cca_zoo.nonparametric

class cca_zoo.nonparametric.KCCA(latent_dimensions: int = 1, copy_data=True, random_state=None, c: Iterable[float] | float = None, eps=0.001, kernel: Iterable[str | float | callable] = None, gamma: Iterable[float] = None, degree: Iterable[float] = None, coef0: Iterable[float] = None, kernel_params: Iterable[dict] = None)[source]

A class used to fit KCCA model. This model extends MCCA to nonlinear relationships by using kernel functions on each view.

The objective function of KCCA is:

\[ \begin{align}\begin{aligned}\begin{split}\alpha_{opt}=\underset{\alpha}{\mathrm{argmax}}\{\sum_i\sum_{j\neq i} \alpha_i^TK_i^TK_j\alpha_j \}\\\end{split}\\\text{subject to:}\\c_i\alpha_i^TK_i\alpha_i + (1-c_i)\alpha_i^TK_i^TK_i\alpha_i=1\end{aligned}\end{align} \]

where $K_i$ are the kernel matrices for each view and $c_i$ are the regularization parameters for each view.

Parameters:

latent_dimensions (int, optional) – Number of latent dimensions to use, by default 1
copy_data (bool, optional) – Whether to copy the data, by default True
random_state (int, optional) – Random seed for reproducibility, by default None
c (Union[Iterable[float], float], optional) – Regularization parameter or list of parameters for each view, by default None. If None, it will be set to zero for each view.
eps (float, optional) – Small value to add to the diagonal of the kernel matrices, by default 1e-3
kernel (Iterable[Union[float, callable]], optional) – Kernel function or list of functions for each view, by default None. If None, it will use a linear kernel for each view.
gamma (Iterable[float], optional) – Gamma parameter or list of parameters for the RBF kernel for each view, by default None. Ignored if kernel is not RBF.
degree (Iterable[float], optional) – Degree parameter or list of parameters for the polynomial kernel for each view, by default None. Ignored if kernel is not polynomial.
coef0 (Iterable[float], optional) – Coef0 parameter or list of parameters for the polynomial or sigmoid kernel for each view, by default None. Ignored if kernel is not polynomial or sigmoid.
kernel_params (Iterable[dict], optional) – Additional parameters or list of parameters for the kernel function for each view, by default None.

Examples

>>> from cca_zoo.linear import KCCA
>>> import numpy as np
>>> rng=np.random.RandomState(0)
>>> X1 = rng.random((10,5))
>>> X2 = rng.random((10,5))
>>> X3 = rng.random((10,5))
>>> model = KCCA()
>>> model.fit((X1,X2,X3)).score((X1,X2,X3))
array([0.96893666])

factor_loadings(views: Iterable[ndarray], normalize=True, **kwargs)

Returns the factor loadings for each view

Parameters:

views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –
normalize (bool, optional) – Whether to normalize the factor loadings. Default is True.
kwargs (any additional keyword arguments required by the given model) –

Returns:

factor_loadings

Return type:

list of numpy arrays

fit(views: Iterable[ndarray], y=None, **kwargs)

Fits the model to the given data

Parameters:

views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –
y (None) –
kwargs (any additional keyword arguments required by the given model) –

Returns:

self

Return type:

object

fit_transform(views: Iterable[ndarray], **kwargs)

Fits the model to the given data and returns the transformed views

Parameters:

views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –
kwargs (any additional keyword arguments required by the given model) –

Returns:

transformed_views

Return type:

list of numpy arrays

get_metadata_routing()

Get metadata routing of this object.

Please check User Guide on how the routing mechanism works.

Returns:: routing – A MetadataRequest encapsulating routing information.
Return type:: MetadataRequest

get_params(deep=True)

Get parameters for this estimator.

Parameters:: deep (bool, default=True) – If True, will return the parameters for this estimator and contained subobjects that are estimators.
Returns:: params – Parameter names mapped to their values.
Return type:: dict

pairwise_correlations(views: Iterable[ndarray], **kwargs)

Returns the pairwise correlations between the views in each dimension

Parameters:

views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –
kwargs (any additional keyword arguments required by the given model) –

Returns:

pairwise_correlations

Return type:

numpy array of shape (n_views, n_views, latent_dimensions)

score(views: Iterable[ndarray], y=None, **kwargs)

Returns the average pairwise correlation between the views

Parameters:

views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –
y (None) –
kwargs (any additional keyword arguments required by the given model) –

Returns:

score

Return type:

float

set_fit_request(*, views: bool | None | str = '$UNCHANGED$') → KCCA

Request metadata passed to the fit method.

Note that this method is only relevant if enable_metadata_routing=True (see sklearn.set_config()). Please see User Guide on how the routing mechanism works.

The options for each parameter are:

True: metadata is requested, and passed to fit if provided. The request is ignored if metadata is not provided.
False: metadata is not requested and the meta-estimator will not pass it to fit.
None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.
str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains the existing request. This allows you to change the request for some parameters and not others.

New in version 1.3.

Note

This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside a pipeline.Pipeline. Otherwise it has no effect.

Parameters:: views (str, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED) – Metadata routing for views parameter in fit.
Returns:: self – The updated object.
Return type:: object

set_params(**params)

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Parameters:: **params (dict) – Estimator parameters.
Returns:: self – Estimator instance.
Return type:: estimator instance

set_score_request(*, views: bool | None | str = '$UNCHANGED$') → KCCA

Request metadata passed to the score method.

Note that this method is only relevant if enable_metadata_routing=True (see sklearn.set_config()). Please see User Guide on how the routing mechanism works.

The options for each parameter are:

True: metadata is requested, and passed to score if provided. The request is ignored if metadata is not provided.
False: metadata is not requested and the meta-estimator will not pass it to score.
None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.
str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains the existing request. This allows you to change the request for some parameters and not others.

New in version 1.3.

Note

This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside a pipeline.Pipeline. Otherwise it has no effect.

Parameters:: views (str, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED) – Metadata routing for views parameter in score.
Returns:: self – The updated object.
Return type:: object

set_transform_request(*, views: bool | None | str = '$UNCHANGED$') → KCCA

Request metadata passed to the transform method.

Note that this method is only relevant if enable_metadata_routing=True (see sklearn.set_config()). Please see User Guide on how the routing mechanism works.

The options for each parameter are:

True: metadata is requested, and passed to transform if provided. The request is ignored if metadata is not provided.
False: metadata is not requested and the meta-estimator will not pass it to transform.
None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.
str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains the existing request. This allows you to change the request for some parameters and not others.

New in version 1.3.

Note

This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside a pipeline.Pipeline. Otherwise it has no effect.

Parameters:: views (str, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED) – Metadata routing for views parameter in transform.
Returns:: self – The updated object.
Return type:: object

transform(views: Iterable[ndarray], **kwargs)

Parameters:

views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –
kwargs (any additional keyword arguments required by the given model) –

Returns:

transformed_views

Return type:

list of numpy arrays

class cca_zoo.nonparametric.KGCCA(latent_dimensions: int = 1, copy_data=True, random_state=None, c: Iterable[float] | float = None, kernel: Iterable[float | callable] = None, gamma: Iterable[float] = None, degree: Iterable[float] = None, coef0: Iterable[float] = None, kernel_params: Iterable[dict] = None, view_weights: Iterable[float] = None, eps: float = 1e-06)[source]

A class used to fit KGCCA model. This model extends GCCA to nonlinear relationships by using kernel functions on each view.

The objective function of KGCCA is:

\[\]

alpha_{opt}=underset{alpha}{mathrm{argmax}}{ sum_ialpha_i^TK_i^TT }\

text{subject to:}

T^TT=1

where $K_i$ are the kernel matrices for each view and $T$ is the auxiliary vector.

Parameters:

latent_dimensions (int, optional) – Number of latent dimensions to use, by default 1
copy_data (bool, optional) – Whether to copy the data, by default True
random_state (int, optional) – Random seed for reproducibility, by default None
c (Union[Iterable[float], float], optional) – Regularization parameter or list of parameters for each view, by default None. If None, it will be set to zero for each view.
kernel (Iterable[Union[float, callable]], optional) – Kernel function or list of functions for each view, by default None. If None, it will use a linear kernel for each view.
gamma (Iterable[float], optional) – Gamma parameter or list of parameters for the RBF kernel for each view, by default None. Ignored if kernel is not RBF.
degree (Iterable[float], optional) – Degree parameter or list of parameters for the polynomial kernel for each view, by default None. Ignored if kernel is not polynomial.
coef0 (Iterable[float], optional) – Coef0 parameter or list of parameters for the polynomial or sigmoid kernel for each view, by default None. Ignored if kernel is not polynomial or sigmoid.
kernel_params (Iterable[dict], optional) – Additional parameters or list of parameters for the kernel function for each view, by default None.
view_weights (Iterable[float], optional) – Weights for each view in the objective function, by default None. If None, it will use equal weights for each view.

References

Tenenhaus, Arthur, Cathy Philippe, and Vincent Frouin. “Kernel generalized canonical correlation analysis.” Computational Statistics & Data Analysis 90 (2015): 114-131.

Examples

>>> from cca_zoo.linear import KGCCA
>>> import numpy as np
>>> rng=np.random.RandomState(0)
>>> X1 = rng.random((10,5))
>>> X2 = rng.random((10,5))
>>> X3 = rng.random((10,5))
>>> model = KGCCA()
>>> model.fit((X1,X2,X3)).score((X1,X2,X3))
array([0.97019284])

factor_loadings(views: Iterable[ndarray], normalize=True, **kwargs)

Returns the factor loadings for each view

Parameters:

views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –
normalize (bool, optional) – Whether to normalize the factor loadings. Default is True.
kwargs (any additional keyword arguments required by the given model) –

Returns:

factor_loadings

Return type:

list of numpy arrays

fit(views: Iterable[ndarray], y=None, K=None, **kwargs)

Fits the model to the given data

Parameters:

views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –
y (None) –
kwargs (any additional keyword arguments required by the given model) –

Returns:

self

Return type:

object

fit_transform(views: Iterable[ndarray], **kwargs)

Fits the model to the given data and returns the transformed views

Parameters:

views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –
kwargs (any additional keyword arguments required by the given model) –

Returns:

transformed_views

Return type:

list of numpy arrays

get_metadata_routing()

Get metadata routing of this object.

Please check User Guide on how the routing mechanism works.

Returns:: routing – A MetadataRequest encapsulating routing information.
Return type:: MetadataRequest

get_params(deep=True)

Get parameters for this estimator.

Parameters:: deep (bool, default=True) – If True, will return the parameters for this estimator and contained subobjects that are estimators.
Returns:: params – Parameter names mapped to their values.
Return type:: dict

pairwise_correlations(views: Iterable[ndarray], **kwargs)

Returns the pairwise correlations between the views in each dimension

Parameters:

views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –
kwargs (any additional keyword arguments required by the given model) –

Returns:

pairwise_correlations

Return type:

numpy array of shape (n_views, n_views, latent_dimensions)

score(views: Iterable[ndarray], y=None, **kwargs)

Returns the average pairwise correlation between the views

Parameters:

views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –
y (None) –
kwargs (any additional keyword arguments required by the given model) –

Returns:

score

Return type:

float

set_fit_request(*, K: bool | None | str = '$UNCHANGED$', views: bool | None | str = '$UNCHANGED$') → KGCCA

Request metadata passed to the fit method.

Note that this method is only relevant if enable_metadata_routing=True (see sklearn.set_config()). Please see User Guide on how the routing mechanism works.

The options for each parameter are:

True: metadata is requested, and passed to fit if provided. The request is ignored if metadata is not provided.
False: metadata is not requested and the meta-estimator will not pass it to fit.
None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.
str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains the existing request. This allows you to change the request for some parameters and not others.

New in version 1.3.

Note

This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside a pipeline.Pipeline. Otherwise it has no effect.

Parameters:

K (str, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED) – Metadata routing for K parameter in fit.
views (str, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED) – Metadata routing for views parameter in fit.

Returns:

self – The updated object.

Return type:

object

set_params(**params)

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Parameters:: **params (dict) – Estimator parameters.
Returns:: self – Estimator instance.
Return type:: estimator instance

set_score_request(*, views: bool | None | str = '$UNCHANGED$') → KGCCA

Request metadata passed to the score method.

Note that this method is only relevant if enable_metadata_routing=True (see sklearn.set_config()). Please see User Guide on how the routing mechanism works.

The options for each parameter are:

True: metadata is requested, and passed to score if provided. The request is ignored if metadata is not provided.
False: metadata is not requested and the meta-estimator will not pass it to score.
None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.
str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains the existing request. This allows you to change the request for some parameters and not others.

New in version 1.3.

Note

This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside a pipeline.Pipeline. Otherwise it has no effect.

Parameters:: views (str, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED) – Metadata routing for views parameter in score.
Returns:: self – The updated object.
Return type:: object

set_transform_request(*, views: bool | None | str = '$UNCHANGED$') → KGCCA

Request metadata passed to the transform method.

Note that this method is only relevant if enable_metadata_routing=True (see sklearn.set_config()). Please see User Guide on how the routing mechanism works.

The options for each parameter are:

True: metadata is requested, and passed to transform if provided. The request is ignored if metadata is not provided.
False: metadata is not requested and the meta-estimator will not pass it to transform.
None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.
str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains the existing request. This allows you to change the request for some parameters and not others.

New in version 1.3.

Note

This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside a pipeline.Pipeline. Otherwise it has no effect.

Parameters:: views (str, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED) – Metadata routing for views parameter in transform.
Returns:: self – The updated object.
Return type:: object

transform(views: Iterable[ndarray], **kwargs)

Parameters:

views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –
kwargs (any additional keyword arguments required by the given model) –

Returns:

transformed_views

Return type:

list of numpy arrays

class cca_zoo.nonparametric.KTCCA(latent_dimensions: int = 1, copy_data=True, random_state=None, eps=0.001, c: Iterable[float] | float = None, kernel: Iterable[float | callable] = None, gamma: Iterable[float] = None, degree: Iterable[float] = None, coef0: Iterable[float] = None, kernel_params: Iterable[dict] = None)[source]

A class used to fit KTCCA model. This model extends TCCA to nonlinear relationships by using kernel functions on each view.

The objective function of KTCCA is:

\[ \begin{align}\begin{aligned}\begin{split}\alpha_{opt}=\underset{\alpha}{\mathrm{argmax}}\{ \alpha_1^TK_1^T\otimes \alpha_2^TK_2^T\otimes \cdots \otimes \alpha_m^TK_m^T\alpha \}\\\end{split}\\\text{subject to:}\\c_i\alpha_i^TK_i\alpha_i + (1-c_i)\alpha_i^TK_i^TK_i\alpha_i=1\end{aligned}\end{align} \]

where $K_i$ are the kernel matrices for each view and $c_i$ are the regularization parameters for each view.

References

Kim, Tae-Kyun, Shu-Fai Wong, and Roberto Cipolla. “Tensor canonical correlation analysis for action classification.” 2007 IEEE Conference on Computer Vision and Pattern Recognition. IEEE, 2007

Examples

>>> from cca_zoo.linear import KTCCA
>>> rng=np.random.RandomState(0)
>>> X1 = rng.random((10,5))
>>> X2 = rng.random((10,5))
>>> X3 = rng.random((10,5))
>>> model = KTCCA()
>>> model.fit((X1,X2,X3)).score((X1,X2,X3))
array([1.69896269])

correlations(views: Iterable[ndarray], **kwargs)

Predicts the correlation for the given data using the fit model

Parameters:

views – list/tuple of numpy arrays or array likes with the same number of rows (samples)
kwargs – any additional keyword arguments required by the given model

factor_loadings(views: Iterable[ndarray], normalize=True, **kwargs)

Returns the factor loadings for each view

Parameters:

views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –
normalize (bool, optional) – Whether to normalize the factor loadings. Default is True.
kwargs (any additional keyword arguments required by the given model) –

Returns:

factor_loadings

Return type:

list of numpy arrays

fit(views: Iterable[ndarray], y=None, **kwargs)

Fits the model to the given data

Parameters:

views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –
y (None) –
kwargs (any additional keyword arguments required by the given model) –

Returns:

self

Return type:

object

fit_transform(views: Iterable[ndarray], **kwargs)

Fits the model to the given data and returns the transformed views

Parameters:

views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –
kwargs (any additional keyword arguments required by the given model) –

Returns:

transformed_views

Return type:

list of numpy arrays

get_metadata_routing()

Get metadata routing of this object.

Please check User Guide on how the routing mechanism works.

Returns:: routing – A MetadataRequest encapsulating routing information.
Return type:: MetadataRequest

get_params(deep=True)

Get parameters for this estimator.

Parameters:: deep (bool, default=True) – If True, will return the parameters for this estimator and contained subobjects that are estimators.
Returns:: params – Parameter names mapped to their values.
Return type:: dict

pairwise_correlations(views: Iterable[ndarray], **kwargs)

Returns the pairwise correlations between the views in each dimension

Parameters:

views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –
kwargs (any additional keyword arguments required by the given model) –

Returns:

pairwise_correlations

Return type:

numpy array of shape (n_views, n_views, latent_dimensions)

score(views: Iterable[ndarray], **kwargs)

Returns the higher order correlations in each dimension

Parameters:

views – list/tuple of numpy arrays or array likes with the same number of rows (samples)
kwargs – any additional keyword arguments required by the given model

set_fit_request(*, views: bool | None | str = '$UNCHANGED$') → KTCCA

Request metadata passed to the fit method.

Note that this method is only relevant if enable_metadata_routing=True (see sklearn.set_config()). Please see User Guide on how the routing mechanism works.

The options for each parameter are:

True: metadata is requested, and passed to fit if provided. The request is ignored if metadata is not provided.
False: metadata is not requested and the meta-estimator will not pass it to fit.
None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.
str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains the existing request. This allows you to change the request for some parameters and not others.

New in version 1.3.

Note

This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside a pipeline.Pipeline. Otherwise it has no effect.

Parameters:: views (str, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED) – Metadata routing for views parameter in fit.
Returns:: self – The updated object.
Return type:: object

set_params(**params)

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Parameters:: **params (dict) – Estimator parameters.
Returns:: self – Estimator instance.
Return type:: estimator instance

set_score_request(*, views: bool | None | str = '$UNCHANGED$') → KTCCA

Request metadata passed to the score method.

Note that this method is only relevant if enable_metadata_routing=True (see sklearn.set_config()). Please see User Guide on how the routing mechanism works.

The options for each parameter are:

True: metadata is requested, and passed to score if provided. The request is ignored if metadata is not provided.
False: metadata is not requested and the meta-estimator will not pass it to score.
None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.
str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains the existing request. This allows you to change the request for some parameters and not others.

New in version 1.3.

Note

This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside a pipeline.Pipeline. Otherwise it has no effect.

Parameters:: views (str, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED) – Metadata routing for views parameter in score.
Returns:: self – The updated object.
Return type:: object

set_transform_request(*, views: bool | None | str = '$UNCHANGED$') → KTCCA

Request metadata passed to the transform method.

Note that this method is only relevant if enable_metadata_routing=True (see sklearn.set_config()). Please see User Guide on how the routing mechanism works.

The options for each parameter are:

True: metadata is requested, and passed to transform if provided. The request is ignored if metadata is not provided.
False: metadata is not requested and the meta-estimator will not pass it to transform.
None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.
str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains the existing request. This allows you to change the request for some parameters and not others.

New in version 1.3.

Note

This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside a pipeline.Pipeline. Otherwise it has no effect.

Parameters:: views (str, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED) – Metadata routing for views parameter in transform.
Returns:: self – The updated object.
Return type:: object

transform(views: Iterable[ndarray], **kwargs)

Parameters:

views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –
kwargs (any additional keyword arguments required by the given model) –

Returns:

transformed_views

Return type:

list of numpy arrays

class cca_zoo.nonparametric.NCCA(latent_dimensions: int = 1, copy_data=True, accept_sparse=False, random_state: int | RandomState = None, nearest_neighbors=None, gamma: Iterable[float] = None)[source]

A class used to fit nonparametric (NCCA) model. This model extends CCA to nonlinear relationships by using local linear projections based on nearest neighbors.

Parameters:

latent_dimensions (int, optional) – Number of latent dimensions to use, by default 1
copy_data (bool, optional) – Whether to copy the data, by default True
accept_sparse (bool, optional) – Whether to accept sparse data as input, by default False
random_state (Union[int, np.random.RandomState], optional) – Random seed for reproducibility, by default None
nearest_neighbors (int, optional) – Number of nearest neighbors to use for local linear projections, by default None. If None, it will use the square root of the number of samples.
gamma (Iterable[float], optional) – Bandwidth parameter or list of parameters for the RBF kernel for each view, by default None. If None, it will use the median heuristic.

References

Michaeli, Tomer, Weiran Wang, and Karen Livescu. “Nonparametric canonical correlation analysis.” International conference on machine learning. PMLR, 2016.

Example

>>> from cca_zoo.linear import NCCA
>>> X1 = np.random.rand(10,5)
>>> X2 = np.random.rand(10,5)
>>> model = NCCA()
>>> model.fit((X1,X2)).score((X1,X2))
array([1.])

factor_loadings(views: Iterable[ndarray], normalize=True, **kwargs)

Returns the factor loadings for each view

Parameters:

views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –
normalize (bool, optional) – Whether to normalize the factor loadings. Default is True.
kwargs (any additional keyword arguments required by the given model) –

Returns:

factor_loadings

Return type:

list of numpy arrays

fit(views: Iterable[ndarray], y=None, **kwargs)[source]

Fits the model to the given data

Parameters:

views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –
y (None) –
kwargs (any additional keyword arguments required by the given model) –

Returns:

self

Return type:

object

fit_transform(views: Iterable[ndarray], **kwargs)

Fits the model to the given data and returns the transformed views

Parameters:

views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –
kwargs (any additional keyword arguments required by the given model) –

Returns:

transformed_views

Return type:

list of numpy arrays

get_metadata_routing()

Get metadata routing of this object.

Please check User Guide on how the routing mechanism works.

Returns:: routing – A MetadataRequest encapsulating routing information.
Return type:: MetadataRequest

get_params(deep=True)

Get parameters for this estimator.

Parameters:: deep (bool, default=True) – If True, will return the parameters for this estimator and contained subobjects that are estimators.
Returns:: params – Parameter names mapped to their values.
Return type:: dict

pairwise_correlations(views: Iterable[ndarray], **kwargs)

Returns the pairwise correlations between the views in each dimension

Parameters:

views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –
kwargs (any additional keyword arguments required by the given model) –

Returns:

pairwise_correlations

Return type:

numpy array of shape (n_views, n_views, latent_dimensions)

score(views: Iterable[ndarray], y=None, **kwargs)

Returns the average pairwise correlation between the views

Parameters:

views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –
y (None) –
kwargs (any additional keyword arguments required by the given model) –

Returns:

score

Return type:

float

set_fit_request(*, views: bool | None | str = '$UNCHANGED$') → NCCA

Request metadata passed to the fit method.

Note that this method is only relevant if enable_metadata_routing=True (see sklearn.set_config()). Please see User Guide on how the routing mechanism works.

The options for each parameter are:

True: metadata is requested, and passed to fit if provided. The request is ignored if metadata is not provided.
False: metadata is not requested and the meta-estimator will not pass it to fit.
None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.
str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains the existing request. This allows you to change the request for some parameters and not others.

New in version 1.3.

Note

This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside a pipeline.Pipeline. Otherwise it has no effect.

Parameters:: views (str, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED) – Metadata routing for views parameter in fit.
Returns:: self – The updated object.
Return type:: object

set_params(**params)

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Parameters:: **params (dict) – Estimator parameters.
Returns:: self – Estimator instance.
Return type:: estimator instance

set_score_request(*, views: bool | None | str = '$UNCHANGED$') → NCCA

Request metadata passed to the score method.

Note that this method is only relevant if enable_metadata_routing=True (see sklearn.set_config()). Please see User Guide on how the routing mechanism works.

The options for each parameter are:

True: metadata is requested, and passed to score if provided. The request is ignored if metadata is not provided.
False: metadata is not requested and the meta-estimator will not pass it to score.
None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.
str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains the existing request. This allows you to change the request for some parameters and not others.

New in version 1.3.

Note

This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside a pipeline.Pipeline. Otherwise it has no effect.

Parameters:: views (str, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED) – Metadata routing for views parameter in score.
Returns:: self – The updated object.
Return type:: object

set_transform_request(*, views: bool | None | str = '$UNCHANGED$') → NCCA

Request metadata passed to the transform method.

Note that this method is only relevant if enable_metadata_routing=True (see sklearn.set_config()). Please see User Guide on how the routing mechanism works.

The options for each parameter are:

True: metadata is requested, and passed to transform if provided. The request is ignored if metadata is not provided.
False: metadata is not requested and the meta-estimator will not pass it to transform.
None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.
str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains the existing request. This allows you to change the request for some parameters and not others.

New in version 1.3.

Note

This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside a pipeline.Pipeline. Otherwise it has no effect.

Parameters:: views (str, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED) – Metadata routing for views parameter in transform.
Returns:: self – The updated object.
Return type:: object

transform(views: Iterable[ndarray], **kwargs)[source]

Parameters:

views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –
kwargs (any additional keyword arguments required by the given model) –

Returns:

transformed_views

Return type:

list of numpy arrays