pyrfm.random_feature.OrthogonalRandomFeature¶
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class
pyrfm.random_feature.OrthogonalRandomFeature(n_components=100, gamma=0.5, distribution='gaussian', random_fourier=True, use_offset=False, random_state=None)[source]¶ Bases:
sklearn.base.BaseEstimator,sklearn.base.TransformerMixinApproximates feature map of the RBF or dot kernel by Orthogonal Random Feature map.
- Parameters
n_components (int (default=100)) – Number of Monte Carlo samples per original features. Equals the dimensionality of the computed (mapped) feature space. If n_components is not a n-tuple of n_features, it is automatically changed to the smallest n-tuple of the n_features that is bigger than n_features, which is bigger than n_components. That is, ceil(n_components/n_features)*n_features.
gamma (float (default=0.5)) – Bandwidth parameter. gamma = 1/2sigma^2, where sigma is a std parameter for the Gaussian distribution.
distribution (str or function (default="gaussian")) – A function for sampling random bases. Its arguments must be random_state and size. For str, “gaussian” (or “normal”), “rademacher”, “laplace”, or “uniform” can be used.
random_fourier (boolean (default=True)) – Whether to approximate the RBF kernel or not. If True, this class samples random_offset_ in the fit method and computes the cosine of structured_matrix-feature_vector product + random_offset_ in transform. If False, OrthogonalRandomFeature does not sample it and computes just structured_matrix-feature_vector product (i.e., approximates dot product kernel).
use_offset (bool (default=False)) – If True, Z(x) = (cos(w_1x+b_1), cos(w_2x+b_2), … , cos(w_Dx+b_D), where w is random_weights and b is offset (D=n_components). If False, Z(x) = (cos(w_1x), …, cos(w_{D/2}x), sin(w_1x), …, sin(w_{D/2}x)).
random_state (int, RandomState instance or None, optional (default=None)) – If int, random_state is the seed used by the random number generator; If np.RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random.
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random_weights_¶ - Type
array, shape (n_features, n_components) (use_offset=True)
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or(n_components/2, n_features) (otherwise)¶ The sampled basis.
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random_offset_¶ The sampled offset vector. If use_offset=False, random_offset_=None.
- Type
array or None, shape (n_components, )
References
[1] Orthogonal Random Features. Felix Xinnan Yu, Ananda Theertha Suresh, Krzysztof Choromanski, Daniel Holtmann-Rice, and Sanjiv Kumar. In NIPS 2016. (https://arxiv.org/pdf/1610.09072.pdf)
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fit(X, y=None)[source]¶ Generate random weights according to n_features.
- Parameters
X ({array-like, sparse matrix}, shape (n_samples, n_features)) – Training data, where n_samples is the number of samples and n_features is the number of features.
- Returns
self – Returns the transformer.
- Return type
object
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fit_transform(X, y=None, **fit_params)¶ Fit to data, then transform it.
Fits transformer to X and y with optional parameters fit_params and returns a transformed version of X.
- Parameters
X (numpy array of shape [n_samples, n_features]) – Training set.
y (numpy array of shape [n_samples]) – Target values.
- Returns
X_new – Transformed array.
- Return type
numpy array of shape [n_samples, n_features_new]
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get_params(deep=True)¶ Get parameters for this estimator.
- Parameters
deep (boolean, optional) – 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
mapping of string to any
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set_params(**params)¶ Set the parameters of this estimator.
The method works on simple estimators as well as on nested objects (such as pipelines). The latter have parameters of the form
<component>__<parameter>so that it’s possible to update each component of a nested object.- Returns
- Return type
self
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transform(X)[source]¶ Apply the approximate feature map to X.
- Parameters
X ({array-like, sparse matrix}, shape (n_samples, n_features)) – New data, where n_samples is the number of samples and n_features is the number of features.
- Returns
X_new
- Return type
array-like, shape (n_samples, n_components)