Acceleration of the alternating least squares algorithm for principal components analysis

Kuroda, Masahiro; Mori, Yuichi; Iizuka, Masaya; Sakakihara, Michio

doi:10.1016/j.csda.2010.06.001

Cited by 27 publications

(11 citation statements)

References 8 publications

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“…The ALS algorithm is the least squares estimation method and its speed of convergence may be very slow in the application of nonlinear PCA to large mixed data. Improving the convergence of the ALS algorithm is an important topic …”

Section: Resultsmentioning

confidence: 99%

Alternating least squares in nonlinear principal components

Kuroda

Mori

Iizuka

et al. 2013

WIREs Computational Stats

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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.Let X = (X 1 X 2 · · · X p ) be an n × p matrix of observations on n objects and p variables. To quantify 456

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Section: Resultsmentioning

confidence: 99%

Alternating least squares in nonlinear principal components

Kuroda

Mori

Iizuka

et al. 2013

WIREs Computational Stats

Self Cite

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“…ALS is designed to better handle missing values. It can work well for data sets with a small percentage of missing data at random [26].…”

Section: Methodsmentioning

confidence: 99%

Classification of Alzheimer Disease Based on Structural Magnetic Resonance Imaging by Kernel Support Vector Machine Decision Tree

Zhang¹,

Wang²,

Dong³

2014

PIER

190

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Abstract-In this paper we proposed a novel classification system to distinguish among elderly subjects with Alzheimer's disease (AD), mild cognitive impairment (MCI), and normal controls (NC). The method employed the magnetic resonance imaging (MRI) data of 178 subjects consisting of 97 NCs, 57 MCIs, and 24 ADs. First, all these three dimensional (3D) MRI images were preprocessed with atlas-registered normalization. Then, gray matter images were extracted and the 3D images were under-sampled. Afterwards, principle component analysis was applied for feature extraction. In total, 20 principal components (PC) were extracted from 3D MRI data using singular value decomposition (SVD) algorithm, and 2 PCs were extracted from additional information (consisting of demographics, clinical examination, and derived anatomic volumes) using alternating least squares (ALS). On the basic of the 22 features, we constructed a kernel support vector machine decision tree (kSVM-DT). The error penalty parameter C and kernel parameter σ were determined by Particle Swarm Optimization (PSO). The weights ω and biases b were still obtained by quadratic programming method. 5-fold cross validation was employed to obtain the out-of-sample estimate. The results show that the proposed kSVM-DT achieves 80% classification accuracy, better than 74% of the method without kernel. Besides, the PSO exceeds the random selection method in choosing the parameters of the classifier. The computation time to predict a new patient is only 0.022 s.

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“…Hierarchical cluster analysis (Cai et al, 2014) and principal component analysis (Kuroda et al, 2011) were applied to evaluate the component distributions of AAs in textile-dyeing sludge samples. Hierarchical cluster analysis was performed using the Ward method with squared Euclidean distances.…”

Section: Discussionmentioning

confidence: 99%