`tedana.decomposition`.tedpca¶

tedpca(data_cat, data_oc, combmode, mask, adaptive_mask, t2sG, ref_img, tes, algorithm='mdl', kdaw=10.0, rdaw=1.0, out_dir='.', verbose=False, low_mem=False)[source]¶

Use principal components analysis (PCA) to identify and remove thermal noise from multi-echo data.

Parameters

data_cat ((S x E x T) array_like) – Input functional data
data_oc ((S x T) array_like) – Optimally combined time series data
combmode ({‘t2s’, ‘paid’} str) – How optimal combination of echos should be made, where ‘t2s’ indicates using the method of Posse 1999 and ‘paid’ indicates using the method of Poser 2006
mask ((S,) array_like) – Boolean mask array
adaptive_mask ((S,) array_like) – Array where each value indicates the number of echoes with good signal for that voxel. This mask may be thresholded; for example, with values less than 3 set to 0. For more information on thresholding, see make_adaptive_mask.
t2sG ((S,) array_like) – Map of voxel-wise T2* estimates.
ref_img (str or img_like) – Reference image to dictate how outputs are saved to disk
tes (list) – List of echo times associated with data_cat, in milliseconds
algorithm ({‘kundu’, ‘kundu-stabilize’, ‘mdl’, ‘aic’, ‘kic’, float}, optional) – Method with which to select components in TEDPCA. PCA decomposition with the mdl, kic and aic options are based on a Moving Average (stationary Gaussian) process and are ordered from most to least aggressive (see Li et al., 2007). If a float is provided, then it is assumed to represent percentage of variance explained (0-1) to retain from PCA. Default is ‘mdl’.
kdaw (float, optional) – Dimensionality augmentation weight for Kappa calculations. Must be a non-negative float, or -1 (a special value). Default is 10.
rdaw (float, optional) – Dimensionality augmentation weight for Rho calculations. Must be a non-negative float, or -1 (a special value). Default is 1.
out_dir (str, optional) – Output directory.
verbose (bool, optional) – Whether to output files from fitmodels_direct or not. Default: False
low_mem (bool, optional) – Whether to use incremental PCA (for low-memory systems) or not. This is only compatible with the “kundu” or “kundu-stabilize” algorithms. Default: False

Returns

kept_data ((S x T) numpy.ndarray) – Dimensionally reduced optimally combined functional data
n_components (int) – Number of components retained from PCA decomposition

Notes

Notation	Meaning
$\kappa$	Component pseudo-F statistic for TE-dependent (BOLD) model.
$\rho$	Component pseudo-F statistic for TE-independent (artifact) model.
$v$	Voxel
$V$	Total number of voxels in mask
$\zeta$	Something
$c$	Component
$p$	Something else

Steps:

Variance normalize either multi-echo or optimally combined data, depending on settings.
Decompose normalized data using PCA or SVD.
Compute ${\kappa}$ and ${\rho}$ :

${\kappa}_c = \frac{\sum_{v}^V {\zeta}_{c,v}^p * F_{c,v,R_2^*}}{\sum {\zeta}_{c,v}^p} {\rho}_c = \frac{\sum_{v}^V {\zeta}_{c,v}^p * F_{c,v,S_0}}{\sum {\zeta}_{c,v}^p}$
Some other stuff. Something about elbows.
Classify components as thermal noise if they meet both of the following criteria:
- Nonsignificant ${\kappa}$ and ${\rho}$ .
- Nonsignificant variance explained.

Outputs:

This function writes out several files:

Filename	Content
pca_decomposition.json	PCA component table.
pca_mixing.tsv	PCA mixing matrix.
pca_components.nii.gz	Component weight maps.

tedana.decomposition.tedpca¶

`tedana.decomposition`.tedpca¶