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Journal articles on the topic 'Factorization system'

Author: Grafiati

Published: 14 March 2023

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1

Casalino, G., N. Del Buono, and M. Minervini. "Nonnegative Matrix Factorizations Performing Object Detection and Localization." Applied Computational Intelligence and Soft Computing 2012 (2012): 1–19. http://dx.doi.org/10.1155/2012/781987.

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We study the problem of detecting and localizing objects in still, gray-scale images making use of the part-based representation provided by nonnegative matrix factorizations. Nonnegative matrix factorization represents an emerging example of subspace methods, which is able to extract interpretable parts from a set of template image objects and then to additively use them for describing individual objects. In this paper, we present a prototype system based on some nonnegative factorization algorithms, which differ in the additional properties added to the nonnegative representation of data, in order to investigate if any additional constraint produces better results in general object detection via nonnegative matrix factorizations.

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2

Zheng, Weijian, Fengguang Song, Lan Lin, and Zizhong Chen. "Scaling Up Parallel Computation of Tiled QR Factorizations by a Distributed Scheduling Runtime System and Analytical Modeling." Parallel Processing Letters 28, no. 01 (March 2018): 1850004. http://dx.doi.org/10.1142/s0129626418500044.

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Implementing parallel software for QR factorizations to achieve scalable performance on massively parallel manycore systems requires a comprehensive design that includes algorithm redesign, efficient runtime systems, synchronization and communication reduction, and analytical performance modeling. This paper presents a piece of tiled communication-avoiding QR factorization software that is able to scale efficiently for matrices with general dimensions. We design a tiled communication-avoiding QR factorization algorithm and implement it with a fully distributed dynamic scheduling runtime system to minimize both synchronization and communication. The whole class of communication-avoiding QR factorization algorithms uses an important parameter of D (i.e., the number of domains), whose best solution is still unknown so far and requires manual tuning and empirical searching to find it. To that end, we introduce a simplified analytical performance model to determine an optimal number of domains D[Formula: see text]. The experimental results show that our new parallel implementation is faster than a state-of-the-art multicore-based numerical library by up to 30%, and faster than ScaLAPACK by up to 30 times with thousands of CPU cores. Furthermore, using the new analytical model to predict an optimal number of domains is as competitive as exhaustive searching, and exhibits an average performance difference of 1%.

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More, Tejashree, and Prof Surekha Kohle. "Recommendation System Using Matrix Factorization." International Journal for Research in Applied Science and Engineering Technology 10, no. 9 (September 30, 2022): 355–59. http://dx.doi.org/10.22214/ijraset.2022.46615.

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Abstract: In today’s world, people are flooded with a lot of information, and no. of choices are overwhelming. For example, in any online shopping platform such as Amazon, if we search for a particular product, thousands of results appear and it becomes very difficult to select an item from vast pool of options. The growth of digital information and the number of users over the Internet has created a potential problem of information overload. The recommendation system solves this problem by searching through a large volume of data and providing personalized content to the user. This paper describes the introduction to the recommendation system, its three main types – content-based filtering, collaborative filtering, and hybrid filtering, and addresses the data sparsity problem. This paper proposed a collaborative filtering approach using matrix factorization to mitigate the sparsity problem and improve the quality of the recommendation.

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Sadeghi, J., Jalil Naji, and Behnam Pourhassan. "Factorization Method in Oscillator with the Aharonov-Casher System." Advances in Mathematical Physics 2014 (2014): 1–5. http://dx.doi.org/10.1155/2014/965694.

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We review the oscillator with Aharonov-Casher system and study some mathematical foundation about factorization method. The factorization method helps us to obtain the energy spectrum and general wave function for the corresponding system in some spin condition. The factorization method leads us to obtain the raising and lowering operators for the Aharonov-Casher system. The corresponding operators give us the generators of the algebra.

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Echi, Othman, Sami Lazaar, and Mohamed Oueld Abdallahi. "On some orthogonal factorization systems." Journal of Algebra and Its Applications 14, no. 08 (April 27, 2015): 1550120. http://dx.doi.org/10.1142/s0219498815501200.

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The orthogonality relation between arrows in the class of all morphisms of a given category C yields a "concrete" antitone Galois connection between the class of all subclasses of morphisms of C. For a class Σ of morphisms of C, we denote by ⊥Σ (resp., Σ⊥) the class of all morphisms f in C such that f ⊥ g (resp., g ⊥ f) for each morphism g in Σ. A couple (Σ, Γ) of classes of morphisms is said to be an (orthogonal) prefactorization system if If, in addition the pfs satisfies then it will be called a dense prefactorization system. A pair [Formula: see text] of classes of morphisms in a category C is called an (orthogonal) factorization system if it is a prefactorization system and each morphism f in C has a factorization f = me, with [Formula: see text] and [Formula: see text]. This paper provides several examples of factorization systems and dense factorization systems in the category Top of topological spaces.

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Even, Valérian, and Marino Gran. "On factorization systems for surjective quandle homomorphisms." Journal of Knot Theory and Its Ramifications 23, no. 11 (October 2014): 1450060. http://dx.doi.org/10.1142/s0218216514500606.

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We study and compare two factorization systems for surjective homomorphisms in the category of quandles. The first one is induced by the adjunction between quandles and trivial quandles, and a precise description of the two classes of morphisms of this factorization system is given. In doing this we observe that a special class of congruences in the category of quandles always permute in the sense of the composition of relations, a fact that opens the way to some new universal algebraic investigations in the category of quandles. The second factorization system is the one discovered by E. Bunch, P. Lofgren, A. Rapp and D. N. Yetter. We conclude with an example showing a difference between these factorization systems.

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7

Ong, Kyle, Kok-Why Ng, and Su-Cheng Haw. "Neural matrix factorization++ based recommendation system." F1000Research 10 (October 25, 2021): 1079. http://dx.doi.org/10.12688/f1000research.73240.1.

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In recent years, Recommender System (RS) research work has covered a wide variety of Artificial Intelligence techniques, ranging from traditional Matrix Factorization (MF) to complex Deep Neural Networks (DNN). Traditional Collaborative Filtering (CF) recommendation methods such as MF, have limited learning capabilities as it only considers the linear combination between user and item vectors. For learning non-linear relationships, methods like Neural Collaborative Filtering (NCF) incorporate DNN into CF methods. Though, CF methods still suffer from cold start and data sparsity. This paper proposes an improved hybrid-based RS, namely Neural Matrix Factorization++ (NeuMF++), for effectively learning user and item features to improve recommendation accuracy and alleviate cold start and data sparsity. NeuMF++ is proposed by incorporating effective latent representation into NeuMF via Stacked Denoising Autoencoders (SDAE). NeuMF++ can also be seen as the fusion of GMF++ and MLP++. NeuMF is an NCF framework which associates with GMF (Generalized Matrix Factorization) and MLP (Multilayer Perceptrons). NeuMF achieves state-of-the-art results due to the integration of GMF linearity and MLP non-linearity. Concurrently, incorporating latent representations has shown tremendous improvement in GMF and MLP, which result in GMF++ and MLP++. Latent representation obtained through the SDAEs’ latent space allows NeuMF++ to effectively learn user and item features, significantly enhancing its learning capability. However, sharing feature extractions among GMF++ and MLP++ in NeuMF++ might hinder its performance. Hence, allowing GMF++ and MLP++ to learn separate features provides more flexibility and greatly improves its performance. Experiments performed on a real-world dataset have demonstrated that NeuMF++ achieves an outstanding result of a test root-mean-square error of 0.8681. In future work, we can extend NeuMF++ by introducing other auxiliary information like text or images. Different neural network building blocks can also be integrated into NeuMF++ to form a more robust recommendation model.

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Ruchitha, K. Venkata. "Book Recommendation System using Matrix Factorization." International Journal for Research in Applied Science and Engineering Technology 9, no. VI (June 30, 2021): 4578–82. http://dx.doi.org/10.22214/ijraset.2021.36025.

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In recent years, recommender systems became more and more common and area unit applied to a various vary of applications, thanks to development of things and its numerous varieties accessible, that leaves the users to settle on from bumper provided choices. Recommendations generally speed up searches and create it easier for users to access content that they're curious about, and conjointly surprise them with offers they'd haven't sought for. By victimisation filtering strategies for pre-processing the information, recommendations area unit provided either through collaborative filtering or through content-based Filtering. This recommender system recommends books supported the description and features. It identifies the similarity between the books supported its description. It conjointly considers the user previous history so as to advocate the identical book.

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Chawla, Tanvi. "FFT Factorization Technique for OFDM System." International Journal of Computer Applications 54, no. 5 (September 25, 2012): 36–40. http://dx.doi.org/10.5120/8564-2161.

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Alqadri, Mowafaq, Haslinda Ibrahim, and Sharmila Karim. "On Cyclic Triple System and Factorization." Journal of Engineering and Applied Sciences 14, no. 21 (October 31, 2019): 7928–33. http://dx.doi.org/10.36478/jeasci.2019.7928.7933.

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11

Nassirharand, A. "Factorization approach to control system synthesis." Journal of Guidance, Control, and Dynamics 16, no. 2 (March 1993): 402–5. http://dx.doi.org/10.2514/3.21021.

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12

Conte, R., M. Musette, and A. Pickering. "Factorization of the 'classical Boussinesq' system." Journal of Physics A: Mathematical and General 27, no. 8 (April 21, 1994): 2831–36. http://dx.doi.org/10.1088/0305-4470/27/8/020.

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13

Zheng, Xiaolin, Weifeng Ding, Zhen Lin, and Chaochao Chen. "Topic tensor factorization for recommender system." Information Sciences 372 (December 2016): 276–93. http://dx.doi.org/10.1016/j.ins.2016.08.042.

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14

Callier, F. M. "Control system synthesis: A factorization approach." Automatica 22, no. 4 (July 1986): 500–501. http://dx.doi.org/10.1016/0005-1098(86)90058-0.

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Himabindu, Tadiparthi V. R., Vineet Padmanabhan, and Arun K. Pujari. "Conformal matrix factorization based recommender system." Information Sciences 467 (October 2018): 685–707. http://dx.doi.org/10.1016/j.ins.2018.04.004.

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16

Kannan, Ramakrishnan, Mariya Ishteva, and Haesun Park. "Bounded matrix factorization for recommender system." Knowledge and Information Systems 39, no. 3 (December 7, 2013): 491–511. http://dx.doi.org/10.1007/s10115-013-0710-2.

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Kendall, M. Stephen, Judith W. Koslov, and Robert B. Wood. "System reliability analysis using factorization techniques." Quality and Reliability Engineering 8, no. 5 (1992): 471–76. http://dx.doi.org/10.1002/qre.4680080510.

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18

Shen, Yun-Qiu, and Tjalling J. Ypma. "Solving Separable Nonlinear Equations Using LU Factorization." ISRN Mathematical Analysis 2013 (June 24, 2013): 1–5. http://dx.doi.org/10.1155/2013/258072.

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Separable nonlinear equations have the form where the matrix and the vector are continuously differentiable functions of and . We assume that and has full rank. We present a numerical method to compute the solution for fully determined systems () and compatible overdetermined systems (). Our method reduces the original system to a smaller system of equations in alone. The iterative process to solve the smaller system only requires the LU factorization of one matrix per step, and the convergence is quadratic. Once has been obtained, is computed by direct solution of a linear system. Details of the numerical implementation are provided and several examples are presented.

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GONZALEZ, PATRICIA, JOSE C. CABALEIRO, and TOMAS F. PENA. "PARALLEL INCOMPLETE LU FACTORIZATION AS A PRECONDITIONER FOR KRYLOV SUBSPACE METHODS." Parallel Processing Letters 09, no. 04 (December 1999): 467–74. http://dx.doi.org/10.1142/s0129626499000438.

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In this paper we describe a new method for the ILU(0) factorization of sparse systems in distributed memory multiprocessor architectures. This method uses a symbolic reordering technique, so the final system can be grouped in blocks where the rows are independent and the factorization of these entries can be carried out in parallel. The parallel ILU(0) factorization has been tested on the Cray T3E multicomputer using the MPI communication library. The performance was analysed using matrices from the Harwell–Boeing collection.

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Dai, HongLin, and Jiwei Qin. "Collaborative Variational Factorization Machine For Recommender System." International Journal of Autonomous and Adaptive Communications Systems 16, no. 2 (2023): 1. http://dx.doi.org/10.1504/ijaacs.2023.10034575.

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Nitta, Kouichi, Nobuto Katsuta, and Osamu Matoba. "An Optical Parallel System for Prime Factorization." Japanese Journal of Applied Physics 48, no. 9 (September 24, 2009): 09LA02. http://dx.doi.org/10.1143/jjap.48.09la02.

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22

Fralix, Brian H., Johan S. H. van Leeuwaarden, and Onno J. Boxma. "Factorization Identities for Reflected Processes, with Applications." Journal of Applied Probability 50, no. 3 (September 2013): 632–53. http://dx.doi.org/10.1239/jap/1378401227.

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We derive factorization identities for a class of preemptive-resume queueing systems, with batch arrivals and catastrophes that, whenever they occur, eliminate multiple customers present in the system. These processes are quite general, as they can be used to approximate Lévy processes, diffusion processes, and certain types of growth‒collapse processes; thus, all of the processes mentioned above also satisfy similar factorization identities. In the Lévy case, our identities simplify to both the well-known Wiener‒Hopf factorization, and another interesting factorization of reflected Lévy processes starting at an arbitrary initial state. We also show how the ideas can be used to derive transforms for some well-known state-dependent/inhomogeneous birth‒death processes and diffusion processes.

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Fralix, Brian H., Johan S. H. van Leeuwaarden, and Onno J. Boxma. "Factorization Identities for Reflected Processes, with Applications." Journal of Applied Probability 50, no. 03 (September 2013): 632–53. http://dx.doi.org/10.1017/s002190020000975x.

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We derive factorization identities for a class of preemptive-resume queueing systems, with batch arrivals and catastrophes that, whenever they occur, eliminate multiple customers present in the system. These processes are quite general, as they can be used to approximate Lévy processes, diffusion processes, and certain types of growth‒collapse processes; thus, all of the processes mentioned above also satisfy similar factorization identities. In the Lévy case, our identities simplify to both the well-known Wiener‒Hopf factorization, and another interesting factorization of reflected Lévy processes starting at an arbitrary initial state. We also show how the ideas can be used to derive transforms for some well-known state-dependent/inhomogeneous birth‒death processes and diffusion processes.

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24

Furukawa, Kohsuke, and Mingcong Deng. "Robust nonlinear tracking control system design of an uncertain multivariable process driven by a distributed control system device." Transactions of the Institute of Measurement and Control 39, no. 4 (December 7, 2015): 520–36. http://dx.doi.org/10.1177/0142331215611209.

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In this paper, by using a distributed control system (DCS) device, a robust tracking control system is proposed based on robust right coprime factorization for a heat exchanger actuated by a water level process with coupling effects and uncertainties. Firstly, nonlinear models of water level and temperature processes with coupling and uncertainties are given. Secondly, nonlinear feedback tracking control systems corresponding to a multi-input multi-output (MIMO) process are realized by using operator-based robust right coprime factorization. Meanwhile, stability of the control systems is guaranteed by using robust stability conditions compatible with the MIMO process including coupling effects, and to improve the output tracking performance, tracking controllers are designed. Finally, the effectiveness of the proposed design scheme is confirmed by simulation and experimental results.

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Dementieva, Elsa Rachel, Z. K. A. Baizal, and Donni Richasdy. "Food and Beverage Recommendation in EatAja Application Using the Alternating Least Square Method Recommender System." JURNAL MEDIA INFORMATIKA BUDIDARMA 6, no. 4 (October 25, 2022): 2446. http://dx.doi.org/10.30865/mib.v6i4.4549.

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EatAja is a startup in Indonesia that provides a mobile application-based food and beverage ordering solution for restaurants. The EatAja application uses transaction data to recommend food and beverage menus to customers. Previous studies have developed recommender systems using the Apriori and Collaborative Filtering methods. However, there are shortcomings in the recommendation system using both methods, i.e., the lack of personalization factors and low scalability. The learning method with matrix factorization can overcome the problem. In this study, we improve the food and beverage product recommender system in the EatAja application using the Alternating Least Square (ALS) matrix factorization method on Apache Spark. We will compare the results of the recommender system using the ALS method with the Collaborative Filtering method. The comparison uses the Mean Absolute Error (MAE) evaluation method. The results showed that the MAE value decreased by 0.07 with the ALS Matrix factorization method.

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Arabi naree, Somaye, and Maryam Mohammadi. "A new non-negative matrix factorization method to build a recommender system." Journal of Research in Science, Engineering and Technology 8, no. 2 (September 29, 2020): 12–6. http://dx.doi.org/10.24200/jrset.vol8iss2pp12-6.

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The main aim of this paper is to apply non-negative matrix factorization to build a recommender system. In a recommender system there are a group of users that rate to a set of items. These ratings can be represented by a rating matrix. The main problem is to estimate the unknown ratings and then predict the interests of the users to the items which haven’t rated. The main innovation of this paper is to propose a new algorithm to compute matrix factorization in a way that the factorized matrixes would be a good approximation for the initial rating matrix and moreover would be a good source to predict the unknown ratings of the items precisely. The results show that the proposed matrix factorization improves the estimated ratings considerably.

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Arabi naree, Somaye, and Maryam Mohammadi. "A New Non-Negative Matrix Factorization Method to Build a Recommender System." Journal of Management and Accounting Studies 8, no. 3 (September 29, 2020): 56–61. http://dx.doi.org/10.24200/jmas.vol8iss3pp56-61.

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The main aim of this paper is to apply non-negative matrix factorization to build a recommender system. In a recommender system there are a group of users that rate to a set of items. These ratings can be represented by a rating matrix. The main problem is to estimate the unknown ratings and then predict the interests of the users to the items which haven’t rated. The main innovation of this paper is to propose a new algorithm to compute matrix factorization in a way that the factorized matrixes would be a good approximation for the initial rating matrix and moreover would be a good source to predict the unknown ratings of the items precisely. The results show that the proposed matrix factorization improves the estimated ratings considerably.

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Bin, Sheng, and Gengxin Sun. "Matrix Factorization Recommendation Algorithm Based on Multiple Social Relationships." Mathematical Problems in Engineering 2021 (February 26, 2021): 1–8. http://dx.doi.org/10.1155/2021/6610645.

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With the widespread use of social networks, social recommendation algorithms that add social relationships between users to recommender systems have been widely applied. Existing social recommendation algorithms only introduced one type of social relationship to the recommendation system, but in reality, there are often multiple social relationships among users. In this paper, a new matrix factorization recommendation algorithm combined with multiple social relationships is proposed. Through experiment results analysis on the Epinions dataset, the proposed matrix factorization recommendation algorithm has a significant improvement over the traditional and matrix factorization recommendation algorithms that integrate a single social relationship.

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Babarinsa, Olayiwola, and Hailiza Kamarulhaili. "Modified Cramer’s Rule and its Application to Solve Linear Systems in WZ Factorization." MATEMATIKA 35, no. 1 (April 1, 2019): 25–38. http://dx.doi.org/10.11113/matematika.v35.n1.1073.

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The proposed modified methods of Cramer's rule consider the column vector as well as the coefficient matrix concurrently in the linear system. The modified methods can be applied since Cramer's rule is typically known for solving the linear systems in $WZ$ factorization to yield Z-matrix. Then, we presented our results to show that there is no tangible difference in performance time between Cramer's rule and the modified methods in the factorization from improved versions of MATLAB. Additionally, the Frobenius norm of the modified methods in the factorization is better than using Cramer's rule irrespective of the version of MATLAB used.

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Deng, M., A. Inoue, and K. Edahiro. "Fault detection in a thermal process control system with input constraints using a robust right coprime factorization approach." Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 221, no. 6 (September 1, 2007): 819–31. http://dx.doi.org/10.1243/09596518jsce350.

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A fault detection method in an uncertain aluminium plate thermal process control system with input constraints is presented. The method is based on a robust right coprime factorization approach. The detailed explanation is as follows. Based on right coprime factorization dynamics, a model of the thermal process is developed. Using the concept of robust right coprime factorization of non-linear operators, a robust tracking operator system for the process is designed. For checking the tracking operator system, a fault detection design scheme is proposed. Further, simulation and experimental results are also presented to support the theoretical results.

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RANGARAJAN, GOVINDAN. "POLYNOMIAL MAP FACTORIZATION OF SYMPLECTIC MAPS." International Journal of Modern Physics C 14, no. 06 (July 2003): 847–54. http://dx.doi.org/10.1142/s0129183103004991.

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Long-term stability studies of nonlinear Hamiltonian systems require symplectic integration algorithms which are both fast and accurate. In this paper, we study a symplectic integration method wherein the symplectic map representing the Hamiltonian system is refactorized using polynomial symplectic maps. This method is analyzed for the three degree of freedom case. Finally, we apply this algorithm to study a large particle storage ring.

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Monro, G. P. "Logic, sheaves, and factorization systems." Journal of Symbolic Logic 58, no. 3 (September 1993): 872–93. http://dx.doi.org/10.2307/2275101.

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In this paper we extend the models for the “logic of categories” to a wider class of categories than is usually considered. We consider two kinds of logic, a restricted first-order logic and the full higher-order logic of elementary topoi.The restricted first-order logic has as its only logical symbols ∧, ∃, Τ, and =. We interpret this logic in a category with finite limits equipped with a factorization system (in the sense of [4]). We require to satisfy two additional conditions: ⊆ Monos, and any pullback of an arrow in is again in . A category with a factorization system satisfying these conditions will be called an EM-category.The interpretation of the restricted logic in EM-categories is given in §1. In §2 we give an axiomatization for the logic, and in §§3 and 5 we give two completeness proofs for this axiomatization. The first completeness proof constructs an EM-category out of the logic, in the spirit of Makkai and Reyes [8], though the construction used here differs from theirs. The second uses Boolean-valued models and shows that the restricted logic is exactly the ∧, ∃-fragment of classical first-order logic (adapted to categories). Some examples of EM-categories are given in §4.The restricted logic is powerful enough to handle relations, and in §6 we assign to each EM-category a bicategory of relations Rel() and a category of “functional relations” fr. fr is shown to be a regular category, and it turns out that Rel( and Rel(fr) are biequivalent bicategories. In §7 we study complete objects in an EM-category where an object of is called complete if every functional relation into is yielded by a unique morphism into . We write c for the full subcategory of consisting of the complete objects. Complete objects have some, but not all, of the properties that sheaves have in a category of presheaves.

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Rizk, Rawya, Walaa Saber, and Hany Harb. "Conditional clustered matrix factorization based network coordinate system." Journal of Network and Computer Applications 45 (October 2014): 191–202. http://dx.doi.org/10.1016/j.jnca.2014.07.027.

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Vidyasagar, Mathukumalli. "Control System Synthesis: A Factorization Approach, Part I." Synthesis Lectures on Control and Mechatronics 2, no. 1 (June 20, 2011): 1–184. http://dx.doi.org/10.2200/s00351ed1v01y201105crm002.

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Vidyasagar, Mathukumalli. "Control System Synthesis: A Factorization Approach, Part II." Synthesis Lectures on Control and Mechatronics 2, no. 1 (June 20, 2011): 1–227. http://dx.doi.org/10.2200/s00358ed1v01y201105crm003.

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Khargonekar, Pramod P. "Control System Synthesis: A Factorization Approach (M. Vidyasagar)." SIAM Review 29, no. 4 (December 1987): 658–60. http://dx.doi.org/10.1137/1029137.

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Ge, Li, Wei Liu, and Jianqiang Shan. "Development and Application of a New High-Efficiency Sparse Linear System Solver in the Thermal-Hydraulic System Analysis Code." Science and Technology of Nuclear Installations 2017 (2017): 1–10. http://dx.doi.org/10.1155/2017/7072197.

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This paper presents a faster solver named NRLU (Node Reordering Lower Upper) factorization solver to improve the solution speed for the pressure equations, which are formed by RELAP5/MOD3.3. The NRLU solver uses the oriented graph method and minimal fill-ins rule to reorder the structure of the nonsymmetry sparse pressure matrix. It solves the pressure matrix by LU factorization. Then the solver is embedded into the large scale advanced thermal-hydraulic system analysis program RELAP5/MOD3.3. The comparisons of the original solver and the NRLU solver show that the NRLU solver is faster than the original solver in RELAP5/MOD3.3, and the rate enhancement can be 44.44%. The results also show that the NRLU solver can reduce the number of fill-ins effectively. This can improve the calculation speed.

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Garg, Neha, and Sunidhi Shrivastava. "A Multi-View Learning based Clustering Method for Health Care System." International Journal for Research in Applied Science and Engineering Technology 10, no. 5 (May 31, 2022): 3853–59. http://dx.doi.org/10.22214/ijraset.2022.43243.

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Abstract: Patients in hospitals have faced complications due to measurement errors, missing data, privacy issues etc. in electronic medical records. However, these medical records from heterogeneous sources have both structured and unstructured data. In particular, unstructured clinical data is valuable source of information including patient’s records of pathology data, radiology findings, medication order etc. However, to scrutinize, construe and presentation of this unstructured and high dimensional data is one of the significant modeling challenge that clinical support system has faced from many years before. Therefore, there is a need of some standard technique to locate both subjective and objective guesstimates of patient’s condition. Our endowments in this paper are twofold. First, present a multi-view learning technique, i.e. Collective Matrix Factorization to combine the extracted features from multiple views and gives a low dimensional representation of combined clinical data. Second, proposed a Genetic-K-means based clustering algorithm based on Collective Matrix Factorization for heterogeneous clinical records. It has been observed by the experiments that proposed method gives more accurate clustering results than existing method. Keywords: Clinical notes; Collective Matrix Factorization; Genetic; heterogeneous data; K-means; Multi-view learning.

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Garg, Neha, and Sunidhi Shrivastava. "A Multi-View Learning based Clustering Method for Health Care System." International Journal for Research in Applied Science and Engineering Technology 10, no. 5 (May 31, 2022): 3853–59. http://dx.doi.org/10.22214/ijraset.2022.43243.

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Abstract: Patients in hospitals have faced complications due to measurement errors, missing data, privacy issues etc. in electronic medical records. However, these medical records from heterogeneous sources have both structured and unstructured data. In particular, unstructured clinical data is valuable source of information including patient’s records of pathology data, radiology findings, medication order etc. However, to scrutinize, construe and presentation of this unstructured and high dimensional data is one of the significant modeling challenge that clinical support system has faced from many years before. Therefore, there is a need of some standard technique to locate both subjective and objective guesstimates of patient’s condition. Our endowments in this paper are twofold. First, present a multi-view learning technique, i.e. Collective Matrix Factorization to combine the extracted features from multiple views and gives a low dimensional representation of combined clinical data. Second, proposed a Genetic-K-means based clustering algorithm based on Collective Matrix Factorization for heterogeneous clinical records. It has been observed by the experiments that proposed method gives more accurate clustering results than existing method. Keywords: Clinical notes; Collective Matrix Factorization; Genetic; heterogeneous data; K-means; Multi-view learning.

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Shalannanda, Wervyan, Rafi Falih Mulia, Arief Insanu Muttaqien, Naufal Rafi Hibatullah, and Annisabelia Firdaus. "Singular value decomposition model application for e-commerce recommendation system." JITEL (Jurnal Ilmiah Telekomunikasi, Elektronika, dan Listrik Tenaga) 2, no. 2 (September 30, 2022): 103–10. http://dx.doi.org/10.35313/jitel.v2.i2.2022.103-110.

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A recommendation system is one of the most important things in today’s technology. It can suggest products that match the user’s preferences. Many fields utilize this system, including e-commerce, using various algorithms. This paper used the matrix factorization-based algorithm, singular value decomposition (SVD), to make a recommendation system based on users’ similarities. Afterward, we implement the model against the ModCloth Amazon dataset. The results imply that the SVD algorithm yields the best accuracy compared to other matrix factorization-based algorithms with root mean square error (RMSE) of 1.055586. Then, we optimized the SVD algorithm by changing the hyperparameters of the algorithm to generate better accuracy and yield a model with an RMSE value of 1.041784.

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Górecki, Henryk. "Algebraic Condition for Decomposition of Large-Scale Linear Dynamic Systems." International Journal of Applied Mathematics and Computer Science 19, no. 1 (March 1, 2009): 107–12. http://dx.doi.org/10.2478/v10006-009-0010-x.

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Algebraic Condition for Decomposition of Large-Scale Linear Dynamic SystemsThe paper concerns the problem of decomposition of a large-scale linear dynamic system into two subsystems. An equivalent problem is to split the characteristic polynomial of the original system into two polynomials of lower degrees. Conditions are found concerning the coefficients of the original polynomial which must be fulfilled for its factorization. It is proved that knowledge of only one of the symmetric functions of those polynomials of lower degrees is sufficient for factorization of the characteristic polynomial of the original large-scale system. An algorithm for finding all the coefficients of the decomposed polynomials and a general condition of factorization are given. Examples of splitting the polynomials of the fifth and sixth degrees are discussed in detail.

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Baggyalakshmi, N., A. Kavitha, and A. Marimuthu. "Enhanced tensor factorization framework using non-negative and probabilistic tensor factorization approaches for microblogging content propagation modelling." International Journal of Engineering & Technology 7, no. 1.1 (December 21, 2017): 88. http://dx.doi.org/10.14419/ijet.v7i1.1.9204.

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With the aim of identifying the user’s preferences, Content propagation modeling from the micro-blogging sites aids diverse organizations. In existing studies, four user behavior aspects were used by the content propagation model that is to say topic virality, user’s position, user susceptibility and user virality. The propagation occurrences are signified as a tensor factorization model so-called V2S is presented with the aim of deriving the behavioral aspects via which the content propagation is designed. On the other hand, it doesn’t comprise the linguistic patterns in the content that decreases the performance of the content propagation. Moreover, by utilizing advanced tensor approaches, the factorization structure is improved. Therefore the performance of the complete system is decreased meaningfully. With the aim of overcoming the aforesaid problems, Enhanced V2S (EV2S) Tensor Factorization framework is presented in this research that make use of the Probabilistic Latent Tensor Factorization (PLTF) as well as Non-negative Tensor Factorization (NTF) in order to derive the behavioral facets. NTF is presented for decreasing the content propagation errors. By making use of fast gradient descent technique, the unrestrained issue, which happens in this model is solved. This research system identifies the reposts as well as re-tweets in huge datasets proficiently with minimum processing time. From the experimentation outcomes, it is proved that the EV2S-PLTF tensor factorization performs better when compared to the previous tensor frameworks.

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MORIYA, KENTARO, LINJIE ZHANG, and TAKASHI NODERA. "AN APPROXIMATE MATRIX INVERSION PROCEDURE BY PARALLELIZATION OF THE SHERMAN–MORRISON FORMULA." ANZIAM Journal 51, no. 1 (July 2009): 1–9. http://dx.doi.org/10.1017/s1446181109000364.

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AbstractThe Sherman–Morrison formula is one scheme for computing the approximate inverse preconditioner of a large linear system of equations. However, parallelizing a preconditioning approach is not straightforward as it is necessary to include a sequential process in the matrix factorization. In this paper, we propose a formula that improves the performance of the Sherman–Morrison preconditioner by partially parallelizing the matrix factorization. This study shows that our parallel technique implemented on a PC cluster system of eight processing elements significantly reduces the computational time for the matrix factorization compared with the time taken by a single processor. Our study has also verified that the Sherman–Morrison preconditioner performs better than ILU or MR preconditioners.

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Nash, P. L., and L. Y. Chen. "Factorization of the constants of motion." Canadian Journal of Physics 84, no. 8 (August 1, 2006): 717–22. http://dx.doi.org/10.1139/p06-068.

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A complete set of first integrals, or constants of motion, for a model system is constructed using “factorization”, as described below. The system is described by the effective Feynman Lagrangian L = [Formula: see text], with one of the simplest, nontrivial, potentials V(x) = (1/2)m ω2x2 selected for study. Four new, explicitly time-dependent, constants of the motion ci±, i = 1, 2 are defined for this system. While [Formula: see text]ci± ≠ 0, [Formula: see text]ci± = [Formula: see text]ci± + [Formula: see text]ci± + [Formula: see text]ci± + · · · = 0 along an extremal of L. The Hamiltonian H is shown to equal a sum of products of the ci±, and verifies [Formula: see text] = 0. A second, functionally independent constant of motion is also constructed as a sum of the quadratic products of ci±. It is shown that these derived constants of motion are in involution.PACS Nos.: 02.30.Jr, 02.30.Ik, 02.60.Cb, 02.30.Hq, 05.70.Ln, 02.50.–r

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Ran, Xun, Yong Wang, Leo Yu Zhang, and Jun Ma. "A differentially private nonnegative matrix factorization for recommender system." Information Sciences 592 (May 2022): 21–35. http://dx.doi.org/10.1016/j.ins.2022.01.050.

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Lara-Cabrera, Raúl, Álvaro González, Fernando Ortega, and Ángel González-Prieto. "Dirichlet Matrix Factorization: A Reliable Classification-Based Recommender System." Applied Sciences 12, no. 3 (January 24, 2022): 1223. http://dx.doi.org/10.3390/app12031223.

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Traditionally, recommender systems have been approached as regression models aiming to predict the score that a user would give to a particular item. In this work, we propose a recommender system that tackles the problem as a classification task instead of as a regression. The new model, Dirichlet Matrix Factorization (DirMF), provides not only a prediction but also its reliability, hence achieving a better balance between the quality and quantity of the predictions (i.e., reducing the prediction error by limiting the model’s coverage). The experimental results conducted show that the proposed model outperforms other models due to its ability to discard unreliable predictions. Compared to our previous model, which uses the same classification approach, DirMF shows a similar efficiency, outperforming the former on some of the datasets included in the experimental setup.

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Sun, Shaolun, Yuetong Xiao, Yue Huang, Sen Zhang, Heng Zheng, Wendong Xiao, and Xiaoli Su. "Joint Matrix Factorization: A Novel Approach for Recommender System." IEEE Access 8 (2020): 224596–607. http://dx.doi.org/10.1109/access.2020.3044046.

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Chiang, Ying-Chih, Shachar Klaiman, Frank Otto, and Lorenz S. Cederbaum. "The exact wavefunction factorization of a vibronic coupling system." Journal of Chemical Physics 140, no. 5 (February 7, 2014): 054104. http://dx.doi.org/10.1063/1.4863315.

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Cigoli, Alan S., Tomas Everaert, and Marino Gran. "A Relative Monotone-Light Factorization System for Internal Groupoids." Applied Categorical Structures 26, no. 5 (February 12, 2018): 931–42. http://dx.doi.org/10.1007/s10485-018-9515-5.

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Sifa, Rafet, Raheel Yawar, Rajkumar Ramamurthy, and Christian Bauckhage. "Matrix and Tensor Factorization Based Game Content Recommender Systems: A Bottom-Up Architecture and a Comparative Online Evaluation." Proceedings of the AAAI Conference on Artificial Intelligence and Interactive Digital Entertainment 14, no. 1 (September 25, 2018): 102–8. http://dx.doi.org/10.1609/aiide.v14i1.13028.

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Players of digital games face numerous choices as to what kind of games to play and what kind of game content or in-game activities to opt for. Among these, game content plays an important role in keeping players engaged so as to increase revenues for the gaming industry. However, while nowadays a lot of game content is generated using procedural content generation, automatically determining the kind of content that suits players' skills still poses challenges to game developers. Addressing this challenge, we present matrix- and tensor factorization based game content recommender systems for recommending quests in a single player role-playing game. We discuss the theory behind latent factor models for recommender systems and derive an algorithm for tensor factorizations to decompose collections of bipartite matrices. Extensive online bucket type tests reveal that our novel recommender system retained more players and recommended more engaging quests than handcrafted content-based and previous collaborative filtering approaches.

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