Decomposition Methods

MI methods

CSP

Common Spatial Patterns and his happy little buddies!

class brainda.algorithms.decomposition.csp.CSP(n_components: Optional[int] = None, max_components: Optional[int] = None)

Bases: sklearn.base.BaseEstimator, sklearn.base.TransformerMixin

Common Spatial Pattern.

if n_components is None, auto finding the best number of components with gridsearch. The upper searching limit is determined by max_components, default is half of the number of channels.

fit(X: numpy.ndarray, y: numpy.ndarray)
transform(X: numpy.ndarray)
class brainda.algorithms.decomposition.csp.FBCSP(n_components: Optional[int] = None, max_components: Optional[int] = None, n_mutualinfo_components: Optional[int] = None, filterbank: Optional[List[numpy.ndarray]] = None)

Bases: brainda.algorithms.decomposition.base.FilterBank

FBCSP.

FilterBank CSP based on paper [1]_.

References

1

Ang K K, Chin Z Y, Zhang H, et al. Filter bank common spatial pattern (FBCSP) in brain-computer interface[C]//2008 IEEE International Joint Conference on Neural Networks (IEEE World Congress on Computational Intelligence). IEEE, 2008: 2390-2397.

fit(X: numpy.ndarray, y: numpy.ndarray)
transform(X: numpy.ndarray)
class brainda.algorithms.decomposition.csp.FBMultiCSP(n_components: Optional[int] = None, max_components: Optional[int] = None, multiclass: str = 'ovr', ajd_method: str = 'uwedge', n_mutualinfo_components: Optional[int] = None, filterbank: Optional[List[numpy.ndarray]] = None)

Bases: brainda.algorithms.decomposition.base.FilterBank

fit(X: numpy.ndarray, y: numpy.ndarray)
transform(X: numpy.ndarray)
class brainda.algorithms.decomposition.csp.MultiCSP(n_components: Optional[int] = None, max_components: Optional[int] = None, multiclass: str = 'ovr', ajd_method: str = 'uwedge')

Bases: sklearn.base.BaseEstimator, sklearn.base.TransformerMixin

fit(X: numpy.ndarray, y: numpy.ndarray)
transform(X: numpy.ndarray)
class brainda.algorithms.decomposition.csp.SPoC(n_components: Optional[int] = None, max_components: Optional[int] = None)

Bases: sklearn.base.BaseEstimator, sklearn.base.TransformerMixin

Source Power Comodulation (SPoC).

For continuous data, not verified.

fit(X: numpy.ndarray, y: numpy.ndarray)
transform(X: numpy.ndarray)
brainda.algorithms.decomposition.csp.ajd(X: numpy.ndarray, method: str = 'uwedge') → Tuple[numpy.ndarray, numpy.ndarray]

Wrapper of AJD methods.

Parameters

  • X (ndarray) – Input covariance matrices, shape (n_trials, n_channels, n_channels)

  • method (str, optional) – AJD method (default uwedge).

Returns

  • V (ndarray) – The diagonalizer, shape (n_channels, n_filters), usually n_filters == n_channels.

  • D (ndarray) – The mean of quasi diagonal matrices, shape (n_channels,).

brainda.algorithms.decomposition.csp.csp_feature(W: numpy.ndarray, X: numpy.ndarray, n_components: int = 2) → numpy.ndarray

Return CSP features in paper [1]_.

Parameters

  • W (ndarray) – spatial filters from csp_kernel, shape (n_channels, n_filters)

  • X (ndarray) – eeg data, shape (n_trials, n_channels, n_samples)

  • n_components (int, optional) – the first k components to use, usually even number, by default 2

Returns

features of shape (n_trials, n_features)

Return type

ndarray

Raises

ValueError – n_components should less than the number of channels

References

1

Ramoser H, Muller-Gerking J, Pfurtscheller G. Optimal spatial filtering of single trial EEG during imagined hand movement[J]. IEEE transactions on rehabilitation engineering, 2000, 8(4): 441-446.

brainda.algorithms.decomposition.csp.csp_kernel(X: numpy.ndarray, y: numpy.ndarray) → Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray]

The kernel in CSP algorithm based on paper [1]_.

Parameters

  • X (ndarray) – eeg data, shape (n_trials, n_channels, n_samples).

  • y (ndarray) – labels of X, shape (n_trials,).

Returns

  • W (ndarray) – Spatial filters, shape (n_channels, n_filters).

  • D (ndarray) – Eigenvalues of spatial filters, shape (n_filters,).

  • A (ndarray) – Spatial patterns, shape (n_channels, n_patterns).

References

1

Ramoser H, Muller-Gerking J, Pfurtscheller G. Optimal spatial filtering of single trial EEG during imagined hand movement[J]. IEEE transactions on rehabilitation engineering, 2000, 8(4): 441-446.

brainda.algorithms.decomposition.csp.gw_csp_kernel(X: numpy.ndarray, y: numpy.ndarray, ajd_method: str = 'uwedge') → Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray, numpy.ndarray]

Grosse-Wentrup AJD method based on paper [1]_.

Parameters

  • X (ndarray) – eeg data, shape (n_trials, n_channels, n_samples).

  • y (ndarray) – labels, shape (n_trials).

  • ajd_method (str, optional) – ajd methods, ‘uwedge’ ‘rjd’ and ‘ajd_pham’, by default ‘uwedge’.

Returns

  • W (ndarray) – Spatial filters, shape (n_channels, n_filters).

  • D (ndarray) – Eigenvalues of spatial filters, shape (n_filters,).

  • A (ndarray) – Spatial patterns, shape (n_channels, n_patterns).

  • mutual_info (ndarray) – Mutual informaiton values, shape (n_filters).

References

1

Grosse-Wentrup, Moritz, and Martin Buss. “Multiclass common spatial patterns and information theoretic feature extraction.” Biomedical Engineering, IEEE Transactions on 55, no. 8 (2008): 1991-2000.

brainda.algorithms.decomposition.csp.spoc_kernel(X: numpy.ndarray, y: numpy.ndarray) → Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray]

Source Power Comodulation (SPoC) based on paper [1]_.

It is a continous CSP-like method.

Parameters

  • X (ndarray) – eeg data, shape (n_trials, n_channels, n_samples)

  • y (ndarray) – labels, shape (n_trials)

Returns

  • W (ndarray) – Spatial filters, shape (n_channels, n_filters).

  • D (ndarray) – Eigenvalues of spatial filters, shape (n_filters,).

  • A (ndarray) – Spatial patterns, shape (n_channels, n_patterns).

References

1

Sven Dähne, Frank C. Meinecke, Stefan Haufe, Johannes Höhne, Michael Tangermann, Klaus-Robert Müller, and Vadim V. Nikulin. SPoC: a novel framework for relating the amplitude of neuronal oscillations to behaviorally relevant parameters. NeuroImage, 86:111–122, 2014. doi:10.1016/j.neuroimage.2013.07.079.

SSVEP methods

CCA

CCA and its variants.

class brainda.algorithms.decomposition.cca.ECCA(n_components: int = 1, n_jobs: Optional[int] = None)

Bases: sklearn.base.BaseEstimator, sklearn.base.TransformerMixin, sklearn.base.ClassifierMixin

fit(X: Optional[numpy.ndarray], y: Optional[numpy.ndarray], Yf: Optional[numpy.ndarray] = None)
predict(X: numpy.ndarray)
transform(X: numpy.ndarray)
class brainda.algorithms.decomposition.cca.FBECCA(filterbank: List[numpy.ndarray], n_components: int = 1, filterweights: Optional[numpy.ndarray] = None, n_jobs: Optional[int] = None)

Bases: brainda.algorithms.decomposition.base.FilterBankSSVEP, sklearn.base.ClassifierMixin

fit(X: numpy.ndarray, y: numpy.ndarray, Yf: Optional[numpy.ndarray] = None)
predict(X: numpy.ndarray)
class brainda.algorithms.decomposition.cca.FBItCCA(filterbank: List[numpy.ndarray], n_components: int = 1, method: str = 'itcca2', filterweights: Optional[numpy.ndarray] = None, n_jobs: Optional[int] = None)

Bases: brainda.algorithms.decomposition.base.FilterBankSSVEP, sklearn.base.ClassifierMixin

fit(X: numpy.ndarray, y: numpy.ndarray, Yf: Optional[numpy.ndarray] = None)
predict(X: numpy.ndarray)
class brainda.algorithms.decomposition.cca.FBMsCCA(filterbank: List[numpy.ndarray], n_components: int = 1, filterweights: Optional[numpy.ndarray] = None, n_jobs: Optional[int] = None)

Bases: brainda.algorithms.decomposition.base.FilterBankSSVEP, sklearn.base.ClassifierMixin

fit(X: numpy.ndarray, y: numpy.ndarray, Yf: Optional[numpy.ndarray] = None)
predict(X: numpy.ndarray)
class brainda.algorithms.decomposition.cca.FBMsetCCA(filterbank: List[numpy.ndarray], n_components: int = 1, method: str = 'msetcca2', filterweights: Optional[numpy.ndarray] = None, n_jobs: Optional[int] = None)

Bases: brainda.algorithms.decomposition.base.FilterBankSSVEP, sklearn.base.ClassifierMixin

fit(X: numpy.ndarray, y: numpy.ndarray, Yf: Optional[numpy.ndarray] = None)
predict(X: numpy.ndarray)
class brainda.algorithms.decomposition.cca.FBMsetCCAR(filterbank: List[numpy.ndarray], n_components: int = 1, filterweights: Optional[numpy.ndarray] = None, n_jobs: Optional[int] = None)

Bases: brainda.algorithms.decomposition.base.FilterBankSSVEP, sklearn.base.ClassifierMixin

fit(X: numpy.ndarray, y: numpy.ndarray, Yf: Optional[numpy.ndarray] = None)
predict(X: numpy.ndarray)
class brainda.algorithms.decomposition.cca.FBSCCA(filterbank: List[numpy.ndarray], n_components: int = 1, filterweights: Optional[numpy.ndarray] = None, n_jobs: Optional[int] = None)

Bases: brainda.algorithms.decomposition.base.FilterBankSSVEP, sklearn.base.ClassifierMixin

predict(X: numpy.ndarray)
class brainda.algorithms.decomposition.cca.FBTRCA(filterbank: List[numpy.ndarray], n_components: int = 1, ensemble: bool = True, filterweights: Optional[numpy.ndarray] = None, n_jobs: Optional[int] = None)

Bases: brainda.algorithms.decomposition.base.FilterBankSSVEP, sklearn.base.ClassifierMixin

fit(X: numpy.ndarray, y: numpy.ndarray, Yf: Optional[numpy.ndarray] = None)
predict(X: numpy.ndarray)
class brainda.algorithms.decomposition.cca.FBTRCAR(filterbank: List[numpy.ndarray], n_components: int = 1, ensemble: bool = True, filterweights: Optional[numpy.ndarray] = None, n_jobs: Optional[int] = None)

Bases: brainda.algorithms.decomposition.base.FilterBankSSVEP, sklearn.base.ClassifierMixin

fit(X: numpy.ndarray, y: numpy.ndarray, Yf: Optional[numpy.ndarray] = None)
predict(X: numpy.ndarray)
class brainda.algorithms.decomposition.cca.FBTtCCA(filterbank: List[numpy.ndarray], n_components: int = 1, filterweights: Optional[numpy.ndarray] = None, n_jobs: Optional[int] = None)

Bases: brainda.algorithms.decomposition.base.FilterBankSSVEP, sklearn.base.ClassifierMixin

fit(X: numpy.ndarray, y: numpy.ndarray, Yf: Optional[numpy.ndarray] = None, y_sub: Optional[numpy.ndarray] = None)
predict(X: numpy.ndarray)
class brainda.algorithms.decomposition.cca.ItCCA(n_components: int = 1, method: str = 'itcca2', n_jobs: Optional[int] = None)

Bases: sklearn.base.BaseEstimator, sklearn.base.TransformerMixin, sklearn.base.ClassifierMixin

fit(X: Optional[numpy.ndarray], y: Optional[numpy.ndarray], Yf: Optional[numpy.ndarray] = None)
predict(X: numpy.ndarray)
transform(X: numpy.ndarray)
class brainda.algorithms.decomposition.cca.MsCCA(n_components: int = 1, n_jobs: Optional[int] = None)

Bases: sklearn.base.BaseEstimator, sklearn.base.TransformerMixin, sklearn.base.ClassifierMixin

Note: MsCCA heavily depends on Yf, thus the phase information should be included when designs Yf.

fit(X: Optional[numpy.ndarray], y: Optional[numpy.ndarray], Yf: Optional[numpy.ndarray] = None)
predict(X: numpy.ndarray)
transform(X: numpy.ndarray)
class brainda.algorithms.decomposition.cca.MsetCCA(n_components: int = 1, method: str = 'msetcca2', n_jobs: Optional[numpy.ndarray] = - 1)

Bases: sklearn.base.BaseEstimator, sklearn.base.TransformerMixin, sklearn.base.ClassifierMixin

fit(X: numpy.ndarray, y: numpy.ndarray, Yf: Optional[numpy.ndarray] = None)
predict(X: numpy.ndarray)
transform(X: numpy.ndarray)
class brainda.algorithms.decomposition.cca.MsetCCAR(n_components: int = 1, n_jobs: Optional[numpy.ndarray] = - 1)

Bases: sklearn.base.BaseEstimator, sklearn.base.TransformerMixin, sklearn.base.ClassifierMixin

fit(X: numpy.ndarray, y: numpy.ndarray, Yf: Optional[numpy.ndarray] = None)
predict(X: numpy.ndarray)
transform(X: numpy.ndarray)
class brainda.algorithms.decomposition.cca.SCCA(n_components: int = 1, n_jobs: Optional[int] = None)

Bases: sklearn.base.BaseEstimator, sklearn.base.TransformerMixin, sklearn.base.ClassifierMixin

fit(X: Optional[numpy.ndarray] = None, y: Optional[numpy.ndarray] = None, Yf: Optional[numpy.ndarray] = None)
predict(X: numpy.ndarray)
transform(X: numpy.ndarray)
class brainda.algorithms.decomposition.cca.TRCA(n_components: int = 1, ensemble: bool = True, n_jobs: Optional[int] = None)

Bases: sklearn.base.BaseEstimator, sklearn.base.TransformerMixin, sklearn.base.ClassifierMixin

fit(X: numpy.ndarray, y: numpy.ndarray, Yf: Optional[numpy.ndarray] = None)
predict(X: numpy.ndarray)
transform(X: numpy.ndarray)
class brainda.algorithms.decomposition.cca.TRCAR(n_components: int = 1, ensemble: bool = True, n_jobs: Optional[int] = None)

Bases: sklearn.base.BaseEstimator, sklearn.base.TransformerMixin, sklearn.base.ClassifierMixin

fit(X: numpy.ndarray, y: numpy.ndarray, Yf: Optional[numpy.ndarray] = None)
predict(X: numpy.ndarray)
transform(X: numpy.ndarray)
class brainda.algorithms.decomposition.cca.TtCCA(n_components: int = 1, n_jobs: Optional[int] = None)

Bases: sklearn.base.BaseEstimator, sklearn.base.TransformerMixin, sklearn.base.ClassifierMixin

fit(X: Optional[numpy.ndarray], y: Optional[numpy.ndarray], Yf: Optional[numpy.ndarray] = None, y_sub: Optional[numpy.ndarray] = None)
predict(X: numpy.ndarray)
transform(X: numpy.ndarray)

TRCA

Task-related Component Analysis (TRCA) and its variants.

class brainda.algorithms.decomposition.trca.FBSSCOR(n_components: Optional[int] = None, max_components: Optional[int] = None, is_ensemble: bool = False, n_jobs: Optional[int] = None, filterbank: Optional[List[numpy.ndarray]] = None, filterweights: Optional[numpy.ndarray] = None)

Bases: brainda.algorithms.decomposition.base.FilterBank

Filter Bank SSCOR method in paper [1]_., [2]_.

filterbank and weights suggested in the paper.

wp = [

[6, 90], [14, 90], [22, 90], [30, 90], [38, 90], [46, 90], [54, 90], [62, 90], [70, 90], [78, 90]

] ws = [

[4, 100], [10, 100], [16, 100], [24, 100], [32, 100], [40, 100], [48, 100], [56, 100], [64, 100], [72, 100]

]

filterweights:

np.arange(1, 11)**(-1.25) + 0.25

References

1

Kumar G R K, Reddy M R. Designing a sum of squared correlations framework for enhancing SSVEP-based BCIs[J]. IEEE Transactions on Neural Systems and Rehabilitation Engineering, 2019, 27(10): 2044-2050.

2

Kumar G R K, Reddy M R. Correction to “Designing a Sum of Squared Correlations Framework for Enhancing SSVEP Based BCIs”[J]. IEEE Transactions on Neural Systems and Rehabilitation Engineering, 2020, 28(4): 1044-1045.

transform(X: numpy.ndarray)
class brainda.algorithms.decomposition.trca.FBTRCA(n_components: Optional[int] = None, max_components: Optional[int] = None, is_ensemble: bool = False, n_jobs: Optional[int] = None, filterbank: Optional[List[numpy.ndarray]] = None, filterweights: Optional[numpy.ndarray] = None)

Bases: brainda.algorithms.decomposition.base.FilterBank

Filter Bank TRCA method in paper [1]_.

Modified from https://github.com/mnakanishi/TRCA-SSVEP/blob/master/src/filterbank.m and https://github.com/mnakanishi/TRCA-SSVEP/blob/master/src/test_trca.m

filterbank and weights suggested in the paper.

wp = [

[6, 90], [14, 90], [22, 90], [30, 90], [38, 90], [46, 90], [54, 90], [62, 90], [70, 90], [78, 90]

] ws = [

[4, 100], [10, 100], [16, 100], [24, 100], [32, 100], [40, 100], [48, 100], [56, 100], [64, 100], [72, 100]

]

filterweights:

np.arange(1, 11)**(-1.25) + 0.25

Notes

nearly the same as matlab code above

References

1

Nakanishi M, Wang Y, Chen X, et al. Enhancing detection of SSVEPs for a high-speed brain speller using task-related component analysis[J]. IEEE Transactions on Biomedical Engineering, 2017, 65(1): 104-112.

transform(X: numpy.ndarray)
class brainda.algorithms.decomposition.trca.SSCOR(n_components: Optional[int] = None, max_components: Optional[int] = None, transform_method: Optional[str] = None, is_ensemble: bool = False, n_jobs: Optional[int] = None)

Bases: sklearn.base.BaseEstimator, sklearn.base.TransformerMixin

fit(X: numpy.ndarray, y: numpy.ndarray)
transform(X: numpy.ndarray)
class brainda.algorithms.decomposition.trca.TRCA(n_components: Optional[int] = None, max_components: Optional[int] = None, transform_method: Optional[str] = None, is_ensemble: bool = False, n_jobs: Optional[int] = None)

Bases: sklearn.base.BaseEstimator, sklearn.base.TransformerMixin

fit(X: numpy.ndarray, y: numpy.ndarray)
transform(X: numpy.ndarray)
brainda.algorithms.decomposition.trca.sscor_feature(W: numpy.ndarray, X: numpy.ndarray, n_components: int = 1) → numpy.ndarray

Return sscor features.

Modified from https://github.com/mnakanishi/TRCA-SSVEP/blob/master/src/test_sscor.m

Parameters

  • W (ndarray) – spatial filters from csp_kernel, shape (n_channels, n_filters)

  • X (ndarray) – eeg data, shape (n_trials, n_channels, n_samples)

  • n_components (int, optional) – the first k components to use, usually even number, by default 1

Returns

features of shape (n_trials, n_components, n_samples)

Return type

ndarray

Raises

ValueError – n_components should less than half of the number of channels

brainda.algorithms.decomposition.trca.sscor_kernel(X: numpy.ndarray, y: Optional[numpy.ndarray] = None, n_jobs: Optional[int] = None) → Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray]

The kernel part in SSCOR algorithm based on paper[1]_., [2]_.

Modified from https://github.com/mnakanishi/TRCA-SSVEP/blob/master/src/train_sscor.m

Parameters

  • X (ndarray) – EEG data assuming removing mean, shape (n_trials, n_channels, n_samples)

  • y (ndarray) – labels, shape (n_trials, ), not used here

  • n_jobs (int, optional) – the number of jobs to use, default None

Returns

  • W (ndarray) – filters, shape (n_channels, n_filters)

  • D (ndarray) – eigenvalues in descending order

  • A (ndarray) – spatial patterns, shape (n_channels, n_filters)

References

1

Kumar G R K, Reddy M R. Designing a sum of squared correlations framework for enhancing SSVEP-based BCIs[J]. IEEE Transactions on Neural Systems and Rehabilitation Engineering, 2019, 27(10): 2044-2050.

2

Kumar G R K, Reddy M R. Correction to “Designing a Sum of Squared Correlations Framework for Enhancing SSVEP Based BCIs”[J]. IEEE Transactions on Neural Systems and Rehabilitation Engineering, 2020, 28(4): 1044-1045.

brainda.algorithms.decomposition.trca.trca_feature(W: numpy.ndarray, X: numpy.ndarray, n_components: int = 1) → numpy.ndarray

Return trca features.

Modified from https://github.com/mnakanishi/TRCA-SSVEP/blob/master/src/test_trca.m

Parameters

  • W (ndarray) – spatial filters from csp_kernel, shape (n_channels, n_filters)

  • X (ndarray) – eeg data, shape (n_trials, n_channels, n_samples)

  • n_components (int, optional) – the first k components to use, usually even number, by default 1

Returns

features of shape (n_trials, n_components, n_samples)

Return type

ndarray

Raises

ValueError – n_components should less than half of the number of channels

brainda.algorithms.decomposition.trca.trca_kernel(X: numpy.ndarray, y: Optional[numpy.ndarray] = None, n_jobs: Optional[int] = None) → Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray]

The kernel part in TRCA algorithm based on paper[1]_.

Modified from https://github.com/mnakanishi/TRCA-SSVEP/blob/master/src/train_trca.m

Parameters

  • X (ndarray) – EEG data assuming removing mean, shape (n_trials, n_channels, n_samples)

  • y (ndarray) – labels, shape (n_trials, ), not used here

  • n_jobs (int, optional) – the number of jobs to use, default None

Returns

  • W (ndarray) – filters, shape (n_channels, n_filters)

  • D (ndarray) – eigenvalues in descending order

  • A (ndarray) – spatial patterns, shape (n_channels, n_filters)

Notes

trca can be used in each class separately without y labels.

References

1

Nakanishi, Masaki, et al. “Enhancing detection of SSVEPs for a high-speed brain speller using task-related component analysis.” IEEE Transactions on Biomedical Engineering 65.1 (2018): 104-112.

Utils

class brainda.algorithms.decomposition.base.FilterBank(base_estimator: sklearn.base.BaseEstimator, filterbank: Optional[List[numpy.ndarray]], n_jobs: Optional[int] = None)

Bases: sklearn.base.BaseEstimator, sklearn.base.TransformerMixin

fit(X: numpy.ndarray, y: Optional[numpy.ndarray] = None, **kwargs)
transform(X: numpy.ndarray, **kwargs)
transform_filterbank(X: numpy.ndarray)
class brainda.algorithms.decomposition.base.FilterBankSSVEP(filterbank: List[numpy.ndarray], base_estimator: sklearn.base.BaseEstimator, filterweights: Optional[numpy.ndarray] = None, n_jobs: Optional[int] = None)

Bases: brainda.algorithms.decomposition.base.FilterBank

Filter bank analysis for SSVEP.

transform(X: numpy.ndarray)
brainda.algorithms.decomposition.base.generate_cca_references(freqs, srate, T, phases: Optional[numpy.ndarray] = None, n_harmonics: int = 1)
brainda.algorithms.decomposition.base.generate_filterbank(passbands: List[Tuple[float, float]], stopbands: List[Tuple[float, float]], srate: int, order: Optional[int] = None, rp: float = 0.5)
brainda.algorithms.decomposition.base.robust_pattern(W: numpy.ndarray, Cx: numpy.ndarray, Cs: numpy.ndarray) → numpy.ndarray

Transform spatial filters to spatial patterns based on paper [1]_.

Parameters

  • W (ndarray) – Spatial filters, shape (n_channels, n_filters).

  • Cx (ndarray) – Covariance matrix of eeg data, shape (n_channels, n_channels).

  • Cs (ndarray) – Covariance matrix of source data, shape (n_channels, n_channels).

Returns

A – Spatial patterns, shape (n_channels, n_patterns), each column is a spatial pattern.

Return type

ndarray

References

1

Haufe, Stefan, et al. “On the interpretation of weight vectors of linear models in multivariate neuroimaging.” Neuroimage 87 (2014): 96-110.

brainda.algorithms.decomposition.base.sign_flip(u, s, vh=None)

Flip signs of SVD or EIG using the method in paper [1]_.

Parameters

  • u (ndarray) – left singular vectors, shape (M, K).

  • s (ndarray) – singular values, shape (K,).

  • vh (ndarray or None) – transpose of right singular vectors, shape (K, N).

Returns

  • u (ndarray) – corrected left singular vectors.

  • s (ndarray) – singular values.

  • vh (ndarray) – transpose of corrected right singular vectors.

References

1

https://www.sandia.gov/~tgkolda/pubs/pubfiles/SAND2007-6422.pdf