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PrincipalComponents

As of Version 8, PrincipalComponents is part of the built-in Wolfram Language kernel.

PrincipalComponents[matrix]

transforms elements of matrix into principal components.

Details and Options

  • To use PrincipalComponents, you first need to load the Multivariate Statistics Package using Needs["MultivariateStatistics`"].
  • PrincipalComponents gives the principal component transform of matrix.
  • The principal components of matrix are linear transformations of the original columns into uncorrelated columns arranged in order of decreasing variance.
  • The dimensions of PrincipalComponents[matrix] are the same as the dimensions of matrix.
  • The following options can be given:
  • Method Covariancescaling method for decomposition
    WorkingPrecision MachinePrecisionthe precision used in internal computations
  • Possible values of Method are Covariance and Correlation.

Examples

open allclose all

Basic Examples  (1)Summary of the most common use cases

In[1]:=1
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https://wolfram.com/xid/0d73dx0bugn33-dxqp87

Principal components for bivariate data:

In[2]:=2
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https://wolfram.com/xid/0d73dx0bugn33-bphja
Out[2]=2

Options  (2)Common values & functionality for each option

Method  (1)

In[1]:=1
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https://wolfram.com/xid/0d73dx0bugn33-ern7dm

Principal components using correlation scaling:

In[2]:=2
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https://wolfram.com/xid/0d73dx0bugn33-kry59g
Out[2]=2

WorkingPrecision  (1)

In[1]:=1
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https://wolfram.com/xid/0d73dx0bugn33-edbmqb

Precision-20 principal components:

In[2]:=2
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https://wolfram.com/xid/0d73dx0bugn33-bxrb57
Out[2]=2
Wolfram Research (2007), PrincipalComponents, Wolfram Language function, https://reference.wolfram.com/language/MultivariateStatistics/ref/PrincipalComponents.html.
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Wolfram Research (2007), PrincipalComponents, Wolfram Language function, https://reference.wolfram.com/language/MultivariateStatistics/ref/PrincipalComponents.html.

Text

Wolfram Research (2007), PrincipalComponents, Wolfram Language function, https://reference.wolfram.com/language/MultivariateStatistics/ref/PrincipalComponents.html.

✖
Wolfram Research (2007), PrincipalComponents, Wolfram Language function, https://reference.wolfram.com/language/MultivariateStatistics/ref/PrincipalComponents.html.

CMS

Wolfram Language. 2007. "PrincipalComponents." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/MultivariateStatistics/ref/PrincipalComponents.html.

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Wolfram Language. 2007. "PrincipalComponents." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/MultivariateStatistics/ref/PrincipalComponents.html.

APA

Wolfram Language. (2007). PrincipalComponents. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/MultivariateStatistics/ref/PrincipalComponents.html

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Wolfram Language. (2007). PrincipalComponents. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/MultivariateStatistics/ref/PrincipalComponents.html

BibTeX

@misc{reference.wolfram_2025_principalcomponents, author="Wolfram Research", title="{PrincipalComponents}", year="2007", howpublished="\url{https://reference.wolfram.com/language/MultivariateStatistics/ref/PrincipalComponents.html}", note=[Accessed: 04-June-2025 ]}

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@misc{reference.wolfram_2025_principalcomponents, author="Wolfram Research", title="{PrincipalComponents}", year="2007", howpublished="\url{https://reference.wolfram.com/language/MultivariateStatistics/ref/PrincipalComponents.html}", note=[Accessed: 04-June-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_principalcomponents, organization={Wolfram Research}, title={PrincipalComponents}, year={2007}, url={https://reference.wolfram.com/language/MultivariateStatistics/ref/PrincipalComponents.html}, note=[Accessed: 04-June-2025 ]}

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@online{reference.wolfram_2025_principalcomponents, organization={Wolfram Research}, title={PrincipalComponents}, year={2007}, url={https://reference.wolfram.com/language/MultivariateStatistics/ref/PrincipalComponents.html}, note=[Accessed: 04-June-2025 ]}