scholarly journals Collaborative Filtering Recommendation Using Nonnegative Matrix Factorization in GPU-Accelerated Spark Platform

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Bing Tang ◽  
Linyao Kang ◽  
Li Zhang ◽  
Feiyan Guo ◽  
Haiwu He
Keyword(s):  
Collaborative Filtering ◽  
Processing Speed ◽  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Experimental Results ◽  
Computational Time ◽  
Data Sets ◽  
Heterogeneous Cluster ◽  
The Matrix

Nonnegative matrix factorization (NMF) has been introduced as an efficient way to reduce the complexity of data compression and its capability of extracting highly interpretable parts from data sets, and it has also been applied to various fields, such as recommendations, image analysis, and text clustering. However, as the size of the matrix increases, the processing speed of nonnegative matrix factorization is very slow. To solve this problem, this paper proposes a parallel algorithm based on GPU for NMF in Spark platform, which makes full use of the advantages of in-memory computation mode and GPU acceleration. The new GPU-accelerated NMF on Spark platform is evaluated in a 4-node Spark heterogeneous cluster using Google Compute Engine by configuring each node a NVIDIA K80 CUDA device, and experimental results indicate that it is competitive in terms of computational time against the existing solutions on a variety of matrix orders. Furthermore, a GPU-accelerated NMF-based parallel collaborative filtering (CF) algorithm is also proposed, utilizing the advantages of data dimensionality reduction and feature extraction of NMF, as well as the multicore parallel computing mode of CUDA. Using real MovieLens data sets, experimental results have shown that the parallelization of NMF-based collaborative filtering on Spark platform effectively outperforms traditional user-based and item-based CF with a higher processing speed and higher recommendation accuracy.

scholarly journals Matrix Factorization Algorithms for the Identification of Muscle Synergies: Evaluation on Simulated and Experimental Data Sets

2006 ◽  
Vol 95 (4) ◽  
pp. 2199-2212 ◽  
Author(s):  
Matthew C. Tresch ◽  
Vincent C. K. Cheung ◽  
Andrea d'Avella
Keyword(s):  
Matrix Factorization ◽  
Muscle Activation ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Muscle Synergies ◽  
Data Sets ◽  
Data Set ◽  
Activation Patterns ◽  
Muscle Activation Patterns ◽  
Factorization Algorithms

Several recent studies have used matrix factorization algorithms to assess the hypothesis that behaviors might be produced through the combination of a small number of muscle synergies. Although generally agreeing in their basic conclusions, these studies have used a range of different algorithms, making their interpretation and integration difficult. We therefore compared the performance of these different algorithms on both simulated and experimental data sets. We focused on the ability of these algorithms to identify the set of synergies underlying a data set. All data sets consisted of nonnegative values, reflecting the nonnegative data of muscle activation patterns. We found that the performance of principal component analysis (PCA) was generally lower than that of the other algorithms in identifying muscle synergies. Factor analysis (FA) with varimax rotation was better than PCA, and was generally at the same levels as independent component analysis (ICA) and nonnegative matrix factorization (NMF). ICA performed very well on data sets corrupted by constant variance Gaussian noise, but was impaired on data sets with signal-dependent noise and when synergy activation coefficients were correlated. Nonnegative matrix factorization (NMF) performed similarly to ICA and FA on data sets with signal-dependent noise and was generally robust across data sets. The best algorithms were ICA applied to the subspace defined by PCA (ICAPCA) and a version of probabilistic ICA with nonnegativity constraints (pICA). We also evaluated some commonly used criteria to identify the number of synergies underlying a data set, finding that only likelihood ratios based on factor analysis identified the correct number of synergies for data sets with signal-dependent noise in some cases. We then proposed an ad hoc procedure, finding that it was able to identify the correct number in a larger number of cases. Finally, we applied these methods to an experimentally obtained data set. The best performing algorithms (FA, ICA, NMF, ICAPCA, pICA) identified synergies very similar to one another. Based on these results, we discuss guidelines for using factorization algorithms to analyze muscle activation patterns. More generally, the ability of several algorithms to identify the correct muscle synergies and activation coefficients in simulated data, combined with their consistency when applied to physiological data sets, suggests that the muscle synergies found by a particular algorithm are not an artifact of that algorithm, but reflect basic aspects of the organization of muscle activation patterns underlying behaviors.

scholarly journals Nonnegative Matrix Factorization Numerical Method for Integrated Photonic Cavity Based Spectroscopy

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Zhengyu Huang ◽  
Dayuan Xiong ◽  
Guixu Zhang ◽  
Yiqin Shi ◽  
Changning Hao ◽  
...  
Keyword(s):  
High Resolution ◽  
Numerical Method ◽  
Spectral Resolution ◽  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Experimental Results ◽  
Theoretical Results

Nonnegative matrix factorization numerical method has been used to improve the spectral resolution of integrated photonic cavity based spectroscopy. Based on the experimental results for integrated photonic cavity device on Optics Letters 32, 632 (2007), the theoretical results show that the spectral resolution can be improved more than 3 times from 5.5 nm to 1.8 nm. It is a promising way to release the difficulty of fabricating high-resolution devices.

scholarly journals Neighborhood Preserving Convex Nonnegative Matrix Factorization

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Jiang Wei ◽  
Li Min ◽  
Zhang Yongqing
Keyword(s):  
Linear Combination ◽  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Data Sets ◽  
Standard Data ◽  
Manifold Structure ◽  
Data Points ◽  
Data Point ◽  
Updating Procedure

The convex nonnegative matrix factorization (CNMF) is a variation of nonnegative matrix factorization (NMF) in which each cluster is expressed by a linear combination of the data points and each data point is represented by a linear combination of the cluster centers. When there exists nonlinearity in the manifold structure, both NMF and CNMF are incapable of characterizing the geometric structure of the data. This paper introduces a neighborhood preserving convex nonnegative matrix factorization (NPCNMF), which imposes an additional constraint on CNMF that each data point can be represented as a linear combination of its neighbors. Thus our method is able to reap the benefits of both nonnegative data factorization and the purpose of manifold structure. An efficient multiplicative updating procedure is produced, and its convergence is guaranteed theoretically. The feasibility and effectiveness of NPCNMF are verified on several standard data sets with promising results.

NONNEGATIVE TENSOR FACTORIZATION FOR CONTINUOUS EEG CLASSIFICATION

2007 ◽  
Vol 17 (04) ◽  
pp. 305-317 ◽  
Author(s):  
HYEKYOUNG LEE ◽  
YONG-DEOK KIM ◽  
ANDRZEJ CICHOCKI ◽  
SEUNGJIN CHOI
Keyword(s):  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Viterbi Algorithm ◽  
Nonnegative Matrix ◽  
Data Sets ◽  
Tensor Factorization ◽  
Nonnegative Tensor ◽  
Eeg Classification ◽  
Nonnegative Tensor Factorization ◽  
Continuous Eeg

In this paper we present a method for continuous EEG classification, where we employ nonnegative tensor factorization (NTF) to determine discriminative spectral features and use the Viterbi algorithm to continuously classify multiple mental tasks. This is an extension of our previous work on the use of nonnegative matrix factorization (NMF) for EEG classification. Numerical experiments with two data sets in BCI competition, confirm the useful behavior of the method for continuous EEG classification.

scholarly journals Accelerating Nonnegative Matrix Factorization Algorithms Using Extrapolation

2019 ◽  
Vol 31 (2) ◽  
pp. 417-439 ◽  
Author(s):  
Andersen Man Shun Ang ◽  
Nicolas Gillis
Keyword(s):  
Least Squares ◽  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
State Of The Art ◽  
Gradient Methods ◽  
Nonnegative Matrix ◽  
Synthetic Image ◽  
Data Sets ◽  
Extrapolation Scheme ◽  
Factorization Algorithms

We propose a general framework to accelerate significantly the algorithms for nonnegative matrix factorization (NMF). This framework is inspired from the extrapolation scheme used to accelerate gradient methods in convex optimization and from the method of parallel tangents. However, the use of extrapolation in the context of the exact coordinate descent algorithms tackling the nonconvex NMF problems is novel. We illustrate the performance of this approach on two state-of-the-art NMF algorithms: accelerated hierarchical alternating least squares and alternating nonnegative least squares, using synthetic, image, and document data sets.

Measurement and Analysis of the Functional Independence Measure Data by Using Nonnegative Matrix Factorization Method

2013 ◽  
Vol 718-720 ◽  
pp. 630-635 ◽  
Author(s):  
Naoki Yamamoto ◽  
Jun Murakami ◽  
Kei Fujii ◽  
Chiharu Okuma ◽  
Satoko Saito ◽  
...  
Keyword(s):  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Functional Independence Measure ◽  
Factorization Method ◽  
Functional Independence ◽  
Medical Data ◽  
Experimental Results ◽  
Measure Data ◽  
Measurement And Analysis

In this paper, we describe about a manner of adapting the nonnegative matrix factorization (NMF) method to the medical data, especially functional independence measure (FIM) data, and its experimental results. From the results which were obtained by applying the method to actually measured medical data in a hospital, we confirmed that the NMF method was effective to analyze the patients' characteristics related to disability and recovery tendency.

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