检索结果-内蒙古大学图书馆

Speeding up the convergence of the alternating least squares algorithm using vector ε acceleration and restarting for nonlinear principal component analysis

引用

COMPUTATIONAL STATISTICS 2023年第1期38卷 243-262页

作者： Kuroda, Masahiro Mori, Yuichi Iizuka, Masaya Okayama Univ Sci Dept Management Kita Ku 1-1 Ridaicho Okayama 7000005 Japan Okayama Univ Inst Educ & Student Serv Kita Ku 2-1-1 Tsushima Naka Okayama 7008530 Japan

Principal component analysis (PCA) is a widely used descriptive multivariate technique in the analysis of quantitative data. When applying PCA to mixed quantitative and qualitative data, we utilize an optimal scaling technique for quantifying qualitative data. PCA with optimal scaling is called nonlinear PCA. The alternating least squares (ALS) algorithm is used for computing nonlinear PCA. The ALS algorithm is stable in convergence and simple in implementation;however, the algorithm tends to converge slowly for large data matrices owing to its linear convergence. Then the v epsilon-ALS algorithm, which incorporates the vector s accelerator into the ALS algorithm, is used to accelerate the convergence of the ALS algorithm for nonlinear PCA. In this paper, we improve the v epsilon-ALS algorithm via a restarting procedure and further reduce its number of iterations and computation time. The restarting procedure is performed under simple restarting conditions, and it speeds up the convergence of the v epsilon-ALS algorithm. The v epsilon-ALS algorithm with a restarting procedure is referred to as the v epsilon R-ALS algorithm. Numerical experiments examine the performance of the v epsilon R-ALS algorithm by comparing its number of iterations and computation time with those of the ALS and v epsilon-ALS algorithms.

关键词： Nonlinear principal component analysis alternating least squares algorithm Acceleration of convergence Vector epsilon algorithm Restarting procedure

来源：评论

学校读者我要写书评

暂无评论

A novel quantum recommender system

引用

PHYSICA SCRIPTA 2023年第1期98卷 010001-010001页

作者： Gao, Shang Yang, Yu-Guang Beijing Univ Technol Fac Informat Technol Beijing 100124 Peoples R China

Recommendation system is a kind of information filtering system, which plays an increasingly important role in the era of big data. In this work, we present a novel quantum recommender system, which can also be regarded as a quantum version of the matrix reconstruction algorithm. In order to obtain two factors in the quantum state form, a quantum version of the alternating least squares algorithm is designed. And based on the factor matrices, the reconstruction matrix of the original rating matrix is calculated. The complexity analysis shows that our quantum algorithm may achieve an exponential speedup relative to the classical counterpart under certain conditions.

关键词： recommendation system quantum recommendation system alternating least squares algorithm matrix reconstruction

来源：评论

学校读者我要写书评

暂无评论

Canonical Dependency Analysis Using a Bias-Corrected χ² Statistics Matrix

引用

JOURNAL OF STATISTICAL THEORY AND PRACTICE 2024年第1期18卷 7-7页

作者： Tsuchida, Jun Yadohisa, Hiroshi Kyoto Womens Univ Fac Data Sci Kyoto Japan Doshisha Univ Fac Culture & Informat Sci Kyoto Japan

Canonical correlation and canonical covariance analyses are popular dimensional reduction methods when managing two datasets. Because these methods seek a subspace maximizing correlation (or covariance), it is not suitable to apply them to datasets that have a non-linear relationship. To tackle this issue, some researchers have proposed canonical dependency analysis (CDA), which seeks a subspace maximizing dependency. However, applying this method to datasets with categorical variables may not be appropriate because CDA does not consider categorical variables directly. Moreover, some methods are time consuming for hyper-parameter tuning. We therefore propose a quantification method that includes a CDA that minimizes the distance between the dependency matrix and the estimated matrix and a calculation method for a bias-corrected chi(2) statistics matrix in a moderate amount of time. We derived the explicit updated formula of the parameter estimation using the majorization technique and applied a method to calculate a bias-corrected chi(2) statistics matrix without hyper-parameters. We then applied this method to both simulated and real datasets. From the simulated data, the proposed method shows the best performance when the data include some categorical variables. We obtain a reasonable result from the application to real datasets.

关键词： alternating least squares algorithm Canonical correlation analysis Dimensional reduction f-divergence Optimal scaling

来源：评论

学校读者我要写书评

暂无评论

Acceleration of the alternating least squares algorithm for principal components analysis

引用

COMPUTATIONAL STATISTICS & DATA ANALYSIS 2011年第1期55卷 143-153页

作者： Kuroda, Masahiro Mori, Yuichi Iizuka, Masaya Sakakihara, Michio Okayama Univ Sci Dept Socioinformat Kita Ku Okayama 7000005 Japan Okayama Univ Grad Sch Environm Sci Kita Ku Okayama 7008530 Japan Okayama Univ Sci Dept Informat Sci Kita Ku Okayama 7000005 Japan

Principal components analysis (PCA) is a popular descriptive multivariate method for handling quantitative data and it can be extended to deal with qualitative data and mixed measurement level data. The existing algorithms for extended PCA are PRINCIPALS of Young et al.(1978) and PRINCALS of Gifi (1989) in which the alternating least squares algorithm is utilized. These algorithms based on the least squares estimation may require many iterations in their application to very large data sets and variable selection problems and may take a long time to converge. In this paper, we derive a new iterative algorithm for accelerating the convergence of PRINCIPALS and PRINCALS by using the vector epsilon algorithm of Wynn (1962). The proposed acceleration algorithm speeds up the convergence of the sequence of the parameter estimates obtained from PRINCIPALS or PRINCALS. Numerical experiments illustrate the potential of the proposed acceleration algorithm. (C) 2010 Elsevier B.V. All rights reserved.

关键词： alternating least squares algorithm Vector epsilon algorithm Acceleration of convergence PRINCIPALS PRINCALS

来源：评论

学校读者我要写书评

暂无评论

An Information Feature Extraction and Rapid Updating Scheme for Knowledge Centric Networking

An Information Feature Extraction and Rapid Updating Scheme ...

引用

International Conference on Computing, Networking and Communications (ICNC)

作者： Zhang, Qi Jiang, Xiaofeng Chen, Shuangwu Xie, Jinsen Yang, Jian Xing, Ling Univ Sci & Technol China Sch Informat Sci & Technol Hefei Anhui Peoples R China Southwest Univ Sci & Technol Mianyang Sichuan Peoples R China Henan Univ Sci & Technol Sch Informat Engn Luoyang Peoples R China

ISBN: (纸本)9781538692233

Knowledge centric networking (KCN) is a new future internet paradigm that directly accesses key content by assigning each piece of the content a unique knowledge identifier. Knowledge transmission is realized via knowledge routing and forwarding. The knowledge-based routing information has more and longer prefixes than the IP-based ones. Therefore, there are more challenges to achieve the knowledge-based forwarding on the knowledge router in terms of shorter latency, low memory consumption, and fast routing table update. In this paper, we propose a tensorial knowledge-based data structure for the knowledge routing table index. The tensorial knowledge-based data structure employs the CANDECOMP/PARAFAC (CP) decomposition algorithm to extract low-dimensional information features, so the massive memory consumption can be effectively reduced. Meanwhile, we propose a distributed update method which divides the large-scale tensor to many sub-tensors during the content forwarding, leading to computing complexity reduction and low search time. Evaluation results indicate that we can restore the data from the low-dimensional information features with no error which illustrates the feasibility of proposed scheme.

关键词： Knowledge centric networking forwarding tensor CANDECOMP/PARAFAC decomposition alternating least squares algorithm

来源：评论

学校读者我要写书评

暂无评论

PARALLEL ALS algorithm FOR SOLVING LINEAR SYSTEMS IN THE HIERARCHICAL TUCKER REPRESENTATION

引用

SIAM JOURNAL ON SCIENTIFIC COMPUTING 2016年第4期38卷 A2585-A2609页

作者： Etter, Simon Swiss Fed Inst Technol CH-8092 Zurich Switzerland

Tensor network formats are an efficient tool for numerical computations in many dimensions, yet even this tool often becomes too time-and memory-consuming for a single compute node when applied to problems of scientific interest. Intending to overcome such limitations, we present and analyze a parallelization scheme for algorithms based on the hierarchical Tucker representation which distributes the network vertices and their associated computations over a set of distributed-memory processors. We then propose a modified version of the alternating least squares algorithm for solving linear systems amenable to parallelization according to the aforementioned scheme, and highlight technical considerations important for obtaining an efficient and stable implementation. Our numerical experiments support the theoretical assertion that the parallel scaling of this algorithm is constrained only by the dimensionality and the rank uniformity of the targeted problem.

关键词： hierarchical Tucker representation alternating least squares algorithm tree-structured parallelization

来源：评论

学校读者我要写书评

暂无评论

Randomized interpolative decomposition of separated representations

引用

JOURNAL OF COMPUTATIONAL PHYSICS 2015年 281卷 116-134页

作者： Biagioni, David J. Beylkin, Daniel Beylkin, Gregory Natl Renewable Energy Lab Computat Sci Ctr Golden CO 80401 USA Yale Univ Program Appl Math New Haven CT 06511 USA Univ Colorado Dept Appl Math Boulder CO 80309 USA

We introduce an algorithm to compute tensor interpolative decomposition(dubbed CTDID) for the reduction of the separation rank of Canonical Tensor Decompositions (CTDs). Tensor ID selects, for a user-defined accuracy epsilon, a near optimal subset of terms of a CTD to represent the remaining terms via a linear combination of the selected terms. CTD-ID can be used as an alternative to or in combination with the alternating least squares (ALS) algorithm. We present examples of its use within a convergent iteration to compute inverse operators in high dimensions. We also briefly discuss the spectral norm as a computational alternative to the Frobenius norm in estimating approximation errors of tensor ID. We reduce the problem of finding tensor IDs to that of constructing interpolative decompositions of certain matrices. These matrices are generated via randomized projection of the terms of the given tensor. We provide cost estimates and several examples of the new approach to the reduction of separation rank. (C) 2014 Elsevier Inc. All rights reserved.

关键词： Canonical tensor decomposition Interpolative decomposition alternating least squares algorithm Randomized projection Self-guiding tensor iteration

来源：评论

学校读者我要写书评

暂无评论

alternating least squares in nonlinear principal components

引用

WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL STATISTICS 2013年第6期5卷 456-464页

作者： Kuroda, Masahiro Mori, Yuichi Masaya, Iizuka Sakakihara, Michio Okayama Univ Sci Fac Informat Dept Socio Informat Okayama Japan Okayama Univ Grad Sch Environm Sci Okayama Japan Okayama Univ Sci Fac Informat Dept Informat Sci Okayama Japan

Principal components analysis (PCA) is probably the most popular descriptive multivariate method for analyzing quantitative data with ratio and interval scale measures. When applying PCA to nominal and ordinal data, the data are processed by a method such as optimal scaling, which nonlinearly transforms nominal and ordinal data into quantitative data. Therefore, PCA with optimal scaling is called nonlinear PCA. Nonlinear PCA reveals nonlinear relationships among variables with different measurement levels and therefore presents a more flexible alternative to ordinary PCA. The alternating least squares algorithm is utilized for nonlinear PCA. The algorithm alternates between optimal scaling for quantifying nominal and ordinal data and ordinary PCA for analyzing optimally scaled data. This article discusses two nonlinear PCA algorithms, namely, PRINCIPALS and PRINCALS. (C) 2013 Wiley Periodicals, Inc.

关键词： alternating least squares algorithm quantification optimal scaling homogeneity

来源：评论

学校读者我要写书评

暂无评论

Functional fuzzy clusterwise regression analysis

引用

ADVANCES IN DATA ANALYSIS AND CLASSIFICATION 2013年第1期7卷 57-82页

作者： Tan, Tianyu Suk, Hye Won Hwang, Heungsun Lim, Jooseop McGill Univ Dept Psychol Montreal PQ H3A 1B1 Canada Concordia Univ Dept Mkt Montreal PQ Canada

We propose a functional extension of fuzzy clusterwise regression, which estimates fuzzy memberships of clusters and regression coefficient functions for each cluster simultaneously. The proposed method permits dependent and/or predictor variables to be functional, varying over time, space, and other continua. The fuzzy memberships and clusterwise regression coefficient functions are estimated by minimizing an objective function that adopts a basis function expansion approach to approximating functional data. An alternating least squares algorithm is developed to minimize the objective function. We conduct simulation studies to demonstrate the superior performance of the proposed method compared to its non-functional counterpart and to examine the performance of various cluster validity measures for selecting the optimal number of clusters. We apply the proposed method to real datasets to illustrate the empirical usefulness of the proposed method.

关键词： Functional linear models Fuzzy clusterwise regression model alternating least squares algorithm

来源：评论

学校读者我要写书评

暂无评论

Lowdimensional Additive Overlapping Clustering

引用

JOURNAL OF CLASSIFICATION 2012年第3期29卷 297-320页

作者： Depril, Dirk Van Mechelen, Iven Wilderjans, Tom F. Katholieke Univ Leuven Fac Psychol & Educ Sci B-3000 Louvain Belgium

To reveal the structure underlying two-way two-mode object by variable data, Mirkin (1987) has proposed an additive overlapping clustering model. This model implies an overlapping clustering of the objects and a reconstruction of the data, with the reconstructed variable profile of an object being a summation of the variable profiles of the clusters it belongs to. Grasping the additive (overlapping) clustering structure of object by variable data may, however, be seriously hampered in case the data include a very large number of variables. To deal with this problem, we propose a new model that simultaneously clusters the objects in overlapping clusters and reduces the variable space;as such, the model implies that the cluster profiles and, hence, the reconstructed data profiles are constrained to lie in a lowdimensional space. An alternating least squares (ALS) algorithm to fit the new model to a given data set will be presented, along with a simulation study and an illustrative example that makes use of empirical data.

关键词： Additive overlapping clustering Dimensional reduction alternating least squares algorithm Two-way two-mode data Object by variable data

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：