spectrochempy.SVD¶

class SVD(**kwargs)[source]¶

Performs a Singular Value Decomposition of a dataset.

The SVD is commonly written as \(X = U \Sigma V^{T}\).

This class has the attributes : U, s = diag(S) and VT=V \(^T\).

If the dataset contains masked values, the corresponding ranges are ignored in the calculation.

Parameters

dataset (|NDDataset| object) – The input dataset has shape (M, N). M is the number of observations (for examples a series of IR spectra) while N is the number of features (for example the wavenumbers measured in each IR spectrum).
full_matrices (bool, optional, default=False.) – If False , U and VT have the shapes (M, k) and (k, N), respectively, where k = min(M, N). Otherwise the shapes will be (M, M) and (N, N), respectively.
compute_uv (bool, optional, default: True.) – Whether or not to compute U and VT in addition to s.

Examples

>>> dataset = scp.read('irdata/nh4y-activation.spg')
>>> svd = scp.SVD(dataset)
>>> print(svd.ev.data)
[1.185e+04      634 ... 0.001089 0.000975]
>>> print(svd.ev_cum.data)
[   94.54     99.6 ...      100      100]
>>> print(svd.ev_ratio.data)
[   94.54    5.059 ... 8.687e-06 7.779e-06]

Attributes

`SVD.ev`	Explained variance (`NDDataset`).
`SVD.ev_cum`	Cumulative Explained Variance (`NDDataset`).
`SVD.ev_ratio`	Explained Variance per singular values `NDDataset`).
`SVD.sv`	Singular values (`NDDataset`).

ev¶: Explained variance (NDDataset).

ev_cum¶: Cumulative Explained Variance (NDDataset).

ev_ratio¶: Explained Variance per singular values NDDataset).

sv¶: Singular values (NDDataset).