# 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:

- (Albuquerque, NM)

- Publication Date:

- Research Org.:
- Sandia National Laboratories (SNL-NM), Albuquerque, NM

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 959119

- Patent Number(s):
- 7,472,153

- Application Number:
- 10/794,538

- Assignee:
- Sandia Corporation (Albuquerque, NM) ALO

- 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.
doi:. 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 = {Tue Dec 30 00:00:00 EST 2008},

month = {Tue Dec 30 00:00:00 EST 2008}

}