spectrochempy.PCA¶

class PCA(**kwargs)[source]¶

Principal Component Analysis.

This class performs a Principal Component Analysis of a NDDataset, i.e., a linear dimensionality reduction using Singular Value Decomposition (SVD) of the data to perform its projection to a lower dimensional space.

The reduction of a dataset \(X\) with shape (M,`N`) is achieved using the decomposition : \(X = S.L^T\), where \(S\) is the score’s matrix with shape (M, n_pc) and \(L^T\) is the transposed loading’s matrix with shape (n_pc, N).

If the dataset X contains masked values, these values are silently 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).
centered (bool, optional, default:True) – If True the data are centered around the mean values: \(X' = X - mean(X)\).
standardized (bool, optional, default:False) – If True the data are scaled to unit standard deviation: \(X' = X / \sigma\).
scaled (bool, optional, default:False) – If True the data are scaled in the interval [0-1]: \(X' = (X - min(X)) / (max(X)-min(X))\).

See also

EFA: Perform an Evolving Factor Analysis (forward and reverse) of the input NDDataset .
NNMF: Performs a Non Negative Matrix Factorization of a NDDataset .
MCRALS: Performs MCR-ALS of a NDDataset knowing the initial C or St matrix.

Methods

`PCA.plotmerit`([n_pc])	Plots the input dataset, reconstructed dataset and residuals.
`PCA.printev`([n_pc])	Print PCA figures of merit.
`PCA.reconstruct`([n_pc])	Transform data back to the original space using `n_pc` PC's.
`PCA.reduce`([n_pc])	Apply a dimensionality reduction to the X dataset of shape [M, N].
`PCA.scoreplot`(self, *pcs[, colormap, ...])	2D or 3D scoreplot of samples.
`PCA.screeplot`([n_pc])	Scree plot of explained variance + cumulative variance by PCA.

Attributes

`PCA.LT`	LT.
`PCA.S`
`PCA.X`
`PCA.ev`	Explained variances (`NDDataset`).
`PCA.ev_cum`	Cumulative Explained Variances (`NDDataset`).
`PCA.ev_ratio`	Explained variance per singular values (`NDDataset`).