CCA_align¶

CCA_align(L_a, L_b)[source][source]¶

Canonical Correlation Analysis (CCA) alignment between 2 datasets.

From: https://www.nature.com/articles/s41593-019-0555-4#Sec11. Returns manifold directions to transform L_a and L_b into a common space (e.g. L_a_new.T = L_a.T @ M_a, L_b_new.T = L_b.T @ M_b). To transform into a specific patient space, for example putting everything in patient A’s space, use L_(b->a).T = L_b.T @ M_b @ (M_a)^-1, where L_a and L_(b->a) will be aligned in the same space.

Parameters:

L_a (ndarray) – Latent dynamics array for dataset A of shape (m, T), where m is the number of latent dimensions and T is the number of timepoints.
L_b (ndarray) – Latent dynamics array for dataset B of shape (m, T)

Returns:

Tuple containing: M_a : ndarray

Manifold directions for dataset A of shape (m, m)

M_bndarray: Manifold directions for dataset B of shape (m, m)

Return type:

tuple

Examples

>>> import numpy as np
>>> rand = np.random.RandomState(seed=0)
>>> L_a = np.random.randn(5, 10)
>>> L_b = np.random.randn(5, 10)
>>> M_a, M_b = CCA_align(L_a, L_b)
>>> M_a.shape
(5, 5)
>>> (L_b.T @ M_b).shape
(10, 5)