Accurate Low-Rank Approximations Via a Few Iterations of Alternating Least Squares

2017 ◽  
Vol 38 (2) ◽  
pp. 425-433 ◽  
Author(s):  
Arthur Szlam ◽  
Andrew Tulloch ◽  
Mark Tygert
Keyword(s):  
Least Squares ◽  
Alternating Least Squares ◽  
Low Rank ◽  
Low Rank Approximations

scholarly journals An Efficient Compressive Hyperspectral Imaging Algorithm Based on Sequential Computations of Alternating Least Squares

2019 ◽  
Vol 11 (24) ◽  
pp. 2932 ◽  
Author(s):  
Geunseop Lee
Keyword(s):  
Least Squares ◽  
Hyperspectral Imaging ◽  
Optimization Problems ◽  
Tensor Decomposition ◽  
Alternating Least Squares ◽  
Low Rank ◽  
Imaging Data ◽  
Significant Difference ◽  
Multilinear Rank ◽  
Value Decomposition

Hyperspectral imaging is widely used to many applications as it includes both spatial and spectral distributions of a target scene. However, a compression, or a low multilinear rank approximation of hyperspectral imaging data, is required owing to the difficult manipulation of the massive amount of data. In this paper, we propose an efficient algorithm for higher order singular value decomposition that enables the decomposition of a tensor into a compressed tensor multiplied by orthogonal factor matrices. Specifically, we sequentially compute low rank factor matrices from the Tucker-1 model optimization problems via an alternating least squares approach. Experiments with real world hyperspectral imaging revealed that the proposed algorithm could compute the compressed tensor with a higher computational speed, but with no significant difference in accuracy of compression compared to the other tensor decomposition-based compression algorithms.

scholarly journals Alternating Least-Squares for Low-Rank Matrix Reconstruction

2012 ◽  
Vol 19 (4) ◽  
pp. 231-234 ◽  
Author(s):  
Dave Zachariah ◽  
Martin Sundin ◽  
Magnus Jansson ◽  
Saikat Chatterjee
Keyword(s):  
Least Squares ◽  
Alternating Least Squares ◽  
Low Rank ◽  
Matrix Reconstruction ◽  
Rank Matrix ◽  
Low Rank Matrix

Bridging the Gap between Quantitative and Qualitative Historical Research: an application of multiple regression analysis and homogeneity analysis with alternating least squares

1996 ◽  
Vol 8 (3) ◽  
pp. 133-144 ◽  
Author(s):  
María del Mar del Pozo Andrés ◽  
Jacques F A Braster
Keyword(s):  
Least Squares ◽  
Multiple Regression ◽  
Historical Research ◽  
Alternating Least Squares ◽  
Categorical Variables ◽  
Two Dimensional ◽  
Homogeneity Analysis ◽  
Regression Approach ◽  
Dimensional Picture ◽  
Selection Of

In this article we propose two research techniques that can bridge the gap between quantitative and qualitative historical research. These are: (1) a multiple regression approach that gives information about general patterns between numerical variables and the selection of outliers for qualitative analysis; (2) a homogeneity analysis with alternating least squares that results in a two-dimensional picture in which the relationships between categorical variables are graphically presented.

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