surrogate.nystroem.Nystroem

surrogate.nystroem.Nystroem(kernel='rbf', n_components=100, random_state=None)

Approximate a feature map of a kernel using a subset of data.

The Nystroem method approximates a kernel map using a subset of the training data. It constructs an approximate feature map X \mapsto X' such that X'.dot(X'.T) \approx K(X, X).

This is particularly useful when: * n (samples) is moderate/large: The exact kernel method scales as O(n^3). Nystroem reduces complexity to O(n * n_components^2) for training. * k (features) is large: By setting n_components such that k < n_components << n, it projects high-dimensional data into a manageable feature space where distance calculations are cheaper (if followed by a linear model).

Parameters

Name	Type	Description	Default
kernel	str or callable or Kernel	Kernel map to be approximated. Can be a string (e.g., ‘rbf’), a callable, or a spotoptim.surrogate.kernels.Kernel instance. Defaults to ‘rbf’.	'rbf'
n_components	int	Number of features to construct. This corresponds to the number of samples used to construct the basis. Determines the dimension of the transformed feature space. Defaults to 100.	100
random_state	int, RandomState instance or None	Pseudo-random number generator to control the uniform sampling without replacement of n_components of the training data. Defaults to None.	None

Methods

Name	Description
fit	Fit estimator to data.
fit_transform	Fit to data, then transform it.
transform	Apply feature map to X.

fit

surrogate.nystroem.Nystroem.fit(X, y=None)

Fit estimator to data.

Samples a subset of n_components training points to serve as the basis, computes the kernel matrix on these points, and computes the normalization matrix.

Parameters

Name	Type	Description	Default
X	np.ndarray	Training data, shape (n_samples, n_features).	required
y	np.ndarray	Target values (ignored).	None

Returns

Name	Type	Description
Nystroem	Nystroem	Returns the instance itself.

fit_transform

surrogate.nystroem.Nystroem.fit_transform(X, y=None)

Fit to data, then transform it.

Parameters

Name	Type	Description	Default
X	np.ndarray	Training data.	required
y	np.ndarray	Target values.	None

Returns

Name	Type	Description
	np.ndarray	np.ndarray: Transformed data.

transform

surrogate.nystroem.Nystroem.transform(X)

Apply feature map to X.

Computes the kernel between X and the basis vectors, multiplied by the normalization. No sample reduction happens here; the output has the same number of samples as X.

Parameters

Name	Type	Description	Default
X	np.ndarray	Data to transform, shape (n_samples, n_features).	required

Returns

Name	Type	Description
	np.ndarray	np.ndarray: Transformed data, shape (n_samples, n_components).