Prep: weekly mtg 20160203 (Byron, Steve, me) - mobeets/nullSpaceControl GitHub Wiki

Tiny things

• Minimum c-v score: basically 0.

• Covariance scores: unconstrained and habitual are the only ones even slightly on the mark. Finding a discrepancy between the figure in Pete's write-up, and what his code is actually generating. Will look into this...

Explorations

Orthonormalized factors

L = USV', Znew = VZ, M2new = M2*V'

Norms are preserved as long as you're just doing a rotation. Thus, can't stretch with S. Anyway, factors are now orthogonal and sorted by variance.

New volitional hypotheses

• Standard
• Standard, no precursor
• FA w/ 2 PCs + baseline [e.g., RB = eye(2, 10)]
• FA w/ 3-4 PCs + baseline [e.g., RB = eye(3, 10)]

Also, and SVD on latents (in null, row, or full) yields PCs with cursor-relevant interpretation. Thus, tried using RB of these first two axes. Performs about as well as the normal 2 PCs one.

Might consider finding CCA or Procrustes transformation.

Hypothesis performance across days and monkeys

20120525:

20120601:

20131125:

20131205:

Why does habitual fail? aka norms with kinematics-dependence

First for 20120525:

 

Now for 20131125:

 

To do

• what's going on with covariance (det = product of eigenvalues)
• unitary matrix (V^TV = I): L' = (LV^T)(zV) - do norms change?
• 8 kinematics conditions, for each one: performance hit, and learning. correlation with hypothesis performance? bin 1st and last third of data, e.g.