very-good-list.md

TO DO LISTS

TODO JR

• Neuropil signal pre Get Josh to do this?
• Participation ratio
• Does largest SV correspond to any of the variances?
• Fix the model and run on all the data
• 9th Jan
• Add the other variances
• Add a note to the table about whether there's an effect
• More PCs? as many as the number of neurons?
• Thick lines for the PCs. Generally improve graphics
• Dropout repeated cross-folds
• Same number of it and miss trials in the firing rate plot
• Distribution of all neuron firing rates hit vs miss
• Distribution of all neuron correlations etc
• Make the plot matrix (some e.g. populations metrics wont be possible)
• A flag for S1 and S2
• The hit and miss eigenspectrum plots
• Check how the churchlands measure variance
• Make a function to print flags and sessions included etc
• Does the variance predict propagation?
• Distribution plots of different variance flavours
• Classifier plot of different variance flavours
• Discard licks 250ms
• Churchland 2010 natneuro (Do our results match?)
• Log the covariates that are better fit by the logs
• RERUN WITH NEW PCA Viola's PC plot -> trace of the first PC before hit and miss
• Factor analysis
• Merge multiple sessions for the logistic classifier
• Fix markdown checklist
• Make the IO plot to Saxey's recommendation
• Show the distributions of PC loadings before hit and before miss
• Cross-correlation: take the absolute value of each element of cov matrix

TODO ML

• Email Johannas about the oasis nan
• Do fun stuff with the PCs
• Put the deconvolved spike data through the pipeline
• Photostim period length

Glossary

Neural activity matrix

• symbol: $X$
• size ($n_{neurons}$ x $n_{times}$)
• defined by: neural recordings

Synonyms:

• The activity of 1 neuron $i$ is row $i$: $x_i(t)$
• Neural dynamics

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Covariance matrix

• symbol: $C$
• size: ($n_{neurons}$ x $n_{neurons}$)
• defined by: covariance of activity matrix $X$

Synonyms:

• pairwise covariance

------

Principal directions

• symbol: $V$
• size matrix: ($n_{comps}$ x $n_{neurons}$)
• defined by: eigendecomposition $C = V L V^T$, where $L$ is the (diagonal) matrix with eigenvalues

Synonyms:

• Loading matrix
• principal axes
• Eigenvectors
• right singular vectors

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Eigenvalues of Covariance matrix

• symbol: $L$
• size: ($n_{comps}$, $n_{comps}$) = ($n_{neurons}$, $n_{neurons}$) (equal in case of full eigendecomposition)
• defined by: eigendecomposition $ = V L V^T$, where $V$ is the matrix of eigenvectors

Synonyms:

• eigenvalues $\lambda_k$ are on the diagonal
• variance explained = eigenvalues / sum(eigenvalues) = $\frac{\lambda_k}{\sum_k \lambda_k}$

------

Principal Component (Dynamic Activity)

• symbol: $Z$
• size matrix: (n_comps x n_times)
• defined by: $Z = V \cdot X$ (Principal directions dot Neural activity)

Synonyms:

• The activity of one PC $k$ is row $k$: $z_k(t)$
• Neural activity projected onto Principal axes
• Data projected on Principal axes
• Principal components
• PC scores
• Latent activity
• Latent components
• left singular vector dot (diagonal) singular value matrix

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Variances

• variance_pop_mean: take the population mean across cells -> [time]. What is the variance of this vector?
• variance_cell_rates: take the mean across time for all cells -> [n_cells]. What is the variance of this vector?
• mean_cell_variance: take the variance of each cell through time -> [n_cells]. What is the mean of all the cell variances?

References:

• https://stats.stackexchange.com/questions/134282/relationship-between-svd-and-pca-how-to-use-svd-to-perform-pca
• https://stats.stackexchange.com/questions/311908/what-is-pca-components-in-sk-learn
• https://jakevdp.github.io/PythonDataScienceHandbook/05.09-principal-component-analysis.html