Utilities – Dimension Reduction¶

sensorimotor_dependencies.utils.MDS(data, return_matrix=False, return_eigenvalues=False)[source]¶

Parameters:

data ((n, k) array) – Data points matrix (data points = row vectors in the matrix)
return_matrix (bool) – If True, returns the coordinate matrix
return_eigenvalues (bool, optional) – Returns the eigenvalues and their ratios $λ_{i+1}/λ_i$ (False by default).

Returns:

nb (int) – Number of non-zero eigenvalues of $$B = X X^T$$ (where $X$ is the coordinate matrix), thought of as the number of degrees of freedom. The eigenvalues thereof fall into two classes (non-zero and zero eigenvalues) $V_1$ and $V_2$, distinguished as follows: > each $λ ∈ V_1$ has a size closer to other the $λ$’s of $V_1$ than the ones of $V_2$, and conversely. The boundary between $V_1$ and $V_2$ corresponds to the largest ratio $λ_{i+1}/λ_i$, where the $λ_i$ are in decreasing order.
X ((n, dim_rigid_group) array) – If return_matrix == True: Coordinate matrix.

sensorimotor_dependencies.utils.PCA(data, return_matrix=False, return_eigenvalues=False)[source]¶

Principal Component Analysis (PCA) to compute the number of degrees of freedom.

Parameters:

data ((n, k) array) – Data points matrix (data points = row vectors in the matrix)
return_matrix (bool) – If True, returns the matrix of the data points projection on the eigenvectors
return_eigenvalues (bool, optional) – Returns the eigenvalues and their ratios $λ_{i+1}/λ_i$ (False by default).

Returns:

nb (int) – Number of non-zero eigenvalues of the covariance matrix, thought of as the number of degrees of freedom. The eigenvalues thereof fall into two classes (non-zero and zero eigenvalues) $V_1$ and $V_2$, distinguished as follows: > each $λ ∈ V_1$ has a size closer to other the $λ$’s of $V_1$ than the ones of $V_2$, and conversely. The boundary between $V_1$ and $V_2$ corresponds to the largest ratio $λ_{i+1}/λ_i$, where the $λ_i$ are in decreasing order.
Proj ((n, dim_rigid_group) array) – If return_matrix == True: Projection of the data points on the eigenvectors

sensorimotor_dependencies.utils.Rot(euler_angles)[source]¶: Compute rotation matrix corresponding the given Euler angle cf. https://en.wikipedia.org/wiki/Euler_angles#Rotation_matrix