Dimensionality Reduction

This lecture introduces the core concepts of dimensionality reduction.

This tutorial covers multivariate data can be represented in different orthonormal bases.

This tutorial covers how to perform principal component analysis (PCA) by projecting the data onto the eigenvectors of its covariance matrix.

To quickly refresh your knowledge of eigenvalues and eigenvectors, you can watch this short video (4 minutes) for a geometrical explanation. For a deeper understanding, this in-depth video (17 minutes) provides an excellent basis and is beautifully illustrated.

This tutorial covers how to apply principal component analysis (PCA) for dimensionality reduction, using a classic dataset that is often used to benchmark machine learning algorithms: MNIST. We'll also learn how to use PCA for reconstruction and denoising.

You can learn more about MNIST dataset here.

This tutorial covers how dimensionality reduction can be useful for visualizing and inferring structure in your data. To do this, we will compare principal component analysis (PCA) with t-SNE, a nonlinear dimensionality reduction method.

This lecture covers the application of dimensionality reduction applied to multi-dimensional neural recordings using brain-computer interfaces with simultaneous spike recordings.