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Journal articles on the topic 'Khatri-Rao product'

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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 (December 16, 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 class, respectively).

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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 (April 15, 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 (May 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 (August 1, 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 (March 1, 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 (June 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 for treatment combination contrasts in the proposed split-block-plot designs.

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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 (May 14, 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 (May 1, 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 (January 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 symbols. By preserving the Khatri-Rao product, we used a recursive least squares solution to update the estimated subspace at each time instant, then the channel parameters can be estimated adaptively, and the algorithm achieves superior convergence performance. Simulation results validate the effectiveness of the proposed algorithm.

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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 (August 11, 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 single measurement vector (SMV) problem. Based on the basis pursuit de-noising approximate message passing (BPDN-AMP) algorithm, a novel learning AMP network (LAMPnet) algorithm is proposed, which is designed to reduce the false alarm probability when the required detection probability is high. Simulation results show that when the required detection probablity is high, the AMP algorithm based on LAMPnet noticeably outperforms the traditional algorithms with acceptable computational complexity.

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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 (December 29, 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 the sub-sampled Radon matrices. In the present work, we optimize CAXCT deterministically in such a way that the corresponding sub-sampled Radon matrices remain close to the equiangular tight frames for better numerical behaviour. We show that this optimization, involving the Khatri–Rao product, leads to a non-negative sparse approximation. While comparing and contrasting our method with its existing counterparts, we show that the proposed algorithm is computationally less involved. Finally, we demonstrate efficacy of the proposed deterministic sub-sampling strategy in recovering CT images in both noiseless and noisy cases.

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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 (November 28, 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-pairing easily, which can reduce the computational loads and avoid parameter selection problems. Furthermore, we exploit the virtual array concept of the whole co-prime planar array through the cross-correlation matrix obtained from the received signal data and present a matrix reconstruction method using the Khatri–Rao product to tackle the matrix rank deficiency problem in the virtual array condition. The simulation results show that our proposed method can not only achieve high estimation accuracy with low complexity compared to other similar approaches, but also utilize limited sensor number to implement the angle estimation tasks.

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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 (March 5, 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 geometric mean, the arithmetic mean, and the harmonic mean. Moreover, we derive the Chebyshev–Grüss integral inequality via oscillations when μ is a probability Radon measure. These integral inequalities can be reduced to discrete inequalities by setting Ω to be a finite space equipped with the counting measure. Our results provide analog results for matrices and integrable functions. Furthermore, our results include the results for tensor products of operators, and Khatri–Rao/Kronecker/Hadamard products of matrices, which have been not investigated in the literature.

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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 (December 26, 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 (January 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 (March 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 (October 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 (January 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 point are computed using a new algorithm based on Khatri-Rao product. Thus sources are separated with the proposed approach no matter how many active sources there are as long as N≤ 2M-1.Simulation results are presented to show the superiority of the proposed algorithm by comparing it with the existing algorithms.

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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 point are computed using a new algorithm based on Khatri-Rao product. Thus sources are separated with the proposed approach no matter how many active sources there are as long as N≤ 2M-1.Simulation results are presented to show the superiority of the proposed algorithm by comparing it with the existing algorithms.

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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 (September 10, 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 of Kronecker product weights are computed for different key sizes. In the same way verification process is implemented and verified with MSE. This framework gives better result for chosen threshold value.

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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 (March 18, 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 can increase the generalization of the estimation network and improve the accuracy of network around $$10\%$$ 10 % . The estimation performance of the proposed network shows high-resolution results, which can distinguish two adjacent signals with angle difference of $$3^\circ $$ 3 ∘ . Moreover, the proposed estimation network has root mean square estimation error lower than $$1^\circ $$ 1 ∘ when signal noise ratio equals $$-\,10\,{\mathrm {dB}}$$ - 10 dB and can estimate DOAs precisely by only 8 snapshots, which performs much better than prior deep neural network based estimation methods and can estimate multi-DOA results under hostile estimation environments.

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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 (July 30, 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 single measurement vectors (SMVs) via vectorization of sparse covariance matrix. And then, the DOA estimation is formulated as a convex optimization problem by following the concept of a sparse-signal-representation (SSR) of the SMVs. Finally, simulations are carried out to validate the effectiveness of the proposed method. The results show that without knowledge of the number of signals, the proposed method not only has higher DOA resolution than the subspace-based methods in low signal-to-noise ratio (SNR), but also has far lower computational complexity than other sparse-like DOA estimation methods.

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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 (September 30, 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 (May 2012). http://dx.doi.org/10.5897/ijcer12.013.

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