"MultidimensionalScaling" (Machine Learning Method)

Details & Suboptions

  • "MultidimensionalScaling", is a nonlinear distance-based dimensionality reduction method. The method attempts to find a low-dimensional embedding of data using a transformation that preserves the pairwise distances.
  • "MultidimensionalScaling" is able to learn nonlinear manifolds; however, it can be slow when the number of examples is large.
  • The following plots show two-dimensional embeddings learned by the "MultidimensionalScaling" method applied to the benchmarking datasets Fisher's Irises, MNIST and FashionMNIST:
  • Given the distance matrix d_(ij) of data points in the original space, "MultidimensionalScaling" attempts to find the lower-dimensional embeddings , such that distances in the lower-dimensional space match the distances between data points in the original space, ||yi-yj|| d_(ij). The lower-dimensional embeddings are computed by minimizing the embedding cost: i,j [||yi-yj||- d_(ij)]2.
  • The following suboptions can be given:
  • MaxIterationsAutomaticmaximum number of optimization steps
    "MinRelativeChange"Automaticminimum relative change of the cost value to continue the optimization process

Examples

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Basic Examples  (2)

Reduce the dimension of random vectors using the "MultidimensionalScaling" method:

Create and visualize a "Swiss roll" dataset:

Train a nonlinear dimension reducer using "MultidimensionalScaling" on the dataset to map to two-dimensional space:

Find and visualize the data coordinates in the reduced space:

Visualize the dataset in the original space, with each point colored according to its reduced variable:

Scope  (1)

Dataset Visualization  (1)

Load the Fisher Iris dataset from ExampleData:

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

Group the examples by their species:

Reduce the dimension of the features:

Visualize the reduced dataset:

Options  (1)

MaxIterations  (1)

Load the "MNIST" dataset:

Reduce the dimension of images using "MultidimensionalScaling":

Find the reduced features using a different MaxIterations option:

Visualize the obtained features and compare the results: