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Title: Method for exploiting bias in factor analysis using constrained alternating least squares algorithms

Abstract

Bias plays an important role in factor analysis and is often implicitly made use of, for example, to constrain solutions to factors that conform to physical reality. However, when components are collinear, a large range of solutions may exist that satisfy the basic constraints and fit the data equally well. In such cases, the introduction of mathematical bias through the application of constraints may select solutions that are less than optimal. The biased alternating least squares algorithm of the present invention can offset mathematical bias introduced by constraints in the standard alternating least squares analysis to achieve factor solutions that are most consistent with physical reality. In addition, these methods can be used to explicitly exploit bias to provide alternative views and provide additional insights into spectral data sets.

Inventors:
 [1]
  1. Albuquerque, NM
Issue Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
959119
Patent Number(s):
7472153
Application Number:
10/794,538
Assignee:
Sandia Corporation (Albuquerque, NM)
Patent Classifications (CPCs):
G - PHYSICS G01 - MEASURING G01N - INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
G - PHYSICS G06 - COMPUTING G06K - RECOGNITION OF DATA
DOE Contract Number:  
AC04-94AL85000
Resource Type:
Patent
Country of Publication:
United States
Language:
English

Citation Formats

Keenan, Michael R. Method for exploiting bias in factor analysis using constrained alternating least squares algorithms. United States: N. p., 2008. Web.
Keenan, Michael R. Method for exploiting bias in factor analysis using constrained alternating least squares algorithms. United States.
Keenan, Michael R. Tue . "Method for exploiting bias in factor analysis using constrained alternating least squares algorithms". United States. https://www.osti.gov/servlets/purl/959119.
@article{osti_959119,
title = {Method for exploiting bias in factor analysis using constrained alternating least squares algorithms},
author = {Keenan, Michael R},
abstractNote = {Bias plays an important role in factor analysis and is often implicitly made use of, for example, to constrain solutions to factors that conform to physical reality. However, when components are collinear, a large range of solutions may exist that satisfy the basic constraints and fit the data equally well. In such cases, the introduction of mathematical bias through the application of constraints may select solutions that are less than optimal. The biased alternating least squares algorithm of the present invention can offset mathematical bias introduced by constraints in the standard alternating least squares analysis to achieve factor solutions that are most consistent with physical reality. In addition, these methods can be used to explicitly exploit bias to provide alternative views and provide additional insights into spectral data sets.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = {2008},
month = {12}
}

Works referenced in this record:

Application of modified alternating least squares regression to spectroscopic image analysis
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Automated Analysis of SEM X-Ray Spectral Images: A Powerful New Microanalysis Tool
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Rapid Analysis of Raman Image Data Using Two-Way Multivariate Curve Resolution
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Ridge Regression: Biased Estimation for Nonorthogonal Problems
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Multivariate curve resolution applied to spectral data from multiple runs of an industrial process
journal, August 1993