DimensionReduction

DimensionReduction[{example1,example2,…}]

generates a DimensionReducerFunction[…] that projects from the space defined by the examplei to a lower-dimensional approximating manifold.

DimensionReduction[examples,n]

generates a DimensionReducerFunction[…] for an n-dimensional approximating manifold.

DimensionReduction[examples,n,props]

generates the specified properties of the dimensionality reduction.

Details and Options

Examples

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Basic Examples  (3)

Generate a dimension reducer from a list of vectors:

Use this reducer on a new vector:

Use this reducer on a list of new vectors:

Create a reducer with a specified target dimension of 1:

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

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

Train a dimension reducer on a mixed-type dataset:

Reduce the dimension of a new example:

Scope  (7)

Create and visualize random 3D vectors:

Create a dimension reducer from the vectors:

Reduce a new vector:

Reduce the original vectors and visualize them:

Try to reconstruct the original vectors from the reduced ones:

The reconstructed vectors correspond to the original vectors projected on an approximating plane:

The reconstructed vectors can be directly obtained from the original vectors:

Generate a dimension reducer from a list of vectors:

Use the reducer function to impute missing values in other vectors:

Train a dimension reducer on a dataset of images:

Use the reducer on the training set:

Train a dimension reducer on textual data:

Use the reducer on new examples:

Train a dimension reducer on a list of DateObject:

Reduce the dimension of a new DateObject:

A string date can also be given:

Train a dimension reducer on a mixed-type dataset:

Reduce the dimension of a new example:

Train a dimension reducer on a list of associations:

Reduce the dimension of a new example:

Options  (7)

FeatureExtractor  (1)

Train a reducer function on texts preprocessed by custom functions and an extractor method:

FeatureNames  (1)

Train a reducer and give a name to each variable:

Use the association format to reduce a new example:

The list format can still be used:

FeatureTypes  (1)

Train a reducer on a simple dataset:

The first feature has been interpreted as numerical. Use FeatureTypes to enforce the interpretation of the first feature as nominal:

Method  (3)

Generate a reducer function on the features of the Fisher iris dataset using the t-SNE method:

Group the examples by their species:

Reduce the dimension of the features:

Visualize the reduced dataset:

Perform the same operation using a different perplexity value:

Reduce the dimension of some images using the autoencoder method:

Visualize the two-dimensional representation of images:

Generate a nonlinear data manifold with the random noise, known as a Swiss-roll dataset:

Visualize the three-dimensional Swiss-roll dataset:

Train a reducer function using the isometric mapping (isomap) method:

Visualize the two-dimensional embedding of the reduced dataset:

Train a reducer function using the locally linear embedding (LLE) method:

Visualize the two-dimensional embedding of the reduced dataset:

TargetDevice  (1)

Train a reducer function using a fully connected "AutoEncoder" on the system's default GPU and look at its AbsoluteTiming:

Compare the previous timing with the one obtained by using the default CPU computation:

Applications  (5)

Dataset Visualization  (1)

Load the Fisher iris dataset from ExampleData:

Generate a reducer function with the features of each example:

Group the examples by their species:

Reduce the dimension of the features:

Visualize the reduced dataset:

Head-Pose Estimation  (1)

Load 3D geometry data:

Generate a dataset of many heads with random view points, which creates different head poses:

Visualize different head poses:

Generate a reducer function on a dataset of images with different poses using the LLE method:

Visualize a two-dimensional representation of images from a 50×50 input space in which two axes represent up-down and front-side poses:

Image Imputation  (1)

Load the MNIST dataset from ExampleData and keep the images:

Convert images to numerical data and separate the dataset into a training set and a test set:

The dimension of the dataset is 784:

Create a dimension reducer from the training set with a target dimension of 50:

Reduce a vector from the test set:

Visualize the original vector and its reconstructed version:

Replace some values of the vector by Missing[] and visualize it:

Impute missing values with the reducer function:

Visualize the original image, the image with missing values, and the imputed image:

Recommender System  (1)

Get movie ratings of users in a SparseArray form:

The dataset is composed of 100 users and 10 movies. Ratings range from 1 to 5, and Missing[] represents unknown ratings:

Separate the dataset into a training set and a test set:

Generate a dimension reducer from the training set:

Use this dimension reducer to impute (that is, to predict) the missing values for a new user:

Image Search  (1)

Construct a dataset of dog images:

Train a reducer function from this dataset:

Generate a NearestFunction in the reduced space:

Using the NearestFunction, construct a function that displays the nearest image of the dataset:

Use this function on images that are not in the dataset:

This reducer function can also be used to delete image pairs that are too similar:

Wolfram Research (2015), DimensionReduction, Wolfram Language function, https://reference.wolfram.com/language/ref/DimensionReduction.html (updated 2020).

Text

Wolfram Research (2015), DimensionReduction, Wolfram Language function, https://reference.wolfram.com/language/ref/DimensionReduction.html (updated 2020).

CMS

Wolfram Language. 2015. "DimensionReduction." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2020. https://reference.wolfram.com/language/ref/DimensionReduction.html.

APA

Wolfram Language. (2015). DimensionReduction. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/DimensionReduction.html

BibTeX

@misc{reference.wolfram_2024_dimensionreduction, author="Wolfram Research", title="{DimensionReduction}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/DimensionReduction.html}", note=[Accessed: 21-November-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_dimensionreduction, organization={Wolfram Research}, title={DimensionReduction}, year={2020}, url={https://reference.wolfram.com/language/ref/DimensionReduction.html}, note=[Accessed: 21-November-2024 ]}