Principal component analysis (PCA)

tl;dr: identifies an ordered set of orthogonal directions that captures the greatest variance in the data.

  • Obscures spiking variability (output noise) with firing rate variability (temporal changes in time).
  • Typically applied to smoothed or averaged neural data in which the spiking variability has been minimized
  • For raw spike counts, use Factor Analysis, as this can decompose changes in FR from spiking variability. I.e., separate independent noise for each neuron. FA is PCA but with an explicit noise model.

Notes mentioning this note

Gaussian Process Factor Analysis
Dimensionality reduction for neural data
Model-based targeted dimensionality reduction (mTDR)
tl;dr: probabilistic extension of targeted dimensionality reduction ([[TDR]]) that allows task variables to be multi-dimensional. Advantageous for missing data and...
Probabilistic PCA
tl;dr: probabilistic extension of principal component analysis. Advantageous for handling missing data and extending PCA to a Bayesian framework.

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