skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

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

Patent ·
OSTI ID:959119

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.

Research Organization:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Organization:
USDOE
DOE Contract Number:
AC04-94AL85000
Assignee:
Sandia Corporation (Albuquerque, NM)
Patent Number(s):
7,472,153
Application Number:
10/794,538
OSTI ID:
959119
Country of Publication:
United States
Language:
English

References (9)

Application of modified alternating least squares regression to spectroscopic image analysis journal January 2003
Automated Analysis of SEM X-Ray Spectral Images: A Powerful New Microanalysis Tool journal January 2003
Numerical Methods for Least Squares Problems book January 1996
PARAFAC. Tutorial and applications journal October 1997
Rapid Analysis of Raman Image Data Using Two-Way Multivariate Curve Resolution journal June 1998
Advantages of Soft versus Hard Constraints in Self-Modeling Curve Resolution Problems. Alternating Least Squares with Penalty Functions journal August 2003
Ridge Regression: Biased Estimation for Nonorthogonal Problems journal February 1970
Generalized Inverses, Ridge Regression, Biased Linear Estimation, and Nonlinear Estimation journal August 1970
Multivariate curve resolution applied to spectral data from multiple runs of an industrial process journal August 1993

Similar Records

Fast algorithm for the solution of large-scale non-negativity constrained least squares problems.
Journal Article · Tue Jun 01 00:00:00 EDT 2004 · Proposed for publication in Journal of Chemometrics. · OSTI ID:959119

Selected algorithms for the linearly constrained least squares problem: a user's guide. [Usage examples for LSEI and WNNLS, in FORTRAN]
Technical Report · Wed Aug 01 00:00:00 EDT 1979 · OSTI ID:959119

Least squares algorithm for region-of-interest evaluation in emission tomography
Journal Article · Mon Mar 01 00:00:00 EST 1993 · IEEE Transactions on Medical Imaging (Institute of Electrical and Electronics Engineers); (United States) · OSTI ID:959119

Related Subjects