"Linear" (Machine Learning Method)
- Method for DimensionReduction, DimensionReduce, FeatureSpacePlot and FeatureSpacePlot3D.
- Maps the data into a linear lower-dimensional space.
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.
Examplesopen allclose all
Basic Examples (1)
Dataset Visualization (1)
Load the Fisher Iris dataset from ExampleData:
Generate a reducer function using "Linear" with the features of each example:
Group the examples by their species:
Reduce the dimension of the features: