scholarly journals Least-squares bilinear clustering of three-way data

2021 ◽  
Author(s):  
Pieter C. Schoonees ◽  
Patrick J. F. Groenen ◽  
Michel van de Velden
Keyword(s):  
Least Squares ◽  
R Package ◽  
Bilinear Model ◽  
Computational Burden ◽  
Clustering Problem ◽  
The Matrix ◽  
Special Algorithm

AbstractA least-squares bilinear clustering framework for modelling three-way data, where each observation consists of an ordinary two-way matrix, is introduced. The method combines bilinear decompositions of the two-way matrices with clustering over observations. Different clusterings are defined for each part of the bilinear decomposition, which decomposes the matrix-valued observations into overall means, row margins, column margins and row–column interactions. Therefore up to four different classifications are defined jointly, one for each type of effect. The computational burden is greatly reduced by the orthogonality of the bilinear model, such that the joint clustering problem reduces to separate problems which can be handled independently. Three of these sub-problems are specific cases of k-means clustering; a special algorithm is formulated for the row–column interactions, which are displayed in clusterwise biplots. The method is illustrated via an empirical example and interpreting the interaction biplots are discussed. Supplemental materials for this paper are available online, which includes the dedicated R package, .

ExperimentSubset: an R package to manage subsets of Bioconductor Experiment objects

2021 ◽  
Author(s):  
Irzam Sarfraz ◽  
Muhammad Asif ◽  
Joshua D Campbell
Keyword(s):  
Single Cell ◽  
R Package ◽  
Poor Quality ◽  
Data Matrix ◽  
Supplementary Information ◽  
Data Provenance ◽  
Rna Seq ◽  
Efficient Management ◽  
The Matrix ◽  
The Relationship

Abstract Motivation R Experiment objects such as the SummarizedExperiment or SingleCellExperiment are data containers for storing one or more matrix-like assays along with associated row and column data. These objects have been used to facilitate the storage and analysis of high-throughput genomic data generated from technologies such as single-cell RNA sequencing. One common computational task in many genomics analysis workflows is to perform subsetting of the data matrix before applying down-stream analytical methods. For example, one may need to subset the columns of the assay matrix to exclude poor-quality samples or subset the rows of the matrix to select the most variable features. Traditionally, a second object is created that contains the desired subset of assay from the original object. However, this approach is inefficient as it requires the creation of an additional object containing a copy of the original assay and leads to challenges with data provenance. Results To overcome these challenges, we developed an R package called ExperimentSubset, which is a data container that implements classes for efficient storage and streamlined retrieval of assays that have been subsetted by rows and/or columns. These classes are able to inherently provide data provenance by maintaining the relationship between the subsetted and parent assays. We demonstrate the utility of this package on a single-cell RNA-seq dataset by storing and retrieving subsets at different stages of the analysis while maintaining a lower memory footprint. Overall, the ExperimentSubset is a flexible container for the efficient management of subsets. Availability and implementation ExperimentSubset package is available at Bioconductor: https://bioconductor.org/packages/ExperimentSubset/ and Github: https://github.com/campbio/ExperimentSubset. Supplementary information Supplementary data are available at Bioinformatics online.

TOTAL LEAST SQUARES FOR ESTIMATION OF THE GROSS OUTPUT VECTOR

2020 ◽  
Author(s):  
Dmitriy Vladimirovich Ivanov ◽  
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Direct Costs ◽  
Total Least Squares ◽  
Test Cases ◽  
Output Vector ◽  
Final Consumption ◽  
The Matrix

The article proposes the estimation of the gross output vector in the presence of errors in the matrix of direct costs and the final consumption vector. The article suggests the use of the total least squares method for estimating the gross output vector. Test cases showed that the accuracy of the proposed estimates of the gross output vector is higher than the accuracy of the estimates obtained using the classical least squares method (OLS).

Position Estimation of Single Camera Visual System Based on Total Least Squares Algorithm

2012 ◽  
Vol 239-240 ◽  
pp. 1352-1355
Author(s):  
Jing Zhou ◽  
Yin Han Gao ◽  
Chang Yin Liu ◽  
Ji Zhi Li
Keyword(s):  
Visual System ◽  
Least Squares ◽  
Total Least Squares ◽  
Position Estimation ◽  
Feature Points ◽  
Perspective Theory ◽  
Optical Feature ◽  
The Matrix ◽  
Least Squares Algorithm ◽  
Set Up

The position estimation of optical feature points of visual system is the focus factor of the precision of system. For this problem , to present the Total Least Squares Algorithm . Firstly , set up the measurement coordinate system and 3D model between optical feature points, image points and the position of camera according to the position relation ; Second , build the matrix equations between optical feature points and image points ; Then apply in the total least squares to have an optimization calculation ; Finally apply in the coordinate measuring machining to have a simulation comparison experiment , the results indicate that the standard tolerance of attitude coordinate calculated by total least squares is 0.043mm, it validates the effectiveness; Compare with the traditional method based on three points perspective theory, measure the standard gauge of 500mm; the standard tolerance of traditional measurement system is 0.0641mm, the standard tolerance of Total Least Squares Algorithm is 0.0593mm; The experiment proves the Total Least Squares Algorithm is effective and has high precision.

A least-squares method for the determination of the orientation matrix in single-crystal diffractometry

1970 ◽  
Vol 26 (2) ◽  
pp. 295-296 ◽  
Author(s):  
K. Tichý
Keyword(s):  
Single Crystal ◽  
Least Squares ◽  
Least Squares Method ◽  
Reciprocal Vector ◽  
Orientation Matrix ◽  
The Matrix

An appropriate choice of the function minimized permits linearization of the least-squares determination of the matrix which transforms the diffraction indices into the components of the reciprocal vector in the diffractometer φ-axis system of coordinates. The coefficients of the least-squares equations are based on diffraction indices and measured diffractometer angles of three or more non-coplanar setting reflexions.

MAPPED LEAST SQUARES SUPPORT VECTOR MACHINE REGRESSION

2005 ◽  
Vol 19 (03) ◽  
pp. 459-475 ◽  
Author(s):  
SHENG ZHENG ◽  
YUQIU SUN ◽  
JINWEN TIAN ◽  
JAIN LIU
Keyword(s):  
Least Squares ◽  
Matrix Multiplication ◽  
Learning Problems ◽  
Support Vector ◽  
Training Algorithms ◽  
Learning Problem ◽  
Multiplication Operation ◽  
Vector Machines ◽  
The Matrix ◽  
Set Of Points

This paper describes a novel version of regression SVM (Support Vector Machines) that is based on the least-squares error. We show that the solution of this optimization problem can be obtained easily once the inverse of a certain matrix is computed. This matrix, however, depends only on the input vectors, but not on the labels. Thus, if many learning problems with the same set of input vectors but different sets of labels have to be solved, it makes sense to compute the inverse of the matrix just once and then use it for computing all subsequent models. The computational complexity to train an regression SVM can be reduced to O (N2), just a matrix multiplication operation, and thus probably faster than known SVM training algorithms that have O (N2) work with loops. We describe applications from image processing, where the input points are usually of the form {(x0 + dx, y0 + dy) : |dx| < m, |dy| < n} and all such set of points can be translated to the same set {(dx, dy) : |dx| < m, |dy| < n} by subtracting (x0, y0) from all the vectors. The experimental results demonstrate that the proposed approach is faster than those processing each learning problem separately.

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