DOC copyedit kernel approximations docstring
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Lars Buitinck
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@ -22,14 +22,20 @@ class RBFSampler(BaseEstimator, TransformerMixin):
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----------
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gamma: float
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parameter of RBF kernel: exp(-gamma * x**2)
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n_components: int
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number of Monte Carlo samples per original feature.
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Equals the dimensionality of the computed feature space.
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Notes
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-----
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For details see "Random Features for Large-Scale Kernel Machines" by A,
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Rahimi and Benjamin Recht for details."""
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random_state : {int, RandomState}, optional
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If int, random_state is the seed used by the random number generator;
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if RandomState instance, random_state is the random number generator.
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References
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----------
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"Random Features for Large-Scale Kernel Machines" by A, Rahimi and Benjamin
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Recht.
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"""
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def __init__(self, gamma=1., n_components=100., random_state=None):
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self.gamma = gamma
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@ -38,17 +44,19 @@ class RBFSampler(BaseEstimator, TransformerMixin):
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def fit(self, X, y=None):
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"""Fit the model with X.
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Samples random projection according to n_features
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Samples random projection according to n_features.
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Parameters
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----------
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X: array-like, shape (n_samples, n_features)
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Training data, where n_samples in the number of samples
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and n_features is the number of features.
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Returns
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-------
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self : object
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Returns the instance itself
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Returns the transformer.
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"""
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self.random_state = check_random_state(self.random_state)
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@ -71,7 +79,7 @@ class RBFSampler(BaseEstimator, TransformerMixin):
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Returns
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-------
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X_new array-like, shape (n_samples, n_components)
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X_new: array-like, shape (n_samples, n_components)
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"""
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projection = safe_sparse_dot(X, self.random_weights_)
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return (np.sqrt(2.) / np.sqrt(self.n_components)
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@ -84,17 +92,21 @@ class SkewedChi2Sampler(BaseEstimator, TransformerMixin):
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Parameters
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----------
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c: float
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skewedness: float
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"skewedness" parameter of the kernel. Needs to be cross-validated.
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n_components: int
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number of Monte Carlo samples per original feature.
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Equals the dimensionality of the computed feature space.
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Notes
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-----
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See "Random Fourier Approximations for Skewed Multiplicative
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Histogram Kernels" by Fuxin Li, Catalin Ionescu and Cristian
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Sminchisescu for details.
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random_state : {int, RandomState}, optional
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If int, random_state is the seed used by the random number generator;
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if RandomState instance, random_state is the random number generator.
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References
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----------
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"Random Fourier Approximations for Skewed Multiplicative Histogram Kernels"
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by Fuxin Li, Catalin Ionescu and Cristian Sminchisescu.
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"""
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def __init__(self, skewedness=1., n_components=100, random_state=None):
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@ -104,17 +116,19 @@ class SkewedChi2Sampler(BaseEstimator, TransformerMixin):
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def fit(self, X, y=None):
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"""Fit the model with X.
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Samples random projection according to n_features
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Samples random projection according to n_features.
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Parameters
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----------
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X: array-like, shape (n_samples, n_features)
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Training data, where n_samples in the number of samples
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and n_features is the number of features.
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Returns
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-------
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self : object
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Returns the instance itself
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Returns the transformer.
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"""
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self.random_state = check_random_state(self.random_state)
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@ -139,7 +153,7 @@ class SkewedChi2Sampler(BaseEstimator, TransformerMixin):
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Returns
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-------
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X_new array-like, shape (n_samples, n_components)
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X_new: array-like, shape (n_samples, n_components)
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"""
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if (X < 0).any():
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raise ValueError("X may not contain entries smaller than zero.")
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@ -153,29 +167,28 @@ class SkewedChi2Sampler(BaseEstimator, TransformerMixin):
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class AdditiveChi2Sampler(BaseEstimator, TransformerMixin):
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"""Approximate feature map for additive chi^2 kernel.
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uses sampling the fourier transform of the kernel characteristic
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Uses sampling the fourier transform of the kernel characteristic
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at regular intervals L.
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Since the kernel that is to be approximated is additive, the
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components of the input vectors can be treated separately.
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Each entry in the original space is transformed into 2n+1
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features, where n is a parameter of the method.
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Usually, n is 1, 2 or 3.
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Since the kernel that is to be approximated is additive, the components of
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the input vectors can be treated separately. Each entry in the original
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space is transformed into 2n+1 features, where n is a parameter of the
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method. Typical values of n include 1, 2 and 3.
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Optimal choices for the sampling interval L for certain
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data ranges can be computed (see the reference).
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The default values should be reasonable.
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Optimal choices for the sampling interval L for certain data ranges can be
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computed (see the reference). The default values should be reasonable.
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Parameters
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----------
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n: int, one of 1, 2 or 3.
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Gives the number of (complex) sampling points.
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L: float, sampling interval
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sample_steps: int, optional
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Gives the number of (complex) sampling points.
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sample_interval: float, optional
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Sampling interval. Must be specified when sample_steps not in {1,2,3}.
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Notes
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-----
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For details on the algorithm see `"Efficient additive kernels via explicit
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feature maps"
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References
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----------
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`"Efficient additive kernels via explicit feature maps"
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<http://eprints.pascal-network.org/archive/00006964/01/vedaldi10.pdf>`_
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Vedaldi, A. and Zisserman, A.
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- Computer Vision and Pattern Recognition 2010
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@ -196,8 +209,8 @@ class AdditiveChi2Sampler(BaseEstimator, TransformerMixin):
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elif self.sample_steps == 3:
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self.sample_interval = 0.4
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else:
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raise ValueError("If n is not in [1, 2, 3], you need"
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"to provide L")
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raise ValueError("If sample_steps is not in [1, 2, 3], you need"
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"to provide sample_interval")
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return self
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def transform(self, X, y=None):
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@ -209,7 +222,7 @@ class AdditiveChi2Sampler(BaseEstimator, TransformerMixin):
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Returns
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-------
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X_new array-like, shape (n_samples, n_features * (2n + 1))
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X_new: array-like, shape (n_samples, n_features * (2n + 1))
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"""
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# check if X has zeros. Doesn't play well with np.log.
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