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Journal articles on the topic 'Khatri-Rao product'

Author: Grafiati

Published: 6 September 2023

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1

Ploymukda, Arnon, and Pattrawut Chansangiam. "Khatri-Rao Products for Operator Matrices Acting on the Direct Sum of Hilbert Spaces." Journal of Mathematics 2016 (2016): 1–7. http://dx.doi.org/10.1155/2016/8301709.

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We introduce the notion of Khatri-Rao product for operator matrices acting on the direct sum of Hilbert spaces. This notion generalizes the tensor product and Hadamard product of operators and the Khatri-Rao product of matrices. We investigate algebraic properties, positivity, and monotonicity of the Khatri-Rao product. Moreover, there is a unital positive linear map taking Tracy-Singh products to Khatri-Rao products via an isometry.

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2

Ploymukda, Arnon, and Pattrawut Chansangiam. "Norm estimations, continuity, and compactness for Khatri-Rao products of Hilbert Space operators." Malaysian Journal of Fundamental and Applied Sciences 14, no. 4 (2018): 382–86. http://dx.doi.org/10.11113/mjfas.v14n4.881.

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We provide estimations for the operator norm, the trace norm, and the Hilbert-Schmidt norm for Khatri-Rao products of Hilbert space operators. It follows that the Khatri-Rao product is continuous on norm ideals of compact operators equipped with the topologies induced by such norms. Moreover, if two operators are represented by block matrices in which each block is nonzero, then their Khatri-Rao product is compact if and only if both operators are compact. The Khatri-Rao product of two operators are trace-class (Hilbert-Schmidt class) if and only if each factor is trace-class (Hilbert-Schmidt

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3

Ploymukda, Arnon, and Pattrawut Chansangiam. "Inequalities on weighted classical pythagorean means, Tracy-Singh products, and Khatri-Rao products for hermitian operators." Malaysian Journal of Fundamental and Applied Sciences 16, no. 2 (2020): 223–27. http://dx.doi.org/10.11113/mjfas.v16n2.1359.

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We establish a number of operator inequalities between three kinds of means, namely, weighted arithmetic/harmonic/geometric means, and two kinds of operator products, namely, Tracy-Singh products and Khatri-Rao products. These results are valid under certain assumptions relying on (opposite) synchronization, comparability, and spectra of operators. Our results include tensor product of operators, and Tracy-Singh/Khatri-Rao products of matrices as special cases.

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4

Yang, Zhongpeng, Shuangzhe Liu, and Götz Trenkler. "Further inequalities involving the Khatri-Rao product." Linear Algebra and its Applications 430, no. 10 (2009): 2696–704. http://dx.doi.org/10.1016/j.laa.2008.12.004.

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5

ć Hot, Jadranka Mić. "Inequalities involving the Khatri-Rao product of matrices." Journal of Mathematical Inequalities, no. 4 (2009): 617–30. http://dx.doi.org/10.7153/jmi-03-60.

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6

Dong, Sheng, Qingwen Wang, and Lei Hou. "Determinantal inequalities for block Hadamard product and Khatri-Rao product of positive definite matrices." AIMS Mathematics 7, no. 6 (2022): 9648–55. http://dx.doi.org/10.3934/math.2022536.

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<abstract><p>In this paper, we first give an alternative proof for a result of Liu et al. in [Math. Inequal. Appl. 20 (2017) 537–542]. Then we present two inequalities for the block Hadamard product and the Khatri-Rao product respectively. The inequalities obtained extend the result of Liu et al.</p></abstract>

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7

Abubaker, Nabil, Seher Acer, and Cevdet Aykanat. "True Load Balancing for Matricized Tensor Times Khatri-Rao Product." IEEE Transactions on Parallel and Distributed Systems 32, no. 8 (2021): 1974–86. http://dx.doi.org/10.1109/tpds.2021.3053836.

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8

ao Li, Yong, and L. hua Feng. "An Oppenheim type determinantal inequality for the Khatri-Rao product." Operators and Matrices, no. 2 (2021): 693–701. http://dx.doi.org/10.7153/oam-2021-15-47.

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9

Khanna, Saurabh, and Chandra R. Murthy. "On the Restricted Isometry of the Columnwise Khatri–Rao Product." IEEE Transactions on Signal Processing 66, no. 5 (2018): 1170–83. http://dx.doi.org/10.1109/tsp.2017.2781652.

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10

Konishi, Jumpei, Hiroyoshi Yamada, and Yoshio Yamaguchi. "Optimum element arrangements in MIMO radar using Khatri-Rao product virtual array processing." IEICE Communications Express 7, no. 11 (2018): 407–14. http://dx.doi.org/10.1587/comex.2018xbl0104.

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11

WAKAMATSU, Yosuke, Hiroyoshi YAMADA, and Yoshio YAMAGUCHI. "MIMO Doppler Radar Using Khatri-Rao Product Virtual Array for Indoor Human Detection." IEICE Transactions on Communications E99.B, no. 1 (2016): 124–33. http://dx.doi.org/10.1587/transcom.2015isp0029.

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12

Al Zhour, Zeyad Abdel Aziz, and Adem Kilicman. "Extension and generalization inequalities involving the Khatri-Rao product of several positive matrices." Journal of Inequalities and Applications 2006 (2006): 1–21. http://dx.doi.org/10.1155/jia/2006/80878.

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13

Ambroży-Deręgowska, Katarzyna, and Iwona Mejza. "On a construction procedure for split-block-plot designs based on the Khatri–Rao product of incidence matrices." Biometrical Letters 59, no. 1 (2022): 55–63. http://dx.doi.org/10.2478/bile-2022-0005.

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Summary The construction of incomplete split-block-plot (SBP) designs for three-factor experiments is investigated. A semi-Kronecker (Khatri–Rao) product of matrices is used in the construction procedure. With this method some generated designs are obtained where column treatments and subplot treatments are allocated in balanced square lattice designs, while row treatments are in a randomized complete block design. Experiments with an orthogonal block structure are considered. In this paper we consider designs which are generally balanced. This allows us to give the stratum efficiency factors

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14

Chen, Tao, Huanxin Wu, and Zhongkai Zhao. "The Real-Valued Sparse Direction of Arrival (DOA) Estimation Based on the Khatri-Rao Product." Sensors 16, no. 5 (2016): 693. http://dx.doi.org/10.3390/s16050693.

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15

YAMADA, Hiroyoshi, Naoki OZAWA, Yoshio YAMAGUCHI, Keizo HIRANO, and Hiroyuki ITO. "Angular Resolution Improvement of Ocean Surface Current Radar Based on the Khatri-Rao Product Array Processing." IEICE Transactions on Communications E96.B, no. 10 (2013): 2469–74. http://dx.doi.org/10.1587/transcom.e96.b.2469.

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16

Khanna, Saurabh, and Chandra Ramabhadra Murthy. "Corrections to “On the Restricted Isometry of the Columnwise Khatri–Rao Product” [Mar 18 1170-1183]." IEEE Transactions on Signal Processing 67, no. 9 (2019): 2387–88. http://dx.doi.org/10.1109/tsp.2019.2904930.

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17

SHIRAI, Satoshi, Hiroyoshi YAMADA, and Yoshio YAMAGUCHI. "A Novel DOA Estimation Error Reduction Preprocessing Scheme of Correlated Waves for Khatri-Rao Product Extended-Array." IEICE Transactions on Communications E96.B, no. 10 (2013): 2475–82. http://dx.doi.org/10.1587/transcom.e96.b.2475.

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18

JIMI, Keiji, Isamu MATSUNAMI, and Ryohei NAKAMURA. "Improvement of Ranging Accuracy during Interference Avoidance for Stepped FM Radar Using Khatri-Rao Product Extended-Phase Processing." IEICE Transactions on Communications E102.B, no. 1 (2019): 156–64. http://dx.doi.org/10.1587/transcom.2018ebp3042.

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19

Hazawa, Honoka, Hiroyoshi Yamada, and Hiroki Mori. "Evaluation of mode vector for near-field 2-D target imaging using Khatri-Rao product extended array processing." IEICE Communications Express 9, no. 6 (2020): 176–81. http://dx.doi.org/10.1587/comex.2019spl0024.

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20

Yang, Ruo-Nan, Wei-Tao Zhang, and Shun-Tian Lou. "Joint Adaptive Blind Channel Estimation and Data Detection for MIMO-OFDM Systems." Wireless Communications and Mobile Computing 2020 (July 2, 2020): 1–9. http://dx.doi.org/10.1155/2020/2508130.

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In order to track a changing channel in multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems, it is a priority to estimate channel impulse response adaptively. In this paper, we propose an adaptive blind channel estimation method based on parallel factor analysis (PARAFAC). We used an exponential window to weigh the past observations; thus, the cost function can be constructed via a weighted least squares criterion. The minimization of the cost function is equivalent to the decomposition of a third-order tensor, which consists of the weighted OFDM data

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21

Sun, Mengjiang, and Peng Chen. "Neural Network Based AMP Method for Multi-User Detection in Massive Machine-Type Communication." Electronics 9, no. 8 (2020): 1286. http://dx.doi.org/10.3390/electronics9081286.

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In massive machine-type communications (mMTC) scenarios, grant-free non-orthogonal multiple access becomes crucial due to the small transmission latency, limited signaling overhead and the ability to support massive connectivity. In a multi-user detection (MUD) problem, the base station (BS) is unaware of the active users and needs to detect active devices. With sporadic devices transmitting signals at any moment, the MUD problem can be formulated as a multiple measurement vector (MMV) sparse recovery problem. Through the Khatri–Rao product, we prove that the MMV problem is transformed into a

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22

Sonkar, Munnu, Pradip Sasmal, Prasad Theeda, and C. S. Sastry. "Sparsity-driven deterministic sampling strategy for coded aperture x-ray computed tomography." Measurement Science and Technology 33, no. 3 (2021): 034003. http://dx.doi.org/10.1088/1361-6501/ac39d2.

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Abstract The sub-sampling strategies in x-ray computed tomography (CT) have gained importance due to their practical relevance. In this direction of research, also known as coded aperture x-ray computed tomography (CAXCT), both random and deterministic strategies have been proposed in the literature. Of the techniques available, those based on compressive sensing (CS) have recently gained more traction because CS-based ideas efficiently exploit inherent duplication present in the system. The quality of the reconstructed CT images nevertheless depends on the sparse signal recovery properties of

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23

Guo, Chenxi, Xinhong Hao, and Ping Li. "An Improved Trilinear Model-Based Angle Estimation Method for Co-Prime Planar Arrays." Sensors 18, no. 12 (2018): 4180. http://dx.doi.org/10.3390/s18124180.

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Angle estimation methods in two-dimensional co-prime planar arrays have been discussed mainly based on peak searching and sparse recovery. Peak searching methods suffer from heavy computational complexity and sparse recovery methods face some problems in selecting the regularization parameters. In this paper, we propose an improved trilinear model-based method for angle estimation for co-prime planar arrays in the view of trilinear decomposition, namely parallel factor analysis. Due to the principle of trilinear decomposition, our method does not require peak searching and can conduct auto-pai

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24

Ploymukda, Arnon, and Pattrawut Chansangiam. "Chebyshev-Type Integral Inequalities for Continuous Fields of Operators Concerning Khatri–Rao Products and Synchronous Properties." Symmetry 12, no. 3 (2020): 422. http://dx.doi.org/10.3390/sym12030422.

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We consider bounded continuous fields of self-adjoint operators which are parametrized by a locally compact Hausdorff space Ω equipped with a finite Radon measure μ . Under certain assumptions on synchronous Khatri–Rao property of the fields of operators, we obtain Chebyshev-type inequalities concerning Khatri–Rao products. We also establish Chebyshev-type inequalities involving Khatri–Rao products and weighted Pythagorean means under certain assumptions of synchronous monotone property of the fields of operators. The Pythagorean means considered here are three classical symmetric means: the g

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25

Ploymukda, Arnon, and Pattrawut Chansangiam. "Operator inequalities involving Khatri-Rao Sums and Moore-Penrose inverses." Malaysian Journal of Fundamental and Applied Sciences 13, no. 4 (2017): 742–46. http://dx.doi.org/10.11113/mjfas.v0n0.711.

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We establish relations between the Khatri-Rao sum of Hilbert space operators and ordinary products, powers, ordinary inverses, and Moore-Penrose inverses in terms of inequalities. In particular, such relations hold for the tensor sum of operators and the Khatri-Rao sum of complex matrices.

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26

Yang, Zhong-peng, Xian Zhang, and Chong-guang Cao. "Inequalities involving Khatri-Rao products of Hermitian matrices." Korean Journal of Computational & Applied Mathematics 9, no. 1 (2002): 125–33. http://dx.doi.org/10.1007/bf03012344.

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27

Liu, Shuangzhe. "Matrix results on the Khatri-Rao and Tracy-Singh products." Linear Algebra and its Applications 289, no. 1-3 (1999): 267–77. http://dx.doi.org/10.1016/s0024-3795(98)10209-4.

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28

Liu, Shuangzhe. "Several inequalities involving Khatri–Rao products of positive semidefinite matrices." Linear Algebra and its Applications 354, no. 1-3 (2002): 175–86. http://dx.doi.org/10.1016/s0024-3795(02)00338-5.

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29

Ploymukda, Arnon, and Pattrawut Chansangiam. "Concavity and convexity of several maps involving Tracy-Singh products, Khatri-Rao products, and operator-monotone functions of positive operators." ScienceAsia 45, no. 2 (2019): 194. http://dx.doi.org/10.2306/scienceasia1513-1874.2019.45.194.

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30

Al-Zhour, Zeyad Abdel Aziz. "Several new inequalities on operator means of non-negative maps and Khatri–Rao products of positive definite matrices." Journal of King Saud University - Science 26, no. 1 (2014): 21–27. http://dx.doi.org/10.1016/j.jksus.2013.05.002.

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31

Cao, Chong-Guang, Xian Zhang, and Zhong-Peng Yang. "Some inequalities for the Khatri-Rao product of matrices." Electronic Journal of Linear Algebra 9 (January 1, 2002). http://dx.doi.org/10.13001/1081-3810.1090.

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32

SUGUMAR, D., NEETHU SUSAN RAJAN, and P. T. VANATHI. "Separation of MECG and FECG using CCA-EMD Process." International Journal of Electronics Signals and Systems, January 2014, 218–22. http://dx.doi.org/10.47893/ijess.2014.1172.

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Under-determined blind source separation aims to separate N non-stationary sources from M (M<N) mixtures.Paper presents a time-frequency approach (TF) to under-determined blind source separation of N non-stationary sources from M mixtures(M<N). It is based on Wigner-Ville distribution and Khatri-Rao product. Improved method involves a two step approach which involves the estimation of the mixing matrix where negative values of auto WVD of the sources are fully considered and secondly auto-term TF points are extracted.After extracting the auto-term TF points source WVD values at every TF

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33

SUGUMAR, D., NEETHU SUSAN RAJAN, and P. T. VANATHI. "BLIND SOURCE SEPARATION OF AUDIO SIGNALS USING WVD-KR ALGORITHM." International Journal of Electronics Signals and Systems, April 2014, 226–30. http://dx.doi.org/10.47893/ijess.2014.1174.

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Under-determined blind source separation aims to separate N non-stationary sources from M (M<N) mixtures.Paper presents a time-frequency approach (TF) to under-determined blind source separation of N non-stationary sources from M mixtures(M<N). It is based on Wigner-Ville distribution and Khatri-Rao product. Improved method involves a two step approach which involves the estimation of the mixing matrix where negative values of auto WVD of the sources are fully considered and secondly auto-term TF points are extracted.After extracting the auto-term TF points source WVD values at every TF

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34

"Feature Extraction and Analysis in Multimodal Biometric Authentication using Lu Factorization with Kronecker Algebra." International Journal of Innovative Technology and Exploring Engineering 8, no. 11 (2019): 3837–39. http://dx.doi.org/10.35940/ijitee.k2265.0981119.

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Pattern recognition is one of the current and advanced technologies that focus on analysis and construction of pattern is a complex work. For recognition of patterns Vector logic gives good strategies. This paper focuses on pattern recognition in multimodal authentication system by using vector logic. A framework has been proposed to provide more security in biometric aspect. Initially, features are extracted through PCA from the normalized biometric imaginaries, and then using LU factorization key components are extracted. By using convolution kernel methods such as Khatri Rao an application

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35

Yuan, Ye, Shuang Wu, Yong Yang, and Naichang Yuan. "Multi-DOA estimation based on the KR image tensor and improved estimation network." Scientific Reports 11, no. 1 (2021). http://dx.doi.org/10.1038/s41598-021-85864-5.

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AbstractDeep neural networks have shown great performance for direction-of-arrival (DOA) estimation problem, but it is necessary to design some suitable networks to solve the multi-DOA estimation problem. In this paper, we use Khatri–Rao product to increase the degree of freedom of antenna array and obtain the image tensor of covariance matrix, then we propose an improved estimation network to process the tensor. We use the curriculum learning scheme and partial label strategy to develop a CurriculumNet training scheme. The training/validation results shows that the proposed training scheme ca

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36

Zhao, Di, Weijie Tan, Zhongliang Deng, and Gang Li. "Low complexity sparse beamspace DOA estimation via single measurement vectors for uniform circular array." EURASIP Journal on Advances in Signal Processing 2021, no. 1 (2021). http://dx.doi.org/10.1186/s13634-021-00770-2.

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AbstractIn this paper, we present a low complexity sparse beamspace direction-of-arrival (DOA) estimation method for uniform circular array (UCA). In the proposed method, we firstly use the beamspace transformation (BT) to transform the signal model of UCA in element-space domain to that of virtual uniform linear array (ULA) in beamspace domain. Subsequently, by applying the vectoring operator on the virtual ULA-like array signal model, a novel dimension-reduction sparse beamspace signal model is derived based on Khatri-Rao (KR) product, the observation data of which is represented by the sing

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37

Ploymukda, Arnon, and Pattrawut Chansangiam. "Hölder Type Inequalities Involving Tracy-Singh Products and Khatri-Rao Products of Hilbert Space Operators." Communications in Mathematics and Applications 10, no. 3 (2019). http://dx.doi.org/10.26713/cma.v10i3.1227.

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38

AL-Zhour, Zeyad. "New Holder-type inequalities for the Tracy-Singh and Khatri-Rao products of positive matrices." "International Journal of Computer Engineering Research" 3, no. 3 (2012). http://dx.doi.org/10.5897/ijcer12.013.

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