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Автор: Grafiati
Опубліковано: 6 вересня 2023

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Статті в журналах з теми "Khatri-Rao product"

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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Анотація:
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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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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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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Дисертації з теми "Khatri-Rao product"

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Bush, Heather Michele Clyburn. "KHATRI-RAO PRODUCTS AND CONDITIONS FOR THE UNIQUENESS OF PARAFAC SOLUTIONS FOR IxJxK ARRAYS." UKnowledge, 2006. http://uknowledge.uky.edu/gradschool_diss/462.

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One of the differentiating features of PARAFAC decompositions is that, under certain conditions, unique solutions are possible. The search for uniqueness conditions for the PARAFAC Decomposition has a limited past, spanning only three decades. The complex structure of the problem and the need for tensor algebras or other similarly abstract characterizations provided a roadblock to the development of uniqueness conditions. Theoretically, the PARAFAC decomposition surpasses its bilinear counterparts in that it is possible to obtain solutions that do not suffer from the rotational problem. However, not all PARAFAC solutions will be constrained sufficiently so that the resulting decomposition is unique. The work of Kruskal, 1977, provides the most in depth investigation into the conditions for uniqueness, so much so that many have assumed, without formal proof, that his sufficient conditions were also necessary. Aided by the introduction of Khatri-Rao products to represent the PARAFAC decomposition, ten Berge and Sidiropoulos (2002) used the column spaces of Khatri-Rao products to provide the first evidence for countering the claim of necessity, identifying PARAFAC decompositions that were unique when Kruskals condition was not met. Moreover, ten Berge and Sidiropoulos conjectured that, with additional k-rank restrictions, a class of decompositions could be formed where Kruskals condition would be necessary and sufficient. Unfortunately, the column space argument of ten Berge and Sidiropoulos was limited in its application and failed to provide an explanation of why uniqueness occurred. On the other hand, the use of orthogonal complement spaces provided an alternative approach to evaluate uniqueness that would provide a much richer return than the use of column spaces for the investigation of uniqueness. The Orthogonal Complement Space Approach (OCSA), adopted here, would provide: (1) the answers to lingering questions about the occurrence of uniqueness, (2) evidence that necessity would require more than a restriction on k-rank, and (3) an approach that could be extended to cases beyond those investigated by ten Berge and Sidiropoulos.
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2

Khanna, Saurabh. "Bayesian Techniques for Joint Sparse Signal Recovery: Theory and Algorithms." Thesis, 2018. https://etd.iisc.ac.in/handle/2005/5292.

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This thesis contributes new theoretical results, solution concepts, and algorithms concerning the Bayesian recovery of multiple joint sparse vectors from noisy and underdetermined linear measurements. The thesis is written in two parts. The first part focuses on the recovery of nonzero support of multiple joint sparse vectors from their linear compressive measurements, an important canonical problem in multisensor signal processing. The support recovery performance of a well known Bayesian inference technique called Multiple Sparse Bayesian Learning (MSBL) is analyzed using tools from large deviation theory. New improved sufficient conditions are derived for perfect support recovery in MSBL with arbitrarily high probability. We show that the support error probability in MSBL decays exponentially fast with the number of joint sparse vectors and the rate of decay depends on the restricted eigenvalues and null space structure of the self Khatri-Rao product of the sensing matrix used to generate the measurements. New insights into MSBL’s objective are developed which enhance our understanding of MSBL’s ability to recover supports of size greater than the number of measurements available per joint sparse vector. These new insights are formalized into a novel covariance matching framework for sparsity pattern recovery. Next, we characterize the restricted isometry property of a generic Khatri-Rao product matrix in terms of its restricted isometry constants (RICs). Upper bounds for the RICs of Khatri-Rao product matrices are of independent interest as they feature in the sample complexity analysis of several linear inverse problems of fundamental importance, including the above support recovery problem. We derive deterministic and probabilistic upper bounds for the RICs of Khatri-Rao product between two matrices. The newly obtained RIC bounds are then used to derive performance bounds for MSBL based support recovery. Building upon the new insights about MSBL, a novel covariance matching based support recovery algorithm is conceived. It uses a R´enyi divergence objective which reverts to the MSBL’s objective in a special case. We show that the R´enyi divergence objective can be expressed as a difference of two submodular set functions, and hence it can be optimized via an iterative majorization-minimization procedure to generate the support estimate. The resulting algorithm is empirically shown to be several times faster than existing support recovery methods with comparable performance. The second part of the thesis focuses on developing decentralized extensions of MSBL for in-network estimation of multiple joint sparse vectors from linear compressive measurements using a network of nodes. A common issue while implementing decentralized algorithms is the high cost associated with the exchange of information between the network nodes. To mitigate this problem, we examine two different approaches to reduce the amount of inter-node communication in the network. In the first decentralized extension of MSBL, the network nodes exchange information only via a small set of predesignated bridge nodes. For this bridge node based network topology, the MSBL optimization is then performed using decentralized Alternating Directions Method of Multipliers (ADMM). The convergence of decentralized ADMM in a bridge node based network topology for a generic consensus optimization is separately analyzed and a linear rate of convergence is established. Our second decentralized extension of MSBL reduces the communication complexity by adaptively censoring the information exchanged between the nodes of the network by exploiting the inherent sparse nature of the exchanged information. The performance of the proposed decentralized schemes is evaluated using both simulated as well as real-world data.
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Частини книг з теми "Khatri-Rao product"

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Tan, Weijie, Chenglin Zheng, Judong Li, Weiqiang Tan, and Chunguo Li. "A Dictionary Learning-Based Off-Grid DOA Estimation Method Using Khatri-Rao Product." In Lecture Notes in Electrical Engineering, 239–48. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-13-9409-6_29.

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Тези доповідей конференцій з теми "Khatri-Rao product"

1

Ji, Ruowan, Asit Kumar Pradhan, Anoosheh Heidarzadeh, and Krishna R. Narayanan. "Squeezed Random Khatri-Rao Product Codes." In 2021 IEEE Information Theory Workshop (ITW). IEEE, 2021. http://dx.doi.org/10.1109/itw48936.2021.9611422.

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2

Ji, Ruowan, Anoosheh Heidarzadeh, and Krishna R. Narayanan. "Sparse Random Khatri-Rao Product Codes for Distributed Matrix Multiplication." In 2022 IEEE Information Theory Workshop (ITW). IEEE, 2022. http://dx.doi.org/10.1109/itw54588.2022.9965842.

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3

Ballard, Grey, Nicholas Knight, and Kathryn Rouse. "Communication Lower Bounds for Matricized Tensor Times Khatri-Rao Product." In 2018 IEEE International Parallel and Distributed Processing Symposium (IPDPS). IEEE, 2018. http://dx.doi.org/10.1109/ipdps.2018.00065.

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4

Subramaniam, Adarsh M., Anoosheh Heidarzadeh, and Krishna R. Narayanan. "Random Khatri-Rao-Product Codes for Numerically-Stable Distributed Matrix Multiplication." In 2019 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton). IEEE, 2019. http://dx.doi.org/10.1109/allerton.2019.8919859.

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Wakamatsu, Yosuke, Hiroyoshi Yamada, and Yoshio Yamaguchi. "MIMO Doppler radar using Khatri-Rao product virtual array for human location estimation." In 2014 IEEE International Workshop on Electromagnetics; Applications and Student Innovation (iWEM). IEEE, 2014. http://dx.doi.org/10.1109/iwem.2014.6963620.

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6

Konishi, Junpei, Suguru Ohashi, Hiroyoshi Yamada, Yoshio Yamaguchi, and Michiyo Hiramoto. "Resolution enhancement for MIMO radar by using Khatri-Rao product virtual array processing." In 2017 International Symposium on Antennas and Propagation (ISAP). IEEE, 2017. http://dx.doi.org/10.1109/isanp.2017.8228822.

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Hirahara, Daichi. "Simulation Results of Satellite AIS when Utilizing Khatri-Rao (KR) Product Array Processing." In 2020 International Symposium on Antennas and Propagation (ISAP). IEEE, 2021. http://dx.doi.org/10.23919/isap47053.2021.9391136.

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Hazawa, Honoka, Hiroyoshi Yamada, and Hiroki Mori. "Impact of Signal Correlation in 2D Imaging with Khatri-Rao Product Expansion Array." In 2020 International Symposium on Antennas and Propagation (ISAP). IEEE, 2021. http://dx.doi.org/10.23919/isap47053.2021.9391157.

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Ryukawa, Takuya, Hiroyoshi Yamada, Yoshio Yamaguchi, Keizo Hirano, and Hiroyuki Ito. "Velocity and direction estimation by ocean surface current radar using Khatri-Rao product transform." In 2014 IEEE International Workshop on Electromagnetics; Applications and Student Innovation (iWEM). IEEE, 2014. http://dx.doi.org/10.1109/iwem.2014.6963623.

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Ding, Shanshan, Ningning Tong, and Qichao Ge. "High-resolution direction-of-arrival estimation using Khatri-Rao product and spatial sparsity of sources." In 2016 International Symposium on Advances in Electrical, Electronics and Computer Engineering. Paris, France: Atlantis Press, 2016. http://dx.doi.org/10.2991/isaeece-16.2016.59.

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