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"Hadamard" (Machine Learning Method)

Details & Suboptions

  • "Hadamard" is a linear dimensionality-reduction method that does not learn from the data. The method projects input data on a lower-dimensional space using a slice of a HadamardMatrix. This method attempts to approximate a random projection.
  • "Hadamard" is computationally efficient for datasets that have a large number of features; however, since there is no learning, the embedding will not be as good as other methods.
  • The following shows two-dimensional embeddings learned by the "Hadamard" method applied to the benchmark datasets Fisher's Irises, MNIST and FashionMNIST:
  • The "Hadamard" method nearly preserves the pairwise distances of high-dimensional data, similarly to a random projection.
  • DimensionReduce[…,Method"Hadamard", FeatureExtractor"Minimal"] should be used to take full advantage of the computational efficiency of this method.
  • The suboption Method can be used to set the type of the matrix manipulation. Method"Matrix" should only be used for datasets with a small number of inputs and reduced features.
  • The following suboption can be given:
  • Method Automaticmatrix computation method
  • Possible settings for Method include:
  • "Matrix"constructs the Hadamard matrix explicitly
    "Transform"uses a direct transformation for the reduction

Examples

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Basic Examples  (1)

Reduce the dimension of a high-dimensional vector using the "Hadamard" method efficiently:

Wolfram Language code: vectors = RandomReal[1, {10, 10 ^ 6}]; AbsoluteTiming[MaxMemoryUsed[DimensionReduce[vectors, 100, Method -> "Hadamard", FeatureExtractor -> "Minimal"]]]

Options  (1)

Method  (1)

Compare the performance of "Hadamard" with different suboptions on a high-dimensional vector:

Wolfram Language code: vectors = RandomReal[1, {10, 10 ^ 5}]; First@AbsoluteTiming[DimensionReduce[vectors, 1000, Method -> {"Hadamard", Method -> "Matrix"}, FeatureExtractor -> "Minimal"];] First@AbsoluteTiming[DimensionReduce[vectors, 1000, Method -> {"Hadamard", Method -> "Transform"}, FeatureExtractor -> "Minimal"];]

Applications  (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 "Hadamard" with the features of each example:

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

Group the examples by their species:

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

Reduce the dimension of the features:

Wolfram Language code: ListPlot[dr /@ Values[byspecies], PlotLegends -> Keys@byspecies, ... ]