"MultidimensionalScaling" (Machine Learning Method)
- Method for DimensionReduction, DimensionReduce, FeatureSpacePlot and FeatureSpacePlot3D.
- Reduce the dimension of data using a metric multidimensional scaling.
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
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
≈
. The lower-dimensional embeddings
are computed by minimizing the embedding cost: ∑i,j [
yi-yj
-
]2.
- The following suboptions can be given:
-
MaxIterations Automatic maximum number of optimization steps "MinRelativeChange" Automatic minimum relative change of the cost value to continue the optimization process
![](Files/MultidimensionalScaling.en/Image_1.gif)
Examples
open allclose allBasic 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:
Options (1)
MaxIterations (1)
Reduce the dimension of images using "MultidimensionalScaling":
Find the reduced features using a different MaxIterations option: