WOLFRAM

Wolfram Language & System Documentation Center

"PrincipalComponentsAnalysis" (Machine Learning Method)

Details & Suboptions

  • "PrincipalComponentsAnalysis" is a linear dimensionality reduction method. The method projects input data on a linear lower-dimensional space that preserves the maximum variance in the data.
  • The "PrincipalComponentsAnalysis" method works for datasets that have a large number of features and large number of examples; however, the learned manifold can only be linear.
  • The following plots show the results of the "PrincipalComponentsAnalysis" method applied to benchmark datasets including Fisher's Irises, MNIST and FashionMNIST:
  • "PrincipalComponentsAnalysis" is equivalent to the "Linear" and "LatentSemanticAnalysis" methods when the data is standardized.

Examples

open all close all

Basic Examples  (1)

Train a linear dimensionality reduction using the "PrincipalComponentsAnalysis" method from a list of vectors:

Wolfram Language code: reducer = DimensionReduction[{{1, 2, 3}, {2, 3, 5}, {3, 5, 8}, {4, 5, 8.5}}, 2, Method -> "PrincipalComponentsAnalysis"]

Use the trained reducer on new vectors:

Wolfram Language code: reducer[{{6, 7, 14}, {5, 6, 11}, {1, 3, 9}}]

Scope  (1)

Dataset Visualization  (1)

Load the Fisher Iris dataset from ExampleData:

Wolfram Language code: iris = ExampleData[{"MachineLearning", "FisherIris"}, "Data"];
Wolfram Language code: RandomSample[iris, 5]

Generate a reducer function using "PrincipalComponentsAnalysis" with the features of each example:

Wolfram Language code: diris = DimensionReduction[iris[[All, 1]], 2, Method -> "PrincipalComponentsAnalysis"]

Group the examples by their species:

Wolfram Language code: byspecies = GroupBy[iris, Last -> First];

Reduce the dimension of the features:

Wolfram Language code: byspecies = diris /@ byspecies;

Visualize the reduced dataset:

Wolfram Language code: ListPlot[Values[byspecies], PlotLegends -> Keys[byspecies]]