Random Projection Dimensionality Reduction

Introduction

In this lab, we will explore random projection in dimensionality reduction using the scikit-learn library. Random projection is a technique that can be used to reduce the dimensionality of data while preserving the pairwise distances between samples. This can be useful for speeding up computations and reducing memory usage in machine learning algorithms.

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Skills Graph

Import the required libraries

Let's start by importing the required libraries for this lab.

import numpy as np
from sklearn import random_projection

Generate random data

Next, let's generate some random data that we can use for dimensionality reduction.

X = np.random.rand(100, 10000)

Here, we generate a 2D array X with 100 samples and 10,000 features. This will be our original high-dimensional data.

Gaussian random projection

Now, let's apply Gaussian random projection to reduce the dimensionality of our data.

transformer = random_projection.GaussianRandomProjection()
X_new = transformer.fit_transform(X)

In this step, we create an instance of the GaussianRandomProjection class and fit it to our data X. Then, we apply the transformation by calling the fit_transform method. The result is stored in the X_new variable.

Sparse random projection

Next, let's try another type of random projection called sparse random projection.

transformer = random_projection.SparseRandomProjection()
X_new = transformer.fit_transform(X)

Here, we create an instance of the SparseRandomProjection class and apply it to our data X using the fit_transform method. The result is stored in the X_new variable.

Inverse transform

Random projection transformers have an option to compute the inverse of the projection matrix. Let's explore this feature by applying the inverse transform to our projected data.

transformer = random_projection.SparseRandomProjection(compute_inverse_components=True)
X_new = transformer.fit_transform(X)

## Compute the inverse transform
X_new_inversed = transformer.inverse_transform(X_new)

In this step, we create an instance of the SparseRandomProjection class with the compute_inverse_components parameter set to True. Then, we fit the transformer to our data X and apply the transformation. Finally, we compute the inverse transform by calling the inverse_transform method on the projected data X_new.

Verification

To verify the correctness of the inverse transform, we can compare the original data X with the result of the inverse transform.

X_new_again = transformer.transform(X_new_inversed)
np.allclose(X_new, X_new_again)

Here, we apply the transform to the inverse transformed data X_new_inversed and check if it is equal to the original projected data X_new using the np.allclose function.

Summary

In this lab, we learned how to perform random projection for dimensionality reduction using the scikit-learn library. We explored both Gaussian random projection and sparse random projection techniques. We also learned how to compute the inverse transform of the projected data to recover the original data. Random projection can be a useful tool for reducing the dimensionality of high-dimensional data in machine learning tasks.