ruckus.base.CompositeRKHS class

class ruckus.base.CompositeRKHS(components, *, copy_X=True)[source]

Bases: ruckus.base.RKHS

Given a sequence of RKHS’s with Hilbert spaces \(H_1\), …, \(H_n\) and feature maps \(\phi_1\), …, \(\phi_n\), their composition lives in the final Hilbert space \(H_n\) but has feature map \(\phi_n \circ \dots \circ \phi_1\) [1]. Correspondingly, a CompositeRKHS class has the shape_out_ of its final component, the shape_in_ of its first component, and transform() is applied to the data by implementing transform sequentially for each of the component spaces. This is useful for building pipelines and deep kernels.

  1. Cho, Y., Lawrence, S. “Kernel Methods for Deep Learning.” Advances in Neural Information Processing Systems 22 (NIPS 2009)

Parameters

  • components (list of RKHS objects) – The component RKHS objects, listed from the first to be applied to the last.

  • copy_X (bool) – Default = True. If True, input X is copied and stored by the model in the X_fit_ attribute. If no further changes will be done to X, setting copy_X=False saves memory by storing a reference.

Parameters

  • shape_in_ (tuple) – The required shape of the input datapoints, aka the shape of the domain space \(X\).

  • shape_out_ (tuple) – The final shape of the transformed datapoints, aka the shape of the Hilbert space \(H\).

  • X_fit_ (numpy.ndarray of shape (n_samples,)+self.shape_in_) – The data which was used to fit the model.

fit(X, y=None)[source]

Fit the model from data in ``X`.

Parameters

X (numpy.ndarray of shape (n_samples, n_features_1,...,n_features_d)) – Training vector, where n_samples is the number of samples and (n_features_1,...,n_features_d) is the shape of the input data. Must be consistent with preprocessing instructions in self.components[0].take and self.components[0].filter.

Returns

The instance itself

Return type

RKHS

fit_transform(X, y=None)[source]

Fit the model from data in X and transform X.

Parameters

X (numpy.ndarray of shape (n_samples, n_features_1,...,n_features_d)) – Training vector, where n_samples is the number of samples and (n_features_1,...,n_features_d) is the shape of the input data. Must be consistent with preprocessing instructions in self.components[0].take and self.components[0].filter.

Returns

The transformed data

Return type

numpy.ndarray of shape (n_samples,)+self.shape_out_

kernel(X, Y=None)[source]

Evaluates the kernel on X and Y (or X and X) by iterating over component embeddings. As such, CompositeRKHS kernels can only be evaluated after fitting to data.

Parameters

  • X (numpy.ndarray of shape (n_samples, n_features_1,...,n_features_d)) – Data vector, where n_samples is the number of samples and (n_features_1,...,n_features_d) is the shape of the input data. These must match self.shape_in_.

  • Y (numpy.ndarray of shape (n_samples, n_features_1,...,n_features_d)) – Default = None. Data vector, where n_samples is the number of samples and (n_features_1,...,n_features_d) is the shape of the input data. These must match self.shape_in_. If None, X is used.

Returns

The matrix K[i,j] = k(X[i],Y[j])

Return type

numpy.ndarray of shape (n_samples_1,n_samples_2)

transform(X)[source]

Transform X.

Parameters

X (numpy.ndarray of shape (n_samples, n_features_1,...,n_features_d)) – Data vector, where n_samples is the number of samples and (n_features_1,...,n_features_d) is the shape of the input data. These must match self.shape_in_.

Returns

The transformed data

Return type

numpy.ndarray of shape (n_samples,)+self.shape_out_