mdlearn.data.preprocess.decorrelation.spatial
Spatial decorrelation functions.
Functions
|
Perform spatial decorrelation of 2nd order of real signals. |
|
SD4 - Spatial Decorrelation of 4th order of real signals. |
- mdlearn.data.preprocess.decorrelation.spatial.SD2(data: numpy.ndarray, m: Optional[int] = None, verbose: bool = False)
Perform spatial decorrelation of 2nd order of real signals.
- Parameters
data (np.ndarray) – data array of shape (T, 3N) where T is the number of frames in the MD trajectory, N is the number of atoms in the system and 3 is due to the x,y,z coordinates for each atom.
m (Optional[int], default=None) – Dimensionality of the subspace we are interested in. Default value is None, in which case m=n. If m is omitted, U is a square 3n x 3n matrix (as many sources as sensors).
verbose (bool, default=False) – Print progress.
- Returns
Y (np.ndarray) – A 3n x m matrix U (NumPy matrix type), such that \(Y = U \times\)
data
is a 2nd order spatially whitened source extracted from the 3n x T data matrixdata
by performing PCA onm
components of the real data.Y
is a matrix of spatially uncorrelated components.S (np.ndarray) – Eigen values of the
data
covariance matrix.B (np.ndarray) – Eigen vectors of the
data
covariance matrix. The eigen vectors are orthogonal.U (np.ndarray) – The sphering matrix used to transform
data
by \(Y = U \times\)data
.
- Raises
TypeError – If
verbose
is not of type bool.TypeError – If
data
is not of type np.ndarray.ValueError – If
data
does not have 2 dimensions.ValueError – If
m
is greater than 3N, the second dimension ofdata
.
- mdlearn.data.preprocess.decorrelation.spatial.SD4(Y: numpy.ndarray, m: Optional[int] = None, U: Optional[numpy.ndarray] = None, verbose: bool = False) numpy.ndarray
SD4 - Spatial Decorrelation of 4th order of real signals.
SD4 does joint diagonalization of cumulant matrices of order 4 to decorrelate the signals in spatial domain. It allows us to extract signals which are as independent as possible and which were not obtained while performing SD2. Here we consider signals which are spatially decorrelated of order 2, meaning that SD2 should be run first.
- Parameters
Y (np.ndarray) – An
n x T
spatially whitened matrix (n
subspaces,T
samples). May be a numpy array or matrix wheren
is the number of subspaces we are interested in andT
is the number of frames in the MD trajectory.m (Optional[int], default=None) – The number of subspaces we are interested in. Defaults to None, in which case m=k.
U (Optional[np.ndarray], default=None) – Whitening matrix obtained after doing the PCA analysis on
n
components of real data.verbose (bool, default=False) – Print progress.
- Returns
W (np.ndarray) – Separating matrix which is spatially decorrelated of 4th order.
- Raises
ValueError – If
m
is greater thann
, the first dimension ofY
.