Статті в журналах: "MATRIX FACTORIZATION TECHNIQUES"

1

Koren, Yehuda, Robert Bell, and Chris Volinsky. "Matrix Factorization Techniques for Recommender Systems." Computer 42, no. 8 (August 2009): 30–37. http://dx.doi.org/10.1109/mc.2009.263.

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Du, Ke-Lin, M. N. S. Swamy, Zhang-Quan Wang, and Wai Ho Mow. "Matrix Factorization Techniques in Machine Learning, Signal Processing, and Statistics." Mathematics 11, no. 12 (June 12, 2023): 2674. http://dx.doi.org/10.3390/math11122674.

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Compressed sensing is an alternative to Shannon/Nyquist sampling for acquiring sparse or compressible signals. Sparse coding represents a signal as a sparse linear combination of atoms, which are elementary signals derived from a predefined dictionary. Compressed sensing, sparse approximation, and dictionary learning are topics similar to sparse coding. Matrix completion is the process of recovering a data matrix from a subset of its entries, and it extends the principles of compressed sensing and sparse approximation. The nonnegative matrix factorization is a low-rank matrix factorization technique for nonnegative data. All of these low-rank matrix factorization techniques are unsupervised learning techniques, and can be used for data analysis tasks, such as dimension reduction, feature extraction, blind source separation, data compression, and knowledge discovery. In this paper, we survey a few emerging matrix factorization techniques that are receiving wide attention in machine learning, signal processing, and statistics. The treated topics are compressed sensing, dictionary learning, sparse representation, matrix completion and matrix recovery, nonnegative matrix factorization, the Nyström method, and CUR matrix decomposition in the machine learning framework. Some related topics, such as matrix factorization using metaheuristics or neurodynamics, are also introduced. A few topics are suggested for future investigation in this article.

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Behl, Rachna, and Indu Kashyap. "Locus recommendation using probabilistic matrix factorization techniques." Ingeniería Solidaria 17, no. 1 (January 11, 2021): 1–25. http://dx.doi.org/10.16925/2357-6014.2021.01.10.

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Introduction: The present paper is the outcome of the research “Locus Recommendation using Probabilistic Matrix Factorization Techniques” carried out in Manav Rachna International Institute of Research and Studies, India in the year 2019-20. Methodology: Matrix factorization is a model-based collaborative technique for recommending new items to the users. Results: Experimental results on two real-world LBSNs showed that PFM consistently outperforms PMF. This is because the technique is based on gamma distribution to the model user and item matrix. Using gamma distribution is reasonable for check-in frequencies which are all positive in real datasets. However, PMF is based on Gaussian distribution that can allow negative frequency values as well. Conclusion: The motive of the work is to identify the best technique for recommending locations with the highest accuracy and allow users to choose from a plethora of available locations; the best and interesting location based on the individual’s profile. Originality: A rigorous analysis of Probabilistic Matrix Factorization techniques has been performed on popular LBSNs and the best technique for location recommendation has been identified by comparing the accuracy viz RMSE, Precision@N, Recall@N, F1@N of different models. Limitations: User’s contextual information like demographics, social and geographical preferences have not been considered while evaluating the efficiency of probabilistic matrix factorization techniques for POI Recommendations.

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Nguyen, Jennifer, and Mu Zhu. "Content-boosted matrix factorization techniques for recommender systems." Statistical Analysis and Data Mining 6, no. 4 (April 2, 2013): 286–301. http://dx.doi.org/10.1002/sam.11184.

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5

Wang, Fei, Hanghang Tong, and Ching-Yung Lin. "Towards Evolutionary Nonnegative Matrix Factorization." Proceedings of the AAAI Conference on Artificial Intelligence 25, no. 1 (August 4, 2011): 501–6. http://dx.doi.org/10.1609/aaai.v25i1.7927.

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Nonnegative Matrix Factorization (NMF) techniques has aroused considerable interests from the field of artificial intelligence in recent years because of its good interpretability and computational efficiency. However, in many real world applications, the data features usually evolve over time smoothly. In this case, it would be very expensive in both computation and storage to rerun the whole NMF procedure after each time when the data feature changing. In this paper, we propose Evolutionary Nonnegative Matrix Factorization (eNMF), which aims to incrementally update the factorized matrices in a computation and space efficient manner with the variation of the data matrix. We devise such evolutionary procedure for both asymmetric and symmetric NMF. Finally we conduct experiments on several real world data sets to demonstrate the efficacy and efficiency of eNMF.

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Khalane, Vivek, Shekhar Suralkar, and Umesh Bhadade. "Image Encryption Based on Matrix Factorization." International Journal of Safety and Security Engineering 10, no. 5 (November 30, 2020): 655–61. http://dx.doi.org/10.18280/ijsse.100510.

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In this paper, we present a matrix decomposition-based approach for image cryptography. The proposed method consists of decomposing the image into different component and scrambling the components to form the image encryption technique. We use two different type of matrix decomposition techniques to check the efficiency of proposed encryption method. The decomposition techniques used are Independent component analysis (ICA) and Non-Negative Matrix factorization (NMF). The proposed technique has unique user defined parameters (key) such as decomposition method, number of decomposition components and order in which the components are arranged. The unique encryption technique is designed on the basis of these key parameters. The original image can be reconstructed at the decryption end only if the selected parameters are known to the user. The design examples for both decomposition approaches are presented for illustration purpose. We analyze the complexity and encryption time of cryptography system. Results prove that the proposed scheme is more secure as it has less correlation between the input image and the encrypted version of the same as compared to state-of-art methods. The computation time of the proposed approach is found to be comparable.

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Nalavade, Jagannath E., Chandra Sekhar Kolli, and Sanjay Nakharu Prasad Kumar. "Deep embedded clustering with matrix factorization based user rating prediction for collaborative recommendation." Multiagent and Grid Systems 19, no. 2 (October 6, 2023): 169–85. http://dx.doi.org/10.3233/mgs-230039.

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Conventional recommendation techniques utilize various methods to compute the similarity among products and customers in order to identify the customer preferences. However, such conventional similarity computation techniques may produce incomplete information influenced by similarity measures in customers’ preferences, which leads to poor accuracy on recommendation. Hence, this paper introduced the novel and effective recommendation technique, namely Deep Embedded Clustering with matrix factorization (DEC with matrix factorization) for the collaborative recommendation. This approach creates the agglomerative matrix for the recommendation using the review data. The customer series matrix, customer series binary matrix, product series matrix, and product series binary matrix make up the agglomerative matrix. The product grouping is carried out to group the similar products using DEC for retrieving the optimal product. Moreover, the bi-level matching generates the best group customer sequence in which the relevant customers are retrieved using tversky index and angular distance. Also, the final product suggestion is made using matrix factorization, with the goal of recommending to clients the product with the highest rating. Also, according to the experimental results, the developed DEC with the matrix factorization approach produced better results with respect to f-measure values of 0.902, precision values of 0.896, and recall values of 0.908, respectively.

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Tong, Lei, Jing Yu, Chuangbai Xiao, and Bin Qian. "Hyperspectral unmixing via deep matrix factorization." International Journal of Wavelets, Multiresolution and Information Processing 15, no. 06 (November 2017): 1750058. http://dx.doi.org/10.1142/s0219691317500588.

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Hyperspectral unmixing is one of the most important techniques in hyperspectral remote sensing image analysis. During the past decades, many models have been widely used in hyperspectral unmixing, such as nonnegative matrix factorization (NMF) model, sparse regression model, etc. Most recently, a new matrix factorization model, deep matrix, is proposed and shows good performance in face recognition area. In this paper, we introduce the deep matrix factorization (DMF) for hyperspectral unmixing. In this method, the DMF method is applied for hyperspectral unmixing. Compared with the traditional NMF-based unmixing methods, DMF could extract more information with multiple-layer structures. An optimization algorithm is also proposed for DMF with two designed processes. Results on both synthetic and real data have validated the effectiveness of this method, and shown that it has outperformed several state-of-the-art unmixing approaches.

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Yashwanth, A. "Audio Enhancement and Denoising using Online Non-Negative Matrix Factorization and Deep Learning." International Journal for Research in Applied Science and Engineering Technology 10, no. 6 (June 30, 2022): 1703–9. http://dx.doi.org/10.22214/ijraset.2022.44061.

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Abstract: For many years, reducing noise in a noisy speech recording has been a difficult task with numerous applications. This gives scope to use better techniques to enhance the audio and speech and to reduce the noise in the audio. One such technique is Online Non-Negative Matrix Factorization (ONMF). ONMF noise reduction approach primarily generates a noiseless audio signal from an audio sample that has been contaminated by additive noise. Previously many approaches were based on nonnegative matrix factorization to spectrogram measurements. Non-negative Matrix Factorization (NMF) is a standard tool for audio source separation. One major disadvantage of applying NMF on datasets that are large is the time complexity. In this work, we proposed using Online Non-Negative Matrix Factorization. The data can be taken as any speech or music. This method uses less memory than regular non-negative matrix factorization, and it could be used for real-time denoising. This ONMF algorithm is more efficient in memory and time complexity for updates in the dictionary. We have shown that the ONMF method is faster and more efficient for small audio signals on audio simulations. We also implemented this using the Deep Learning approach for comparative study with the Online Non-Negative Matrix Factorization.

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10

Lin, Chih-Jen. "Projected Gradient Methods for Nonnegative Matrix Factorization." Neural Computation 19, no. 10 (October 2007): 2756–79. http://dx.doi.org/10.1162/neco.2007.19.10.2756.

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Nonnegative matrix factorization (NMF) can be formulated as a minimization problem with bound constraints. Although bound-constrained optimization has been studied extensively in both theory and practice, so far no study has formally applied its techniques to NMF. In this letter, we propose two projected gradient methods for NMF, both of which exhibit strong optimization properties. We discuss efficient implementations and demonstrate that one of the proposed methods converges faster than the popular multiplicative update approach. A simple Matlab code is also provided.

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Vishwas, B. C., Abhishek Gadia, and Mainak Chaudhuri. "Implementing a Parallel Matrix Factorization Library on the Cell Broadband Engine." Scientific Programming 17, no. 1-2 (2009): 3–29. http://dx.doi.org/10.1155/2009/710321.

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Matrix factorization (or often called decomposition) is a frequently used kernel in a large number of applications ranging from linear solvers to data clustering and machine learning. The central contribution of this paper is a thorough performance study of four popular matrix factorization techniques, namely, LU, Cholesky, QR and SVD on the STI Cell broadband engine. The paper explores algorithmic as well as implementation challenges related to the Cell chip-multiprocessor and explains how we achieve near-linear speedup on most of the factorization techniques for a range of matrix sizes. For each of the factorization routines, we identify the bottleneck kernels and explain how we have attempted to resolve the bottleneck and to what extent we have been successful. Our implementations, for the largest data sets that we use, running on a two-node 3.2 GHz Cell BladeCenter (exercising a total of sixteen SPEs), on average, deliver 203.9, 284.6, 81.5, 243.9 and 54.0 GFLOPS for dense LU, dense Cholesky, sparse Cholesky, QR and SVD, respectively. The implementations achieve speedup of 11.2, 12.8, 10.6, 13.0 and 6.2, respectively for dense LU, dense Cholesky, sparse Cholesky, QR and SVD, when running on sixteen SPEs. We discuss the interesting interactions that result from parallelization of the factorization routines on a two-node non-uniform memory access (NUMA) Cell Blade cluster.

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12

Abdi, Mohamed Hussein, George Onyango Okeyo, and Ronald Waweru Mwangi. "Matrix Factorization Techniques for Context-Aware Collaborative Filtering Recommender Systems: A Survey." Computer and Information Science 11, no. 2 (March 16, 2018): 1. http://dx.doi.org/10.5539/cis.v11n2p1.

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Collaborative Filtering Recommender Systems predict user preferences for online information, products or services by learning from past user-item relationships. A predominant approach to Collaborative Filtering is Neighborhood-based, where a user-item preference rating is computed from ratings of similar items and/or users. This approach encounters data sparsity and scalability limitations as the volume of accessible information and the active users continue to grow leading to performance degradation, poor quality recommendations and inaccurate predictions. Despite these drawbacks, the problem of information overload has led to great interests in personalization techniques. The incorporation of context information and Matrix and Tensor Factorization techniques have proved to be a promising solution to some of these challenges. We conducted a focused review of literature in the areas of Context-aware Recommender Systems utilizing Matrix Factorization approaches. This survey paper presents a detailed literature review of Context-aware Recommender Systems and approaches to improving performance for large scale datasets and the impact of incorporating contextual information on the quality and accuracy of the recommendation. The results of this survey can be used as a basic reference for improving and optimizing existing Context-aware Collaborative Filtering based Recommender Systems. The main contribution of this paper is a survey of Matrix Factorization techniques for Context-aware Collaborative Filtering Recommender Systems.

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13

Matuszyk, Pawel, João Vinagre, Myra Spiliopoulou, Alípio Mário Jorge, and João Gama. "Forgetting techniques for stream-based matrix factorization in recommender systems." Knowledge and Information Systems 55, no. 2 (August 4, 2017): 275–304. http://dx.doi.org/10.1007/s10115-017-1091-8.

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14

Li, Pengyu, Christine Tseng, Yaxuan Zheng, Joyce A. Chew, Longxiu Huang, Benjamin Jarman, and Deanna Needell. "Guided Semi-Supervised Non-Negative Matrix Factorization." Algorithms 15, no. 5 (April 20, 2022): 136. http://dx.doi.org/10.3390/a15050136.

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Classification and topic modeling are popular techniques in machine learning that extract information from large-scale datasets. By incorporating a priori information such as labels or important features, methods have been developed to perform classification and topic modeling tasks; however, most methods that can perform both do not allow for guidance of the topics or features. In this paper, we propose a novel method, namely Guided Semi-Supervised Non-negative Matrix Factorization (GSSNMF), that performs both classification and topic modeling by incorporating supervision from both pre-assigned document class labels and user-designed seed words. We test the performance of this method on legal documents provided by the California Innocence Project and the 20 Newsgroups dataset. Our results show that the proposed method improves both classification accuracy and topic coherence in comparison to past methods such as Semi-Supervised Non-negative Matrix Factorization (SSNMF), Guided Non-negative Matrix Factorization (Guided NMF), and Topic Supervised NMF.

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FILELIS-PAPADOPOULOS, CHRISTOS K., and GEORGE A. GRAVVANIS. "GENERIC APPROXIMATE SPARSE INVERSE MATRIX TECHNIQUES." International Journal of Computational Methods 11, no. 06 (December 2014): 1350084. http://dx.doi.org/10.1142/s0219876213500849.

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During the last decades explicit preconditioning methods have gained interest among the scientific community, due to their efficiency for solving large sparse linear systems in conjunction with Krylov subspace iterative methods. The effectiveness of explicit preconditioning schemes relies on the fact that they are close approximants to the inverse of the coefficient matrix. Herewith, we propose a Generic Approximate Sparse Inverse (GenASPI) matrix algorithm based on ILU(0) factorization. The proposed scheme applies to matrices of any structure or sparsity pattern unlike the previous dedicated implementations. The new scheme is based on the Generic Approximate Banded Inverse (GenAbI), which is a banded approximate inverse used in conjunction with Conjugate Gradient type methods for the solution of large sparse linear systems. The proposed GenASPI matrix algorithm, is based on Approximate Inverse Sparsity patterns, derived from powers of sparsified matrices and is computed with a modified procedure based on the GenAbI algorithm. Finally, applicability and implementation issues are discussed and numerical results along with comparative results are presented.

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Deepthi, S. Aruna, E. Sreenivasa Rao, and M. N. Giri Prasad. "RTL Implementation of image compression techniques in WSN." International Journal of Electrical and Computer Engineering (IJECE) 9, no. 3 (June 1, 2019): 1750. http://dx.doi.org/10.11591/ijece.v9i3.pp1750-1756.

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<p>The Wireless sensor networks have limitations regarding data redundancy, power and require high bandwidth when used for multimedia data. Image compression methods overcome these problems. Non-negative Matrix Factorization (NMF) method is useful in approximating high dimensional data where the data has non-negative components. Another method of the NMF called (PNMF) Projective Nonnegative Matrix Factorization is used for learning spatially localized visual patterns. Simulation results show the comparison between SVD, NMF, PNMF compression schemes. Compressed images are transmitted from base station to cluster head node and received from ordinary nodes. The station takes on the image restoration. Image quality, compression ratio, signal to noise ratio and energy consumption are the essential metrics measured for compression performance. In this paper, the compression methods are designed using Matlab.The parameters like PSNR, the total node energy consumption are calculated. RTL schematic of NMF SVD, PNMF methods is generated by using Verilog HDL.</p>

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Farina, Gabriele, and Tuomas Sandholm. "Fast Payoff Matrix Sparsification Techniques for Structured Extensive-Form Games." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 5 (June 28, 2022): 4999–5007. http://dx.doi.org/10.1609/aaai.v36i5.20431.

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The practical scalability of many optimization algorithms for large extensive-form games is often limited by the games' huge payoff matrices. To ameliorate the issue, Zhang and Sandholm recently proposed a sparsification technique that factorizes the payoff matrix A into a sparser object A = Â + UVᵀ, where the total combined number of nonzeros of Â, U, and V, is significantly smaller. Such a factorization can be used in place of the original payoff matrix in many optimization algorithm, such as interior-point and second-order methods, thus increasing the size of games that can be handled. Their technique significantly sparsifies poker (end)games, standard benchmarks used in computational game theory, AI, and more broadly. We show that the existence of extremely sparse factorizations in poker games can be tied to their particular Kronecker-product structure. We clarify how such structure arises and introduce the connection between that structure and sparsification. By leveraging such structure, we give two ways of computing strong sparsifications of poker games (as well as any other game with a similar structure) that are i) orders of magnitude faster to compute, ii) more numerically stable, and iii) produce a dramatically smaller number of nonzeros than the prior technique. Our techniques enable—for the first time—effective computation of high-precision Nash equilibria and strategies subject to constraints on the amount of allowed randomization. Furthermore, they significantly speed up parallel first-order game-solving algorithms; we show state-of-the-art speed on a GPU.

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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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Branham, Richard L. "Global Astrometric Solutions with Sparse Matrix Techniques." International Astronomical Union Colloquium 180 (March 2000): 127–31. http://dx.doi.org/10.1017/s0252921100000221.

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AbstractModern astrometric techniques lead to large, linear systems solved by the precepts of least-squares. These systems are usually sparse, and one should take advantage of the sparsity to facilitate their solution. As long as the matrix A of the equations of condition possesses the weak Hall property, characteristic of linear systems derived from astrometric reductions, it is possible to find a sparse Cholesky factor. Before the equations of condition are accumulated, by use of the fast Givens transformation, a symbolic factorization of A using Tewarson’s length of intersection technique determines the ordering of the columns of A that result in low fill-in. The non-null elements are stored in a sparse, dynamic data structure by use of dynamic hashing. Numerical experimentation shows that this competes well with alternatives such as nested dissection, and large, but sparse, linear systems with several thousand unknowns can be solved in a reasonable amount of time, even on personal computers.

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McGraw, Tim, Jisun Kang, and Donald Herring. "Sparse Non-Negative Matrix Factorization for Mesh Segmentation." International Journal of Image and Graphics 16, no. 01 (January 2016): 1650004. http://dx.doi.org/10.1142/s0219467816500042.

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In this paper, we present a method for 3D mesh segmentation based on sparse non-negative matrix factorization (NMF). Image analysis techniques based on NMF have been shown to decompose images into semantically meaningful local features. Since the features and coefficients are represented in terms of non-negative values, the features contribute to the resulting images in an intuitive, additive fashion. Like spectral mesh segmentation, our method relies on the construction of an affinity matrix which depends on the geometric properties of the mesh. We show that segmentation based on the NMF is simpler to implement, and can result in more meaningful segmentation results than spectral mesh segmentation.

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Hepsibah, K., M. S. Heaven, and M. Saravanan. "Image Enhancement based on Nonsubsampled Contourlet Transform using Matrix Factorization Techniques." International Journal of Computer Applications 123, no. 6 (August 18, 2015): 35–38. http://dx.doi.org/10.5120/ijca2015905372.

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Ma, Wenming, Rongjie Shan, and Mingming Qi. "General Collaborative Filtering for Web Service QoS Prediction." Mathematical Problems in Engineering 2018 (December 3, 2018): 1–18. http://dx.doi.org/10.1155/2018/5787406.

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To avoid the expensive and time-consuming evaluation, collaborative filtering (CF) methods have been widely studied for web service QoS prediction in recent years. Among the various CF techniques, matrix factorization is the most popular one. Much effort has been devoted to improving matrix factorization collaborative filtering. The key idea of matrix factorization is that it assumes the rating matrix is low rank and projects users and services into a shared low-dimensional latent space, making a prediction by using the dot product of a user latent vector and a service latent vector. Unfortunately, unlike the recommender systems, QoS usually takes continuous values with very wide range, and the low rank assumption might incur high bias. Furthermore, when the QoS matrix is extremely sparse, the low rank assumption also incurs high variance. To reduce the bias, we must use more complex assumptions. To reduce the variance, we can adopt complex regularization techniques. In this paper, we proposed a neural network based framework, named GCF (general collaborative filtering), with the dropout regularization, to model the user-service interactions. We conduct our experiments on a large real-world dataset, the QoS values of which are obtained from 339 users on 5825 web services. The comprehensive experimental studies show that our approach offers higher prediction accuracy than the traditional collaborative filtering approaches.

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Wu, Qing, Jie Wang, Jin Fan, Gang Xu, Jia Wu, Blake Johnson, Xingfei Li, Quan Do, and Ruiquan Ge. "Improved Coupled Tensor Factorization with Its Applications in Health Data Analysis." Complexity 2019 (February 5, 2019): 1–16. http://dx.doi.org/10.1155/2019/1574240.

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Coupled matrix and tensor factorizations have been successfully used in many data fusion scenarios where datasets are assumed to be exactly coupled. However, in the real world, not all the datasets share the same factor matrices, which makes joint analysis of multiple heterogeneous sources challenging. For this reason, approximate coupling or partial coupling is widely used in real-world data fusion, with exact coupling as a special case of these techniques. However, to fully address the challenge of tensor factorization, in this paper, we propose two improved coupled tensor factorization methods: one for approximately coupled datasets and the other for partially coupled datasets. A series of experiments using both simulated data and three real-world datasets demonstrate the improved accuracy of these approaches over existing baselines. In particular, when experiments on MRI data is conducted, the performance of our method is improved even by 12.47% in terms of accuracy compared with traditional methods.

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Porteous, Ian, Arthur Asuncion, and Max Welling. "Bayesian Matrix Factorization with Side Information and Dirichlet Process Mixtures." Proceedings of the AAAI Conference on Artificial Intelligence 24, no. 1 (July 3, 2010): 563–68. http://dx.doi.org/10.1609/aaai.v24i1.7686.

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Matrix factorization is a fundamental technique in machine learning that is applicable to collaborative filtering, information retrieval and many other areas. In collaborative filtering and many other tasks, the objective is to fill in missing elements of a sparse data matrix. One of the biggest challenges in this case is filling in a column or row of the matrix with very few observations. In this paper we introduce a Bayesian matrix factorization model that performs regression against side information known about the data in addition to the observations. The side information helps by adding observed entries to the factored matrices. We also introduce a nonparametric mixture model for the prior of the rows and columns of the factored matrices that gives a different regularization for each latent class. Besides providing a richer prior, the posterior distribution of mixture assignments reveals the latent classes. Using Gibbs sampling for inference, we apply our model to the Netflix Prize problem of predicting movie ratings given an incomplete user-movie ratings matrix. Incorporating rating information with gathered metadata information, our Bayesian approach outperforms other matrix factorization techniques even when using fewer dimensions.

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Shi, Zihui, and Yaoning Ge. "CMF-SMR: Convolutional matrix factorization for sequential movie recommendations." Applied and Computational Engineering 14, no. 1 (October 23, 2023): 86–95. http://dx.doi.org/10.54254/2755-2721/14/20230769.

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Recommender system (RS) has become an essential component of e-commerce, social media, and other online platforms. Collaborative filtering (CF) is one of the most commonly used techniques in RS that relies on user-item interactions to generate recommendations. However, CF suffers from the cold-start problem, sparsity, and scalability issues. To address these challenges, this work propose a hybrid system called Convolutional Matrix Factorization for Sequential Movie Recommendations (CMF-SMR), which combines matrix factorization (MF) with convolutional neural networks (CNNs). CMF-SMR leverages the non-linear feature extraction capabilities of CNNs and the representation learning abilities of deep learning to enhance the accuracy and robustness of traditional MF-based RS. Specifically, CNNs and MF were used to respectively extract features from user-item interaction data and use them as input for learning user and item representations. The learned representations are then used to predict user-item ratings. This work evaluates the performance of our proposed method on two publicly available datasets, and the experimental results demonstrate that our method outperforms several state-of-the-art techniques in terms of accuracy, scalability, and robustness. Moreover, this work conduct evaluation metrics to demonstrate the accuracy of our proposed method. Overall, our proposed CMF-SMR provides a promising solution for addressing the limitations of traditional CF-based RS and can be applied in various domains, including e-commerce, social media, and personalized content recommendation systems.

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Lin, Chuang, and Meng Pang. "Graph Regularized Nonnegative Matrix Factorization with Sparse Coding." Mathematical Problems in Engineering 2015 (2015): 1–11. http://dx.doi.org/10.1155/2015/239589.

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In this paper, we propose a sparseness constraint NMF method, named graph regularized matrix factorization with sparse coding (GRNMF_SC). By combining manifold learning and sparse coding techniques together, GRNMF_SC can efficiently extract the basic vectors from the data space, which preserves the intrinsic manifold structure and also the local features of original data. The target function of our method is easy to propose, while the solving procedures are really nontrivial; in the paper we gave the detailed derivation of solving the target function and also a strict proof of its convergence, which is a key contribution of the paper. Compared with sparseness constrained NMF and GNMF algorithms, GRNMF_SC can learn much sparser representation of the data and can also preserve the geometrical structure of the data, which endow it with powerful discriminating ability. Furthermore, the GRNMF_SC is generalized as supervised and unsupervised models to meet different demands. Experimental results demonstrate encouraging results of GRNMF_SC on image recognition and clustering when comparing with the other state-of-the-art NMF methods.

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27

Hurd, R. A., and E. Lüneburg. "Diffraction by an anisotropic impedance half plane." Canadian Journal of Physics 63, no. 9 (September 1, 1985): 1135–40. http://dx.doi.org/10.1139/p85-185.

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We solve a new canonical problem: that of a plane wave obliquely incident on an anisotropic imperfectly conducting half plane. An exact closed-form solution is obtained by factorizing a 2 × 2 Wiener–Hopf matrix. The problem had earlier been considered insoluble, but yields to a combination of new and old matrix-factorization techniques.

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Tokala, Srilatha, Murali Krishna Enduri, T. Jaya Lakshmi, and Hemlata Sharma. "Community-Based Matrix Factorization (CBMF) Approach for Enhancing Quality of Recommendations." Entropy 25, no. 9 (September 20, 2023): 1360. http://dx.doi.org/10.3390/e25091360.

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Matrix factorization is a long-established method employed for analyzing and extracting valuable insight recommendations from complex networks containing user ratings. The execution time and computational resources demanded by these algorithms pose limitations when confronted with large datasets. Community detection algorithms play a crucial role in identifying groups and communities within intricate networks. To overcome the challenge of extensive computing resources with matrix factorization techniques, we present a novel framework that utilizes the inherent community information of the rating network. Our proposed approach, named Community-Based Matrix Factorization (CBMF), has the following steps: (1) Model the rating network as a complex bipartite network. (2) Divide the network into communities. (3) Extract the rating matrices pertaining only to those communities and apply MF on these matrices in parallel. (4) Merge the predicted rating matrices belonging to communities and evaluate the root mean square error (RMSE). In our experimentation, we use basic MF, SVD++, and FANMF for matrix factorization, and the Louvain algorithm is used for community division. The experimental evaluation on six datasets shows that the proposed CBMF enhances the quality of recommendations in each case. In the MovieLens 100K dataset, RMSE has been reduced to 0.21 from 1.26 using SVD++ by dividing the network into 25 communities. A similar reduction in RMSE is observed for the datasets of FilmTrust, Jester, Wikilens, Good Books, and Cell Phone.

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Gomathy, Dr C. K. "A Comparing Collaborative Filtering and Hybrid Recommender System for E-Commerce." International Journal for Research in Applied Science and Engineering Technology 9, no. 11 (November 30, 2021): 635–38. http://dx.doi.org/10.22214/ijraset.2021.38844.

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Abstract: Here we are building an collaborative filtering matrix factorization based hybrid recommender system to recommend movies to users based on the sentiment generated from twitter tweets and other vectors generated by the user in their previous activities. To calculate sentiment data has been collected from twitter using developer APIs and scrapping techniques later these are cleaned, stemming, lemetized and generated sentiment values. These values are merged with the movie data taken and create the main data frame.The traditional approaches like collaborative filtering and content-based filtering have limitations like it requires previous user activities for performing recommendations. To reduce this dependency hybrid is used which combines both collaborative and content based filtering techniques with the sentiment generated above. Keywords: machine learning, natural language processing, movie lens data, root mean square equation, matrix factorization, recommenders system, sentiment analysis

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30

Ehrhardt, Torsten, and Frank-Olme Speck. "Transformation techniques towards the factorization of non-rational 2×2 matrix functions." Linear Algebra and its Applications 353, no. 1-3 (September 2002): 53–90. http://dx.doi.org/10.1016/s0024-3795(02)00288-4.

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31

Huang, Yan, Guisheng Liao, Zhen Zhang, Yijian Xiang, Jie Li, and Arye Nehorai. "Fast Narrowband RFI Suppression Algorithms for SAR Systems via Matrix-Factorization Techniques." IEEE Transactions on Geoscience and Remote Sensing 57, no. 1 (January 2019): 250–62. http://dx.doi.org/10.1109/tgrs.2018.2853556.

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Zhang, Zhijun, and Hong Liu. "Application and Research of Improved Probability Matrix Factorization Techniques in Collaborative Filtering." International Journal of Control and Automation 7, no. 8 (August 31, 2014): 79–92. http://dx.doi.org/10.14257/ijca.2014.7.8.08.

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Zheng, Xiaoyao, Yonglong Luo, Liping Sun, and Fulong Chen. "A New Recommender System Using Context Clustering Based on Matrix Factorization Techniques." Chinese Journal of Electronics 25, no. 2 (March 1, 2016): 334–40. http://dx.doi.org/10.1049/cje.2016.03.021.

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Fernsel, Pascal. "Spatially Coherent Clustering Based on Orthogonal Nonnegative Matrix Factorization." Journal of Imaging 7, no. 10 (September 28, 2021): 194. http://dx.doi.org/10.3390/jimaging7100194.

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Classical approaches in cluster analysis are typically based on a feature space analysis. However, many applications lead to datasets with additional spatial information and a ground truth with spatially coherent classes, which will not necessarily be reconstructed well by standard clustering methods. Motivated by applications in hyperspectral imaging, we introduce in this work clustering models based on Orthogonal Nonnegative Matrix Factorization (ONMF), which include an additional Total Variation (TV) regularization procedure on the cluster membership matrix to enforce the needed spatial coherence in the clusters. We propose several approaches with different optimization techniques, where the TV regularization is either performed as a subsequent post-processing step or included into the clustering algorithm. Finally, we provide a numerical evaluation of 12 different TV regularized ONMF methods on a hyperspectral dataset obtained from a matrix-assisted laser desorption/ionization imaging measurement, which leads to significantly better clustering results compared to classical clustering models.

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Sethuraman, Ram, and Akshay Havalgi. "Novel Approach of Neural Collaborative Filter by Pairwise Objective Function with Matrix Factorization." International Journal of Engineering & Technology 7, no. 3.12 (July 20, 2018): 1213. http://dx.doi.org/10.14419/ijet.v7i3.12.17840.

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The concept of deep learning is used in the various fields like text, speech and vision. The proposed work deep neural network is used for recommender system. In this work pair wise objective function is used for emphasis of non-linearity and latent features. The GMF (Gaussian matrix factorization) and MLP techniques are used in this work. The proposed framework is named as NCF which is basically neural network based collaborative filtering. The NCF gives the latent features by reducing the non-linearity and generalizing the matrix. In the proposed work combination of pair-wise and point wise objective function is used and tune by using the concept of cross entropy with Adam optimization. This optimization approach optimizes the gradient descent function. The work is done on 1K and 1M movies lens dataset and it is compared with deep matrix factorization (DMF).

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Yousefi, Bardia, Hamed Akbari, Michelle Hershman, Satoru Kawakita, Henrique C. Fernandes, Clemente Ibarra-Castanedo, Samad Ahadian, and Xavier P. V. Maldague. "SPAER: Sparse Deep Convolutional Autoencoder Model to Extract Low Dimensional Imaging Biomarkers for Early Detection of Breast Cancer Using Dynamic Thermography." Applied Sciences 11, no. 7 (April 5, 2021): 3248. http://dx.doi.org/10.3390/app11073248.

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Early diagnosis of breast cancer unequivocally improves the survival rate of patients and is crucial for disease treatment. With the current developments in infrared imaging, breast screening using dynamic thermography seems to be a great complementary method for clinical breast examination (CBE) prior to mammography. In this study, we propose a sparse deep convolutional autoencoder model named SPAER to extract low-dimensional deep thermomics to aid breast cancer diagnosis. The model receives multichannel, low-rank, approximated thermal bases as input images. SPAER provides a solution for high-dimensional deep learning features and selects the predominant basis matrix using matrix factorization techniques. The model has been evaluated using five state-of-the-art matrix factorization methods and 208 thermal breast cancer screening cases. The best accuracy was for non-negative matrix factorization (NMF)-SPAER + Clinical and NMF-SPAER for maintaining thermal heterogeneity, leading to finding symptomatic cases with accuracies of 78.2% (74.3–82.5%) and 77.7% (70.9–82.1%), respectively. SPAER showed significant robustness when tested for additive Gaussian noise cases (3–20% noise), evaluated by the signal-to-noise ratio (SNR). The results suggest high performance of SPAER for preserveing thermal heterogeneity, and it can be used as a noninvasive in vivo tool aiding CBE in the early detection of breast cancer.

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Xu, Yunxia, Linzhang Lu, Qilong Liu, and Zhen Chen. "Hypergraph-Regularized Lp Smooth Nonnegative Matrix Factorization for Data Representation." Mathematics 11, no. 13 (June 23, 2023): 2821. http://dx.doi.org/10.3390/math11132821.

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Nonnegative matrix factorization (NMF) has been shown to be a strong data representation technique, with applications in text mining, pattern recognition, image processing, clustering and other fields. In this paper, we propose a hypergraph-regularized Lp smooth nonnegative matrix factorization (HGSNMF) by incorporating the hypergraph regularization term and the Lp smoothing constraint term into the standard NMF model. The hypergraph regularization term can capture the intrinsic geometry structure of high dimension space data more comprehensively than simple graphs, and the Lp smoothing constraint term may yield a smooth and more accurate solution to the optimization problem. The updating rules are given using multiplicative update techniques, and the convergence of the proposed method is theoretically investigated. The experimental results on five different data sets show that the proposed method has a better clustering effect than the related state-of-the-art methods in the vast majority of cases.

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Dai, Wen, Xi Liu, Yibo Gao, Lin Chen, Jianglong Song, Di Chen, Kuo Gao, et al. "Matrix Factorization-Based Prediction of Novel Drug Indications by Integrating Genomic Space." Computational and Mathematical Methods in Medicine 2015 (2015): 1–9. http://dx.doi.org/10.1155/2015/275045.

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There has been rising interest in the discovery of novel drug indications because of high costs in introducing new drugs. Many computational techniques have been proposed to detect potential drug-disease associations based on the creation of explicit profiles of drugs and diseases, while seldom research takes advantage of the immense accumulation of interaction data. In this work, we propose a matrix factorization model based on known drug-disease associations to predict novel drug indications. In addition, genomic space is also integrated into our framework. The introduction of genomic space, which includes drug-gene interactions, disease-gene interactions, and gene-gene interactions, is aimed at providing molecular biological information for prediction of drug-disease associations. The rationality lies in our belief that association between drug and disease has its evidence in the interactome network of genes. Experiments show that the integration of genomic space is indeed effective. Drugs, diseases, and genes are described with feature vectors of the same dimension, which are retrieved from the interaction data. Then a matrix factorization model is set up to quantify the association between drugs and diseases. Finally, we use the matrix factorization model to predict novel indications for drugs.

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Ma, Xiaoxuan, Zhiwen Li, and Hengyou Wang. "Deep Matrix Factorization Based on Convolutional Neural Networks for Image Inpainting." Entropy 24, no. 10 (October 20, 2022): 1500. http://dx.doi.org/10.3390/e24101500.

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In this work, we formulate the image in-painting as a matrix completion problem. Traditional matrix completion methods are generally based on linear models, assuming that the matrix is low rank. When the original matrix is large scale and the observed elements are few, they will easily lead to over-fitting and their performance will also decrease significantly. Recently, researchers have tried to apply deep learning and nonlinear techniques to solve matrix completion. However, most of the existing deep learning-based methods restore each column or row of the matrix independently, which loses the global structure information of the matrix and therefore does not achieve the expected results in the image in-painting. In this paper, we propose a deep matrix factorization completion network (DMFCNet) for image in-painting by combining deep learning and a traditional matrix completion model. The main idea of DMFCNet is to map iterative updates of variables from a traditional matrix completion model into a fixed depth neural network. The potential relationships between observed matrix data are learned in a trainable end-to-end manner, which leads to a high-performance and easy-to-deploy nonlinear solution. Experimental results show that DMFCNet can provide higher matrix completion accuracy than the state-of-the-art matrix completion methods in a shorter running time.

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40

Sompairac, Nicolas, Petr V. Nazarov, Urszula Czerwinska, Laura Cantini, Anne Biton, Askhat Molkenov, Zhaxybay Zhumadilov, et al. "Independent Component Analysis for Unraveling the Complexity of Cancer Omics Datasets." International Journal of Molecular Sciences 20, no. 18 (September 7, 2019): 4414. http://dx.doi.org/10.3390/ijms20184414.

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Independent component analysis (ICA) is a matrix factorization approach where the signals captured by each individual matrix factors are optimized to become as mutually independent as possible. Initially suggested for solving source blind separation problems in various fields, ICA was shown to be successful in analyzing functional magnetic resonance imaging (fMRI) and other types of biomedical data. In the last twenty years, ICA became a part of the standard machine learning toolbox, together with other matrix factorization methods such as principal component analysis (PCA) and non-negative matrix factorization (NMF). Here, we review a number of recent works where ICA was shown to be a useful tool for unraveling the complexity of cancer biology from the analysis of different types of omics data, mainly collected for tumoral samples. Such works highlight the use of ICA in dimensionality reduction, deconvolution, data pre-processing, meta-analysis, and others applied to different data types (transcriptome, methylome, proteome, single-cell data). We particularly focus on the technical aspects of ICA application in omics studies such as using different protocols, determining the optimal number of components, assessing and improving reproducibility of the ICA results, and comparison with other popular matrix factorization techniques. We discuss the emerging ICA applications to the integrative analysis of multi-level omics datasets and introduce a conceptual view on ICA as a tool for defining functional subsystems of a complex biological system and their interactions under various conditions. Our review is accompanied by a Jupyter notebook which illustrates the discussed concepts and provides a practical tool for applying ICA to the analysis of cancer omics datasets.

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Alshammari, Aadil, and Mohammed Alshammari. "A Recommendation Engine Model for Giant Social Media Platforms using a Probabilistic Approach." Engineering, Technology & Applied Science Research 13, no. 5 (October 13, 2023): 11904–10. http://dx.doi.org/10.48084/etasr.6325.

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Existing recommender system algorithms often find it difficult to interpret and, as a result, to extract meaningful recommendations from social media. Because of this, there is a growing demand for more powerful algorithms that are able to extract information from low-dimensional spaces. One such approach would be the cutting-edge matrix factorization technique. Facebook is one of the most widely used social networking platforms. It has more than one billion monthly active users who engage with each other on the platform by sharing status updates, images, events, and other types of content. Facebook's mission includes fostering stronger connections between individuals, and to that end, the platform employs techniques from recommender systems in an effort to better comprehend the actions and patterns of its users, after which it suggests forming new connections with other users. However, relatively little study has been done in this area to investigate the low-dimensional spaces included within the black box system by employing methods such as matrix factorization. Using a probabilistic matrix factorization approach, the interactions that users have with the posts of other users, such as liking, commenting, and other similar activities, were utilized in an effort to generate a list of potential friends that the user who is the focus of this work may not yet be familiar with. The proposed model performed better in terms of suggestion accuracy in comparison to the original matrix factorization, which resulted in the creation of a recommendation list that contained more correct information.

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42

Nourani, Esmaeil, Farshad Khunjush, and F. Erdoğan Sevilgen. "Virus–human protein–protein interaction prediction using Bayesian matrix factorization and projection techniques." Biocybernetics and Biomedical Engineering 38, no. 3 (2018): 574–85. http://dx.doi.org/10.1016/j.bbe.2018.04.006.

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43

Harrison, Brent, and David Roberts. "A Review of Student Modeling Techniques in Intelligent Tutoring Systems." Proceedings of the AAAI Conference on Artificial Intelligence and Interactive Digital Entertainment 8, no. 5 (June 30, 2021): 61–66. http://dx.doi.org/10.1609/aiide.v8i5.12574.

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In this paper, we survey techniques used in intelligent tutoring systems (ITSs) to model student knowledge. The three techniques that we review in detail are knowledge tracing, performance factor analysis, and matrix factorization. We also briefly cover other techniques that have been used. This review is meant to be a repository of knowledge for those who want to integrate these techniques into serious games. It is also meant to increase awareness and interest as to the techniques available that can be integrated into serious games.

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44

Casalino, Gabriella, Ciro Castiello, Nicoletta Del Buono, and Corrado Mencar. "A framework for intelligent Twitter data analysis with non-negative matrix factorization." International Journal of Web Information Systems 14, no. 3 (August 20, 2018): 334–56. http://dx.doi.org/10.1108/ijwis-11-2017-0081.

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Purpose The purpose of this paper is to propose a framework for intelligent analysis of Twitter data. The purpose of the framework is to allow users to explore a collection of tweets by extracting topics with semantic relevance. In this way, it is possible to detect groups of tweets related to new technologies, events and other topics that are automatically discovered. Design/methodology/approach The framework is based on a three-stage process. The first stage is devoted to dataset creation by transforming a collection of tweets in a dataset according to the vector space model. The second stage, which is the core of the framework, is centered on the use of non-negative matrix factorizations (NMF) for extracting human-interpretable topics from tweets that are eventually clustered. The number of topics can be user-defined or can be discovered automatically by applying subtractive clustering as a preliminary step before factorization. Cluster analysis and word-cloud visualization are used in the last stage to enable intelligent data analysis. Findings The authors applied the framework to a case study of three collections of Italian tweets both with manual and automatic selection of the number of topics. Given the high sparsity of Twitter data, the authors also investigated the influence of different initializations mechanisms for NMF on the factorization results. Numerical comparisons confirm that NMF could be used for clustering as it is comparable to classical clustering techniques such as spherical k-means. Visual inspection of the word-clouds allowed a qualitative assessment of the results that confirmed the expected outcomes. Originality/value The proposed framework enables a collaborative approach between users and computers for an intelligent analysis of Twitter data. Users are faced with interpretable descriptions of tweet clusters, which can be interactively refined with few adjustable parameters. The resulting clusters can be used for intelligent selection of tweets, as well as for further analytics concerning the impact of products, events, etc. in the social network.

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Wu, Hsiao-Chun, Shih Yu Chang, Tho Le-Ngoc, and Yiyan Wu. "Efficient Rank-Adaptive Least-Square Estimation and Multiple-Parameter Linear Regression Using Novel Dyadically Recursive Hermitian Matrix Inversion." International Journal of Antennas and Propagation 2012 (2012): 1–10. http://dx.doi.org/10.1155/2012/891932.

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Least-square estimation (LSE) and multiple-parameter linear regression (MLR) are the important estimation techniques for engineering and science, especially in the mobile communications and signal processing applications. The majority of computational complexity incurred in LSE and MLR arises from a Hermitian matrix inversion. In practice, the Yule-Walker equations are not valid, and hence the Levinson-Durbin algorithm cannot be employed for general LSE and MLR problems. Therefore, the most efficient Hermitian matrix inversion method is based on the Cholesky factorization. In this paper, we derive a new dyadic recursion algorithm for sequential rank-adaptive Hermitian matrix inversions. In addition, we provide the theoretical computational complexity analyses to compare our new dyadic recursion scheme and the conventional Cholesky factorization. We can design a variable model-order LSE (MLR) using this proposed dyadic recursion approach thereupon. Through our complexity analyses and the Monte Carlo simulations, we show that our new dyadic recursion algorithm is more efficient than the conventional Cholesky factorization for the sequential rank-adaptive LSE (MLR) and the associated variable model-order LSE (MLR) can seek the trade-off between the targeted estimation performance and the required computational complexity. Our proposed new scheme can benefit future portable and mobile signal processing or communications devices.

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Singh, Bharat, and Om Prakash Vyas. "A PSO Based Approach for Producing Optimized Latent Factor in Special Reference to Big Data." International Journal of Service Science, Management, Engineering, and Technology 7, no. 3 (July 2016): 55–70. http://dx.doi.org/10.4018/ijssmet.2016070104.

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Now a day's application deal with Big Data has tremendously been used in the popular areas. To tackle with such kind of data various approaches have been developed by researchers in the last few decades. A recent investigated techniques to factored the data matrix through a known latent factor in a lower size space is the so called matrix factorization. In addition, one of the problems with the NMF approaches, its randomized valued could not provide absolute optimization in limited iteration, but having local optimization. Due to this, the authors have proposed a new approach that considers the initial values of the decomposition to tackle the issues of computationally expensive. They have devised an algorithm for initializing the values of the decomposed matrix based on the PSO. In this paper, the auhtors have intended a genetic algorithm based technique while incorporating the nonnegative matrix factorization. Through the experimental result, they will show the proposed method converse very fast in comparison to other low rank approximation like simple NMF multiplicative, and ACLS technique.

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47

Qian, Bin, Lei Tong, Zhenmin Tang, and Xiaobo Shen. "Nonnegative matrix factorization with region sparsity learning for hyperspectral unmixing." International Journal of Wavelets, Multiresolution and Information Processing 15, no. 06 (November 2017): 1750063. http://dx.doi.org/10.1142/s0219691317500631.

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Hyperspectral unmixing is one of the most important techniques in the remote sensing image analysis tasks. In recent decades, nonnegative matrix factorization (NMF) has been shown to be effective for hyperspectral unmixing due to the strong discovery of the latent structure. Most NMFs put emphasize on the spectral information, but ignore the spatial information, which is very crucial for analyzing hyperspectral data. In this paper, we propose an improved NMF method, namely NMF with region sparsity learning (RSLNMF), to simultaneously consider both spectral and spatial information. RSLNMF defines a new sparsity learning model based on a small homogeneous region that is obtained via the graph cut algorithm. Thus RSLNMF is able to explore the relationship of spatial neighbor pixels within each region. An efficient optimization scheme is developed for the proposed RSLNMF, and its convergence is theoretically guaranteed. Experiments on both synthetic and real hyperspectral data validate the superiority of the proposed method over several state-of-the-art unmixing approaches.

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48

Agrawal, Pallavi, and Madhu Shandilya. "Model-Based Method for Acoustic Echo Cancelation and Near-End Speaker Extraction: Non-negative Matrix Factorization." Journal of Telecommunications and Information Technology 2 (June 29, 2018): 15–22. http://dx.doi.org/10.26636/jtit.2018.122617.

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Rapid escalation of wireless communication and hands-free telephony creates a problem with acoustic echo in full-duplex communication applications. In this paper a simulation of model-based acoustic echo cancelation and near-end speaker extraction using statistical methods relying on nonnegative matrix factorization (NMF) is proposed. Acoustic echo cancelation using the NMF algorithm is developed and its implementation is presented, along with all positive, real time elements and factorization techniques. Experimental results are compared against the widely used existing adaptive algorithms which have a disadvantage in terms of long impulse response, increased computational load and wrong convergence due to change in near-end enclosure. All these shortcomings have been eliminated in the statistical method of NMF that reduces echo and enhances audio signal processing.

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Cai, Weihong, Xin Du, and Jianlong Xu. "A Personalized QoS Prediction Method for Web Services via Blockchain-Based Matrix Factorization." Sensors 19, no. 12 (June 19, 2019): 2749. http://dx.doi.org/10.3390/s19122749.

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Personalized quality of service (QoS) prediction plays an important role in helping users build high-quality service-oriented systems. To obtain accurate prediction results, many approaches have been investigated in recent years. However, these approaches do not fully address untrustworthy QoS values submitted by unreliable users, leading to inaccurate predictions. To address this issue, inspired by blockchain with distributed ledger technology, distributed consensus mechanisms, encryption algorithms, etc., we propose a personalized QoS prediction method for web services that we call blockchain-based matrix factorization (BMF). We develop a user verification approach based on homomorphic hash, and use the Byzantine agreement to remove unreliable users. Then, matrix factorization is employed to improve the accuracy of predictions and we evaluate the proposed BMF on a real-world web services dataset. Experimental results show that the proposed method significantly outperforms existing approaches, making it much more effective than traditional techniques.

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Jiang, Xiaoyu, and Kicheon Hong. "Exact Determinants of Some Special Circulant Matrices Involving Four Kinds of Famous Numbers." Abstract and Applied Analysis 2014 (2014): 1–12. http://dx.doi.org/10.1155/2014/273680.

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Circulant matrix family is used for modeling many problems arising in solving various differential equations. The RSFPLR circulant matrices and RSLPFL circulant matrices are two special circulant matrices. The techniques used herein are based on the inverse factorization of polynomial. The exact determinants of these matrices involving Perrin, Padovan, Tribonacci, and the generalized Lucas number are given, respectively.

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