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"Linear" (Machine Learning Method)

Details & Suboptions

  • "Linear" is a linear dimensionality reduction method. The method learns a low-dimensional representation of data via a linear mapping.
  • "Linear" works for datasets that have a large number of features, large number of examples and possibly many missing values (and hence can be used for collaborative filtering); however it can fail for datasets with nonlinear manifolds.
  • The following plots show the results of the "Linear" method applied to benchmark datasets Fisher's Irises, MNIST and FashionMNIST:
  • Depending on the data, the "Linear" method either first standardizes the data (it effectively becomes the "PrincipalComponentsAnalysis" method) or keeps the data as is (it effectively becomes the "LatentSemanticAnalysis" method).
  • Learned parameters are a matrix of size where and are the original and final dimensions of the data. The reduction is done through a matrix multiplication.
  • Parameters are found by minimizing the reconstruction error (mean squared error) of the training data.
  • Internally, procedures like singular value decomposition, alternating least squares and power iteration are used.

Examples

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Basic Examples  (1)

Train a linear dimensionality reduction using the "Linear" 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 -> "Linear"]

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 "Linear" with the features of each example:

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

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]]