Dimensionality Reduction
Dimensionality reduction addresses a central question in neuroscience: when many neurons encode a behavioural variable such as movement direction, do they act independently, or do they share a lower-dimensional population signal?
This unit explores that question across three connected settings. In the homework, you will use PCA to extract low-dimensional features from extracellular spike waveforms recorded with a tetrode array, a standard step in spike sorting. In the first in-person session, you will then apply PCA to neural population activity recorded during a reach-planning task and learn how to interpret singular values, neuron loadings, trial weights, and low-dimensional PCA projections.
The final session goes beyond classical PCA and introduces probabilistic models of neural population activity. Using toy data and real recordings, you will compare probabilistic PCA (PPCA) and factor analysis (FA), examine how explicit noise models change the interpretation of low-dimensional structure, and finally study Gaussian process factor analysis (GPFA) as a model for smooth neural trajectories over time.
The goal of the unit is not to give a fully formal treatment of every method, but to build practical intuition for when and why different dimensionality reduction techniques are useful in neuroscience.
Sessions
PCA for Feature Extraction in Spike Sorting
Apply PCA to extracellular recordings for clustering spikes and identifying individual units
Dimensionality Reduction on Neural Population Activity
Use principal component analysis (PCA) and singular value decomposition (SVD) to explore low-dimensional structure in neural population activity.
Probabilistic Dimensionality Reduction with PPCA, FA, and GPFA
This notebook goes beyond plain PCA and introduces three different generative models for dimensionality reduction: probabilistic PCA (PPCA), factor analysis (FA), and Gaussian process factor analysis (GPFA).