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Dimensionality Reduction

Level
Beginner

Neuromatch Academy aims to introduce traditional and emerging tools of computational neuroscience to trainees. It is appropriate for student population ranging from undergraduates to faculty in academic settings and also includes industry professionals. In addition to teaching the technical details of computational methods, Neuromatch Academy also provide a curriculum centered on modern neuroscience concepts taught by leading professors along with explicit instruction on how and why to apply models. 

 

This course introduces the core concepts of dimensionality reduction and provides an application of dimensionality reduction applied to multi-dimensional neural recordings using brain-computer interfaces with simultaneous spike recordings.

Course Features
Lectures
Interactive Tutorials
Discussion Forum
Suggested Reading
Recordings of question and answer sessions
Lessons of this Course
1
1
Duration:
31:43
Speaker:

This lecture is part of the Neuromatch Academy (NMA), a massive, interactive online summer school held in 2020 that provided participants with experiences spanning from hands-on modeling experience to meta-science interpretation skills across just about everything that could reasonably be included in the label "computational neuroscience". 

 

This lecture introduces the core concepts of dimensionality reduction.

2
2
Duration:
4:48

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

 

    Overview of this tutorial:

    • Generate correlated multivariate data
    • Define an arbitrary orthonormal basis
    • Project the data onto the new basis

     

    3
    3
    Duration:
    6:33

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

    Overview of this tutorial:

    • Calculate the eigenvectors of the sample covariance matrix.
    • Perform PCA by projecting data onto the eigenvectors of the covariance matrix.
    • Plot and explore the eigenvalues.

    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.

    4
    4
    Duration:
    5:35

    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.

    Overview of this tutorial:

    • Perform PCA on MNIST
    • Calculate the variance explained
    • Reconstruct data with different numbers of PCs
    • (Bonus) Examine denoising using PCA

    You can learn more about MNIST dataset here.

    5
    5
    Duration:
    4:17

    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.

    Overview of the tutorial:

    • Visualize MNIST in 2D using PCA
    • Visualize MNIST in 2D using t-SNE
    6
    6
    Duration:
    30:15
    Speaker:

    This lecture is part of the Neuromatch Academy (NMA), a massive, interactive online summer school held in 2020 that provided participants with experiences spanning from hands-on modeling experience to meta-science interpretation skills across just about everything that could reasonably be included in the label "computational neuroscience". 

     

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