Wolfram Language & System 10.4 (2016)|Legacy Documentation

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DimensionReduction

DimensionReduction[{vec1,vec2,}]
generates a DimensionReducerFunction[] that projects to the lower-dimensional approximating manifold defined by the vectors .

DimensionReduction[vecs,n]
generates a DimensionReducerFunction[] for an n-dimensional approximating manifold.

DimensionReduction[vecs,n,props]
generates the specified properties of the dimensionality reduction.

Details and OptionsDetails and Options

  • DimensionReduction[vecs] yields a DimensionReducerFunction[] that can be applied to data to perform dimension reduction.
  • The vectors must be numerical and must all be of the same length.
  • DimensionReduction[vecs] automatically chooses an appropriate dimension for the target approximating manifold.
  • DimensionReduction[vecs] is equivalent to DimensionReduction[vecs,Automatic].
  • In DimensionReduction[,props], props can be a single property or a list of properties. Possible properties include:
  • "ReducerFunction"DimensionReducerFunction[] (default)
    "ReducedVectors"reduction of the vectors vecs
    "ReconstructedVectors"reconstruction of vecs after reduction and inversion
    "ImputedVectors"missing values in vecs replaced by imputed values
  • The following options can be given:
  • MethodAutomaticwhich reduction algorithm to use
    PerformanceGoalAutomaticaspect of performance to optimize
  • Possible settings for PerformanceGoal include:
  • "Memory"minimize the storage requirements of the reducer function
    "Quality"maximize reduction quality
    "Speed"maximize reduction speed
    "TrainingSpeed"minimize the time spent producing the reducer
  • PerformanceGoal{goal1,goal2,} will automatically combine , , etc.
  • Possible settings for Method include:
  • Automaticautomatically chosen method
    "PrincipalComponentsAnalysis"principal components analysis method
    "LatentSemanticAnalysis"latent semantic analysis method
    "LowRankMatrixFactorization"use a low-rank matrix factorization algorithm

ExamplesExamplesopen allclose all

Basic Examples  (2)Basic Examples  (2)

Generate a dimension reducer from a list of vectors:

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Use this reducer on a new vector:

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Use this reducer on a list of new vectors:

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Create a reducer with a specified target dimension of 1:

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Apply the reducer to the vectors used to generate the reducer:

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Obtain both the reducer and the reduced vectors in one step:

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Introduced in 2015
(10.1)