-rotational (NR) shot as compared with an instep kick from the spatiotemporal data. For this purpose, simulated EMG activities obtained from NR shots and instep kicks were analyzed using principal component analysis (PCA). The PCA was conducted using an input matrix constructed from the time-normalized average and the standard deviation of the EMG activities (101 data x (15 muscles; iliacus, gluteus maximus, rectus femoris, biceos femoris, vastus lateralis, vastus medialis, vastus intermedius, semimembranosus, semitendinosus, sartorius, tensor fasciae latae muscle, adductor magnus muscle, adductor longus muscle, gasctrocnemius, and tibialis anterior)). The PCA revealed that the 3rd, 4th and 8th principal component vectors (PCVs) of the 10 generated PCVs were related to achieving the NR shot (p < 0.05).

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Liu, Jingxiang, Dan Wang, and Junghui Chen. "Monitoring Framework Based on Generalized Tensor PCA for Three-Dimensional Batch Process Data." Industrial & Engineering Chemistry Research 59, no. 22 (April 29, 2020): 10493–508. http://dx.doi.org/10.1021/acs.iecr.9b06244.

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Filisbino, Tiene A., Gilson A. Giraldi, and Carlos E. Thomaz. "Comparing Ranking Methods for Tensor Components in Multilinear and Concurrent Subspace Analysis with Applications in Face Images." International Journal of Image and Graphics 15, no. 01 (January 2015): 1550006. http://dx.doi.org/10.1142/s0219467815500060.

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In the area of multi-dimensional image databases modeling, the multilinear principal component analysis (MPCA) and concurrent subspace analysis (CSA) approaches were independently proposed and applied for mining image databases. The former follows the classical principal component analysis (PCA) paradigm that centers the sample data before subspace learning. The CSA, on the other hand, performs the learning procedure using the raw data. Besides, the corresponding tensor components have been ranked in order to identify the principal tensor subspaces for separating sample groups for face image analysis and gait recognition. In this paper, we first demonstrate that if CSA receives centered input samples and we consider full projection matrices then the obtained solution is equal to the one generated by MPCA. Then, we consider the general problem of ranking tensor components. We examine the theoretical aspects of typical solutions in this field: (a) Estimating the covariance structure of the database; (b) Computing discriminant weights through separating hyperplanes; (c) Application of Fisher criterium. We discuss these solutions for tensor subspaces learned using centered data (MPCA) and raw data (CSA). In the experimental results we focus on tensor principal components selected by the mentioned techniques for face image analysis considering gender classification as well as reconstruction problems.

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Taguchi, Y.-h., and Turki Turki. "Projection in genomic analysis: A theoretical basis to rationalize tensor decomposition and principal component analysis as feature selection tools." PLOS ONE 17, no. 9 (September 29, 2022): e0275472. http://dx.doi.org/10.1371/journal.pone.0275472.

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Identifying differentially expressed genes is difficult because of the small number of available samples compared with the large number of genes. Conventional gene selection methods employing statistical tests have the critical problem of heavy dependence of P-values on sample size. Although the recently proposed principal component analysis (PCA) and tensor decomposition (TD)-based unsupervised feature extraction (FE) has often outperformed these statistical test-based methods, the reason why they worked so well is unclear. In this study, we aim to understand this reason in the context of projection pursuit (PP) that was proposed a long time ago to solve the problem of dimensions; we can relate the space spanned by singular value vectors with that spanned by the optimal cluster centroids obtained from K-means. Thus, the success of PCA- and TD-based unsupervised FE can be understood by this equivalence. In addition to this, empirical threshold adjusted P-values of 0.01 assuming the null hypothesis that singular value vectors attributed to genes obey the Gaussian distribution empirically corresponds to threshold-adjusted P-values of 0.1 when the null distribution is generated by gene order shuffling. For this purpose, we newly applied PP to the three data sets to which PCA and TD based unsupervised FE were previously applied; these data sets treated two topics, biomarker identification for kidney cancers (the first two) and the drug discovery for COVID-19 (the thrid one). Then we found the coincidence between PP and PCA or TD based unsupervised FE is pretty well. Shuffling procedures described above are also successfully applied to these three data sets. These findings thus rationalize the success of PCA- and TD-based unsupervised FE for the first time.

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Taguchi, Y.-h., and Turki Turki. "Tensor-Decomposition-Based Unsupervised Feature Extraction Applied to Prostate Cancer Multiomics Data." Genes 11, no. 12 (December 11, 2020): 1493. http://dx.doi.org/10.3390/genes11121493.

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The large p small n problem is a challenge without a de facto standard method available to it. In this study, we propose a tensor-decomposition (TD)-based unsupervised feature extraction (FE) formalism applied to multiomics datasets, in which the number of features is more than 100,000 whereas the number of samples is as small as about 100, hence constituting a typical large p small n problem. The proposed TD-based unsupervised FE outperformed other conventional supervised feature selection methods, random forest, categorical regression (also known as analysis of variance, or ANOVA), penalized linear discriminant analysis, and two unsupervised methods, multiple non-negative matrix factorization and principal component analysis (PCA) based unsupervised FE when applied to synthetic datasets and four methods other than PCA based unsupervised FE when applied to multiomics datasets. The genes selected by TD-based unsupervised FE were enriched in genes known to be related to tissues and transcription factors measured. TD-based unsupervised FE was demonstrated to be not only the superior feature selection method but also the method that can select biologically reliable genes. To our knowledge, this is the first study in which TD-based unsupervised FE has been successfully applied to the integration of this variety of multiomics measurements.

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Yan, Ronghua, Jinye Peng, and Dongmei Ma. "Dimensionality Reduction Based on PARAFAC Model." Journal of Imaging Science and Technology 63, no. 6 (November 1, 2019): 60501–1. http://dx.doi.org/10.2352/j.imagingsci.technol.2019.63.6.060501.

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Abstract In hyperspectral image analysis, dimensionality reduction is a preprocessing step for hyperspectral image (HSI) classification. Principal component analysis (PCA) reduces the spectral dimension and does not utilize the spatial information of an HSI. To solve it, the tensor decompositions have been successfully applied to joint noise reduction in spatial and spectral dimensions of hyperspectral images, such as parallel factor analysis (PARAFAC). However, the PARAFAC method does not reduce the dimension in the spectral dimension. To improve it, two new methods were proposed in this article, that is, combine PCA and PARAFAC to reduce both the dimension in the spectral dimension and the noise in the spatial and spectral dimensions. The experimental results indicate that the new methods improve the classification compared with the PARAFAC method.

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Munia, Tamanna T. K., and Selin Aviyente. "Multivariate Analysis of Bivariate Phase-Amplitude Coupling in EEG Data Using Tensor Robust PCA." IEEE Transactions on Neural Systems and Rehabilitation Engineering 29 (2021): 1268–79. http://dx.doi.org/10.1109/tnsre.2021.3092890.

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Skantze, Viktor, Mikael Wallman, Ann-Sofie Sandberg, Rikard Landberg, Mats Jirstrand, and Carl Brunius. "Identifying Metabotypes From Complex Biological Data Using PARAFAC." Current Developments in Nutrition 5, Supplement_2 (June 2021): 882. http://dx.doi.org/10.1093/cdn/nzab048_017.

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Abstract Objectives Research have identified large individual variation in physiological response to diet, which has led to more focused investigations in precision nutrition. One approach towards personalized nutrition is to identify groups of differential responders, so called metabotypes (i.e., clusters of individuals with similar metabolic profiles and/or regulation). Metabotyping has previously been addressed using matrix decomposition tools like principal component analysis (PCA) on data organized in matrix form. However, metabotyping using data from more complex experimental designs, involving e.g., repeated measures over time or multiple treatments (tensor data), requires new methods. Methods We developed a workflow for detecting metabotypes from experimental tensor data. The workflow is based on tensor decomposition, specifically PARAFAC which is conceptually similar to PCA but extended to multidimensional data. Metabotypes, based on metabolomics data were identified from PARAFAC scores using k-means clustering and validated by their association to anthropometric and clinical baseline data. Additionally, we evaluated the robustness of the metabotypes using bootstrapping. Furthermore, we applied the workflow to identify metabotypes using data from a crossover acute post-prandial dietary intervention study on 17 overweight males (BMI 25–30 kg/m2, 41–67 y of age) undergoing three dietary interventions (pickled herring, baked herring and baked beef), measuring 80 metabolites (from GC-MS metabolomics) at 8 time points (0–7h). Results We identified two metabotypes characterized by differences in amino acid levels, predominantly in the beef diet, that were also associated with creatinine (p = 0.007). The metabotype with higher postprandial amino acid levels was also associated with higher fasting creatinine compared to the other metabotype. Conclusions The results stress the potential of PARAFAC to discover metabotypes from complex study designs. The workflow is not restricted to our data structure and can be applied to any type of tensor data. However, PARAFAC is sensitive to data pre-processing and further studies where differential metabotypes are related to clinical endpoints are highly warranted. Funding Sources This work has been supported by the Swedish Foundation for Strategic Research and Formas, which is gratefully acknowledged.

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Salmanpour, Mohammad R., Seyed Masoud Rezaeijo, Mahdi Hosseinzadeh, and Arman Rahmim. "Deep versus Handcrafted Tensor Radiomics Features: Prediction of Survival in Head and Neck Cancer Using Machine Learning and Fusion Techniques." Diagnostics 13, no. 10 (May 11, 2023): 1696. http://dx.doi.org/10.3390/diagnostics13101696.

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Background: Although handcrafted radiomics features (RF) are commonly extracted via radiomics software, employing deep features (DF) extracted from deep learning (DL) algorithms merits significant investigation. Moreover, a “tensor’’ radiomics paradigm where various flavours of a given feature are generated and explored can provide added value. We aimed to employ conventional and tensor DFs, and compare their outcome prediction performance to conventional and tensor RFs. Methods: 408 patients with head and neck cancer were selected from TCIA. PET images were first registered to CT, enhanced, normalized, and cropped. We employed 15 image-level fusion techniques (e.g., dual tree complex wavelet transform (DTCWT)) to combine PET and CT images. Subsequently, 215 RFs were extracted from each tumor in 17 images (or flavours) including CT only, PET only, and 15 fused PET-CT images through the standardized-SERA radiomics software. Furthermore, a 3 dimensional autoencoder was used to extract DFs. To predict the binary progression-free-survival-outcome, first, an end-to-end CNN algorithm was employed. Subsequently, we applied conventional and tensor DFs vs. RFs as extracted from each image to three sole classifiers, namely multilayer perceptron (MLP), random-forest, and logistic regression (LR), linked with dimension reduction algorithms. Results: DTCWT fusion linked with CNN resulted in accuracies of 75.6 ± 7.0% and 63.4 ± 6.7% in five-fold cross-validation and external-nested-testing, respectively. For the tensor RF-framework, polynomial transform algorithms + analysis of variance feature selector (ANOVA) + LR enabled 76.67 ± 3.3% and 70.6 ± 6.7% in the mentioned tests. For the tensor DF framework, PCA + ANOVA + MLP arrived at 87.0 ± 3.5% and 85.3 ± 5.2% in both tests. Conclusions: This study showed that tensor DF combined with proper machine learning approaches enhanced survival prediction performance compared to conventional DF, tensor and conventional RF, and end-to-end CNN frameworks.

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Gorgannejad, S., M. Reisi Gahrooei, K. Paynabar, and R. W. Neu. "Quantitative prediction of the aged state of Ni-base superalloys using PCA and tensor regression." Acta Materialia 165 (February 2019): 259–69. http://dx.doi.org/10.1016/j.actamat.2018.11.047.

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Verma, Gaurav, Siddhisanket Raskar, Murali Emani, and Barbara Chapman. "Cross-Feature Transfer Learning for Efficient Tensor Program Generation." Applied Sciences 14, no. 2 (January 6, 2024): 513. http://dx.doi.org/10.3390/app14020513.

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Tuning tensor program generation involves navigating a vast search space to find optimal program transformations and measurements for a program on the target hardware. The complexity of this process is further amplified by the exponential combinations of transformations, especially in heterogeneous environments. This research addresses these challenges by introducing a novel approach that learns the joint neural network and hardware features space, facilitating knowledge transfer to new, unseen target hardware. A comprehensive analysis is conducted on the existing state-of-the-art dataset, TenSet, including a thorough examination of test split strategies and the proposal of methodologies for dataset pruning. Leveraging an attention-inspired technique, we tailor the tuning of tensor programs to embed both neural network and hardware-specific features. Notably, our approach substantially reduces the dataset size by up to 53% compared to the baseline without compromising Pairwise Comparison Accuracy (PCA). Furthermore, our proposed methodology demonstrates competitive or improved mean inference times with only 25–40% of the baseline tuning time across various networks and target hardware. The attention-based tuner can effectively utilize schedules learned from previous hardware program measurements to optimize tensor program tuning on previously unseen hardware, achieving a top-5 accuracy exceeding 90%. This research introduces a significant advancement in autotuning tensor program generation, addressing the complexities associated with heterogeneous environments and showcasing promising results regarding efficiency and accuracy.

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Kleshchenko, E. I., M. P. Yakovenko, D. A. Kayumova, M. G. Kulagina, E. V. Borovikova, E. P. Apalkova, and A. F. Komarov. "Сharacteristics of nervous system damage in children born with a very low and extremely low birthweight and perinatal hypoxic brain injury." Kuban Scientific Medical Bulletin 27, no. 2 (April 12, 2020): 70–80. http://dx.doi.org/10.25207/1608-6228-2020-27-2-70-80.

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Aim. To determine the frequency of structural damage to the pyramidal tract in the region of crus posterius capsulae internae in children with a birthweight of less than one and a half kilograms with perinatal hypoxic damage to the nervous system using the value of fractional anisotropy according to diffusion-tensor magnetic resonance imaging at 39 weeks of post-conceptual age (PCA).Materials and methods. The study included 68 children born with a very low birthweight and 59 children with an extremely low birthweight demonstrating brain structural changes at 39 weeks of postconceptual age according to neurosonography. At 39 weeks of postconceptual age, the children included in the study underwent diffuse tensor magnetic resonance imaging (DT MRI) with the determination of fractional anisotropy.Results. At 39 weeks of PCA, all children had impaired neurological status. During DT MRI, the area of interest was crus posterius capsulae internae. Significant differences in the nature of structural damage to the pyramidal tract in the area of interest between children born with a very low and extremely low birthweight were not observed.Conclusion. Damage to the pyramidal tract was observed in 22.0% of children born with an extremely low birthweight, and in 13.2% of children born with a very low birthweight; partial destruction of the pathways was noted in 47.5% and 45.6% of children, respectively. Intact pyramidal tracts were visualized in 30.5% of children born with an extremely low birthweight and 41.2% of children born with a very low birhtweight.

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Kerkour-El Miad, Aissa, and A. Kerour-El Miad. "Application of Principal Component Analysis (PCA) for the Choice of Parameters of a Micromechanical Model." Key Engineering Materials 820 (September 2019): 75–84. http://dx.doi.org/10.4028/www.scientific.net/kem.820.75.

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The main objective of this work is to apply the Principal Component Analysis (PCA) to the key parameters of a micromechanical model, namely the shape parameter of inclusion (grain) (ratio =a/b) and γ viscoplastic parameter in view of a better simulation. In this work, the sensitivity of the model to parameters and γ is evaluated on the stabilized global stress during cyclic Tension-Compression (TC) loadings and out-of-phase Tension–Torsion, with a sinusoidal waveform and a phase lag of 90 between the two sinusoidal signals TT90 loadings. Indeed several values of and γ are pulled thanks to these loading, we use later the PCA in order to choose the couple (, γ) adequate to launch our simulation. The model used is expressed as part of the self-consistent approach and time-dependent plasticity. Based on the Eshelby tensor, this model considers that the elastic behavior is compressible. For a polycrystalline structure, the grains are deformed by crystallographic sliding located in the most favorably oriented systems and which support a strong constrained stress . Keywords: PCA, grain shape , viscoplastic parameter γ, Self-consistent model, Non-incremental interaction law, Elasto-inelastic. TC and TT90 loading

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Zhang, Fan, Xiaoping Wang, and Ke Sun. "A Report on Multilinear PCA Plus GTDA to Deal With Face Image." Cybernetics and Information Technologies 16, no. 1 (March 1, 2016): 146–57. http://dx.doi.org/10.1515/cait-2016-0012.

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Abstract Because face images are naturally two-dimensional data, there have been several 2D feature extraction methods to deal with facial images while there are few 2D effective classifiers. Meanwhile, there is an increasing interest in the multilinear subspace analysis and many methods have been proposed to operate directly on these tensorial data during the past several years. One of these popular unsupervised multilinear algorithms is Multilinear Principal Component Analysis (MPCA) while another of the supervised multilinear algorithm is Multilinear Discriminant Analysis (MDA). Then a MPCA+MDA method has been introduced to deal with the tensorial signal. However, due to the no convergence of MDA, it is difficult for MPCA+MDA to obtain a precise result. Hence, to overcome this limitation, a new MPCA plus General Tensor Discriminant Analysis (GTDA) solution with well convergence is presented for tensorial face images feature extraction in this paper. Several experiments are carried out to evaluate the performance of MPCA+GTDA on different databases and the results show that this method has the potential to achieve comparative effect as MPCA+MDA.

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Caporale, Alessandra Stella, Marco Nezzo, Maria Giovanna Di Trani, Alessandra Maiuro, Roberto Miano, Pierluigi Bove, Alessandro Mauriello, Guglielmo Manenti, and Silvia Capuani. "Acquisition Parameters Influence Diffusion Metrics Effectiveness in Probing Prostate Tumor and Age-Related Microstructure." Journal of Personalized Medicine 13, no. 5 (May 20, 2023): 860. http://dx.doi.org/10.3390/jpm13050860.

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This study aimed to investigate the Diffusion-Tensor-Imaging (DTI) potential in the detection of microstructural changes in prostate cancer (PCa) in relation to the diffusion weight (b-value) and the associated diffusion length lD. Thirty-two patients (age range = 50–87 years) with biopsy-proven PCa underwent Diffusion-Weighted-Imaging (DWI) at 3T, using single non-zero b-value or groups of b-values up to b = 2500 s/mm2. The DTI maps (mean-diffusivity, MD; fractional-anisotropy, FA; axial and radial diffusivity, D// and D┴), visual quality, and the association between DTI-metrics and Gleason Score (GS) and DTI-metrics and age were discussed in relation to diffusion compartments probed by water molecules at different b-values. DTI-metrics differentiated benign from PCa tissue (p ≤ 0.0005), with the best discriminative power versus GS at b-values ≥ 1500 s/mm2, and for b-values range 0–2000 s/mm2, when the lD is comparable to the size of the epithelial compartment. The strongest linear correlations between MD, D//, D┴, and GS were found at b = 2000 s/mm2 and for the range 0–2000 s/mm2. A positive correlation between DTI parameters and age was found in benign tissue. In conclusion, the use of the b-value range 0–2000 s/mm2 and b-value = 2000 s/mm2 improves the contrast and discriminative power of DTI with respect to PCa. The sensitivity of DTI parameters to age-related microstructural changes is worth consideration.

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Turki, Turki, Sanjiban Sekhar Roy, and Y. H. Taguchi. "Optimized Tensor Decomposition and Principal Component Analysis Outperforming State-of-the-Art Methods When Analyzing Histone Modification Chromatin Immunoprecipitation Profiles." Algorithms 16, no. 9 (August 23, 2023): 401. http://dx.doi.org/10.3390/a16090401.

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It is difficult to identify histone modification from datasets that contain high-throughput sequencing data. Although multiple methods have been developed to identify histone modification, most of these methods are not specific to histone modification but are general methods that aim to identify protein binding to the genome. In this study, tensor decomposition (TD) and principal component analysis (PCA)-based unsupervised feature extraction with optimized standard deviation were successfully applied to gene expression and DNA methylation. The proposed method was used to identify histone modification. Histone modification along the genome is binned within the region of length L. Considering principal components (PCs) or singular value vectors (SVVs) that PCA or TD attributes to samples, we can select PCs or SVVs attributed to regions. The selected PCs and SVVs further attribute p-values to regions, and adjusted p-values are used to select regions. The proposed method identified various histone modifications successfully and outperformed various state-of-the-art methods. This method is expected to serve as a de facto standard method to identify histone modification. For reproducibility and to ensure the systematic analysis of our study is applicable to datasets from different gene expression experiments, we have made our tools publicly available for download from gitHub.

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Agajo, James, Emeshili O. Joseph, Emmanuel Eronu, and Evans Ashigwuike. "An Algorithm for Spectrum Hole Detection using Convex Optimization And Tensor Analysis In Cognitive Radio Network." Journal of Biomedical Engineering and Medical Imaging 6, no. 6 (December 31, 2019): 01–24. http://dx.doi.org/10.14738/jbemi.66.8010.

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The issue of speed and accuracy is one major challenge in the area of Spectrum hole detection in Cognitive Radio Network(CRN), owing to some of the techniques used in the previous past, noise is sometimes recorded against spectrum hole, and this is mostly due to the method adopted , the need for a more compact procedure as become necessary. An Algorithm for Spectrum Hole Detecting using Convex Optimization and Tensor analysis in Cognitive Radio Network seeks to present a way out of it. The tensor analysis will provide an infinite representation Spectrum data from the wideband, while Convex optimization will help split the large data by grouping it into various spectrum segment, based on the objective function, this grouping will help improve on the speed of Spectrum hole detection. Principal Component Analysis(PCA) checks the level of correction using orthogonal transformation, the use of Eigen Values and Eigen Vectors will further help linearize the function by finding the roots. Covariance matrix will help further check how the variable varies together. It describes the dimension of the spectrum data. Diagonisation is used to extract the matrix with the spectrum data using singular value decomposition; finally, Bayesian inference will optimise decision making for spectrum data.

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Biroli, Giulio, Chiara Cammarota, and Federico Ricci-Tersenghi. "How to iron out rough landscapes and get optimal performances: averaged gradient descent and its application to tensor PCA." Journal of Physics A: Mathematical and Theoretical 53, no. 17 (April 8, 2020): 174003. http://dx.doi.org/10.1088/1751-8121/ab7b1f.

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Rhee, Hannah S., and Joseph F. Y. Hoh. "Immunohistochemical Analysis of Myosin Heavy Chain Expression in Laryngeal Muscles of the Rabbit, Cat, and Baboon." Journal of Histochemistry & Cytochemistry 56, no. 10 (June 23, 2008): 929–50. http://dx.doi.org/10.1369/jhc.2008.951756.

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We studied myosin heavy chain (MyHC) expression and fiber type distribution in laryngeal muscles in the rabbit, cat, and baboon using immunohistochemistry with highly MyHC-specific antibodies. Two types of variation in MyHC expression were found: between muscles of different function within species and within specific muscles between species. Within species, thyroarytenoid (Ta), an adductor, had faster MyHCs and fiber type profiles than the abductor, posterior cricoarytenoid (PCA), which expressed faster MyHCs than the vocal fold tensor, cricothyroid (CT). Between species, laryngeal muscles generally expressed faster MyHCs in small animals than in larger ones: extraocular (EO) MyHC was expressed in the Ta and PCA of the rabbit but not in the cat and baboon, whereas 2B MyHC was expressed in these muscles of the cat but not of the baboon. The CT expressed only MyHC isoforms and fiber types found in the limb muscles of the same species. These results are discussed in light of the hypothesis that the between-species variations in laryngeal muscle fiber types are evolutionary adaptations in response to changes in body mass and respiratory frequency. Within-species variations in fiber types ensure that protective closure of the glottis is always faster than movements regulating airflow during respiration.

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LU, Zheng-Liang, and U. Hou LOK. "Dimension-Reduced Modeling for Local Volatility Surface via Unsupervised Learning." Romanian Journal of Information Science and Technology 27, no. 3-4 (September 30, 2024): 255–66. http://dx.doi.org/10.59277/romjist.2024.3-4.01.

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Volatility is a key factor for option pricing. It displays skewness across different strike prices and maturity days when implied by the Black-Scholes formula. This phenomenon is called the volatility smile. The local volatility model is popular because it fits this smile. It assumes the volatilities a deterministic function of underlying asset and time. These volatilities form the local volatility surface (LVS). LVS evolves over time and this dynamics can be high-dimensional and fluctuating. In this research, we show that the LVS may be described by a small number of orthogonal factors. This is accomplished by studying the LVS dynamics with time series data on option prices and extracting their essences via principal component analysis (PCA) and multilinear PCA (MPCA). We aim at recognizing these dominant components. In this case, the dimensions of LVS are reduced, and these dominant components are used to reconstruct the LVS. Numerical results show that the reconstructed LVS retains the important characteristics while filtering out noise well. In particular, over 80% of observations are within 10% in the maximum absolute relative difference (MARD). Moreover, MPCA provides an extra degree of freedom for reconstruction as well as interpretation because it preserves the tensor structure.

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Liang, Peidong, Chentao Zhang, Habte Tadesse Likassa, and Jielong Guo. "New Robust Tensor PCA via Affine Transformations and L 2,1 Norms for Exact Tubal Low-Rank Recovery from Highly Corrupted and Correlated Images in Signal Processing." Mathematical Problems in Engineering 2022 (March 31, 2022): 1–14. http://dx.doi.org/10.1155/2022/3002348.

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In this latest work, the Newly Modified Robust Tensor Principal Component Analysis (New RTPCA) using affine transformation and L 2,1 norms is proposed to remove the outliers and heavy sparse noises in signal processing. This process is done by decomposing the original data matrix as the low-rank heavy sparse noises. The determination of the potential variables is casted as constrained convex optimization problem, and the Alternating Direction Method of Multipliers (ADMM) method is considered to reduce the computational loads in an iterative manner. The simulation results validate the effectiveness of the new method as compared with that of the state-of-the-art methods.

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Uhliar, Matej. "Atomic partial charge model in chemistry: chemical accuracy of theoretical approaches for diatomic molecules." Acta Chimica Slovaca 17, no. 1 (January 1, 2024): 1–11. http://dx.doi.org/10.2478/acs-2024-0001.

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Abstract Atomic partial charges cannot be physically measured but they play a significant role in many chemical theories and theoretical models. Therefore, they are, evaluated from experimentally acquired properties or calculated by quantum chemistry computational methods. This study is focused on determining chemical accuracy of various theoretical methods of computing atomic partial charges based on quantum chemistry. Values of gas-phase atomic partial charges were acquired by Mulliken (MUL) population analysis, natural bond analysis (NBO), Merz-Singh-Kollman (MSK) scheme, and atomic polar tensor (APT) charges computed considering Density Functional Theory and ab initio Møller-Plesset up to the second order levels. Correlations between the calculated values were determined by principal component analysis (PCA) and further confirmed by linear regression. The best agreement between experimentally evaluated atomic partial charges and theoretical values was obtained with the MSK scheme.

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Qing, Yuhao, and Wenyi Liu. "Hyperspectral Image Classification Based on Multi-Scale Residual Network with Attention Mechanism." Remote Sensing 13, no. 3 (January 20, 2021): 335. http://dx.doi.org/10.3390/rs13030335.

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In recent years, image classification on hyperspectral imagery utilizing deep learning algorithms has attained good results. Thus, spurred by that finding and to further improve the deep learning classification accuracy, we propose a multi-scale residual convolutional neural network model fused with an efficient channel attention network (MRA-NET) that is appropriate for hyperspectral image classification. The suggested technique comprises a multi-staged architecture, where initially the spectral information of the hyperspectral image is reduced into a two-dimensional tensor, utilizing a principal component analysis (PCA) scheme. Then, the constructed low-dimensional image is input to our proposed ECA-NET deep network, which exploits the advantages of its core components, i.e., multi-scale residual structure and attention mechanisms. We evaluate the performance of the proposed MRA-NET on three public available hyperspectral datasets and demonstrate that, overall, the classification accuracy of our method is 99.82 %, 99.81%, and 99.37, respectively, which is higher compared to the corresponding accuracy of current networks such as 3D convolutional neural network (CNN), three-dimensional residual convolution structure (RES-3D-CNN), and space–spectrum joint deep network (SSRN).

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Chen, Hanxin, Shaoyi Li, and Menglong Li. "Multi-Channel High-Dimensional Data Analysis with PARAFAC-GA-BP for Nonstationary Mechanical Fault Diagnosis." International Journal of Turbomachinery, Propulsion and Power 7, no. 3 (June 28, 2022): 19. http://dx.doi.org/10.3390/ijtpp7030019.

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Conventional signal processing methods such as Principle Component Analysis (PCA) focus on the decomposition of signals in the 2D time–frequency domain. Parallel factor analysis (PARAFAC) is a novel method used to decompose multi-dimensional arrays, which focuses on analyzing the relevant feature information by deleting the duplicated information among the multiple measurement points. In the paper, a novel hybrid intelligent algorithm for the fault diagnosis of a mechanical system was proposed to analyze the multiple vibration signals of the centrifugal pump system and multi-dimensional complex signals created by pressure and flow information. The continuous wavelet transform was applied to analyze the high-dimensional multi-channel signals to construct the 3D tensor, which makes use of the advantages of the parallel factor decomposition to extract feature information of the complex system. The method was validated by diagnosing the nonstationary failure modes under the faulty conditions with impeller blade damage, impeller perforation damage and impeller edge damage. The correspondence between different fault characteristics of a centrifugal pump in a time and frequency information matrix was established. The characteristic frequency ranges of the fault modes are effectively presented. The optimization method for a PARAFAC-BP neural network is proposed using a genetic algorithm (GA) to significantly improve the accuracy of the centrifugal pump fault diagnosis.

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Þórðarson, Andri Freyr, Andreas Baum, Mónica García, Sergio M. Vicente-Serrano, and Anders Stockmarr. "Gap-Filling of NDVI Satellite Data Using Tucker Decomposition: Exploiting Spatio-Temporal Patterns." Remote Sensing 13, no. 19 (October 6, 2021): 4007. http://dx.doi.org/10.3390/rs13194007.

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Remote sensing satellite images in the optical domain often contain missing or misleading data due to overcast conditions or sensor malfunctioning, concealing potentially important information. In this paper, we apply expectation maximization (EM) Tucker to NDVI satellite data from the Iberian Peninsula in order to gap-fill missing information. EM Tucker belongs to a family of tensor decomposition methods that are known to offer a number of interesting properties, including the ability to directly analyze data stored in multidimensional arrays and to explicitly exploit their multiway structure, which is lost when traditional spatial-, temporal- and spectral-based methods are used. In order to evaluate the gap-filling accuracy of EM Tucker for NDVI images, we used three data sets based on advanced very-high resolution radiometer (AVHRR) imagery over the Iberian Peninsula with artificially added missing data as well as a data set originating from the Iberian Peninsula with natural missing data. The performance of EM Tucker was compared to a simple mean imputation, a spatio-temporal hybrid method, and an iterative method based on principal component analysis (PCA). In comparison, imputation of the missing data using EM Tucker consistently yielded the most accurate results across the three simulated data sets, with levels of missing data ranging from 10 to 90%.

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Lien, Chung-Yueh, Tseng-Tse Chen, En-Tung Tsai, Yu-Jer Hsiao, Ni Lee, Chong-En Gao, Yi-Ping Yang, et al. "Recognizing the Differentiation Degree of Human Induced Pluripotent Stem Cell-Derived Retinal Pigment Epithelium Cells Using Machine Learning and Deep Learning-Based Approaches." Cells 12, no. 2 (January 4, 2023): 211. http://dx.doi.org/10.3390/cells12020211.

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Induced pluripotent stem cells (iPSCs) can be differentiated into mesenchymal stem cells (iPSC-MSCs), retinal ganglion cells (iPSC-RGCs), and retinal pigmental epithelium cells (iPSC-RPEs) to meet the demand of regeneration medicine. Since the production of iPSCs and iPSC-derived cell lineages generally requires massive and time-consuming laboratory work, artificial intelligence (AI)-assisted approach that can facilitate the cell classification and recognize the cell differentiation degree is of critical demand. In this study, we propose the multi-slice tensor model, a modified convolutional neural network (CNN) designed to classify iPSC-derived cells and evaluate the differentiation efficiency of iPSC-RPEs. We removed the fully connected layers and projected the features using principle component analysis (PCA), and subsequently classified iPSC-RPEs according to various differentiation degree. With the assistance of the support vector machine (SVM), this model further showed capabilities to classify iPSCs, iPSC-MSCs, iPSC-RPEs, and iPSC-RGCs with an accuracy of 97.8%. In addition, the proposed model accurately recognized the differentiation of iPSC-RPEs and showed the potential to identify the candidate cells with ideal features and simultaneously exclude cells with immature/abnormal phenotypes. This rapid screening/classification system may facilitate the translation of iPSC-based technologies into clinical uses, such as cell transplantation therapy.

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Journal articles on the topic 'Tensor PCA'

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