244 lines
8.0 KiB
Python
244 lines
8.0 KiB
Python
"""
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The :mod:`sklearn.kernel_approximation` module implements several
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approximate kernel feature maps base on Fourier transforms.
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"""
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# Author: Andreas Mueller <amueller@ais.uni-bonn.de>
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#
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# License: BSD Style.
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import numpy as np
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from .base import BaseEstimator
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from .base import TransformerMixin
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from .utils import check_random_state
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from .utils.extmath import safe_sparse_dot
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class RBFSampler(BaseEstimator, TransformerMixin):
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"""Approximates feature map of an RBF kernel by Monte Carlo approximation
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of its Fourier transform.
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Parameters
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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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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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self.n_components = n_components
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self.random_state = random_state
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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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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 transformer.
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"""
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self.random_state = check_random_state(self.random_state)
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n_features = X.shape[1]
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self.random_weights_ = (np.sqrt(self.gamma) *
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self.random_state.normal(size=(n_features, self.n_components)))
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self.random_offset_ = self.random_state.uniform(0,
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2 * np.pi, size=self.n_components)
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return self
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def transform(self, X, y=None):
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"""Apply the approximate feature map to X.
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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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New 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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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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* np.cos(projection + self.random_offset_))
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class SkewedChi2Sampler(BaseEstimator, TransformerMixin):
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"""Approximates feature map of the "skewed chi-squared" kernel by Monte
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Carlo approximation of its Fourier transform.
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Parameters
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----------
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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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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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self.skewedness = skewedness
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self.n_components = n_components
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self.random_state = random_state
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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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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 transformer.
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"""
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self.random_state = check_random_state(self.random_state)
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n_features = X.shape[1]
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uniform = self.random_state.uniform(size=(n_features,
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self.n_components))
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# transform by inverse CDF of sech
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self.random_weights_ = (1. / np.pi
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* np.log(np.tan(np.pi / 2. * uniform)))
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self.random_offset_ = self.random_state.uniform(0,
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2 * np.pi, size=self.n_components)
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return self
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def transform(self, X, y=None):
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"""Apply the approximate feature map to X.
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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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New 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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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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projection = safe_sparse_dot(np.log(X + self.skewedness),
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self.random_weights_)
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return (np.sqrt(2.) / np.sqrt(self.n_components)
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* np.cos(projection + self.random_offset_))
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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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at regular intervals L.
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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 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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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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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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"""
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def __init__(self, sample_steps=2, sample_interval=None):
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self.sample_steps = sample_steps
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self.sample_interval = sample_interval
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def fit(self, X, y=None):
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"""Set parameters."""
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if self.sample_interval == None:
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# See reference, figure 2 c)
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if self.sample_steps == 1:
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self.sample_interval = 0.8
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elif self.sample_steps == 2:
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self.sample_interval = 0.5
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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 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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"""Apply approximate feature map to X.
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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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Returns
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-------
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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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if (X <= 0).any():
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raise ValueError("Entries of X must be strictly positive.")
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X_new = []
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# zeroth component
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# 1/cosh = sech
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X_new.append(np.sqrt(X * self.sample_interval / np.cosh(0)))
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log_step = self.sample_interval * np.log(X)
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step = 2 * X * self.sample_interval
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for j in xrange(1, self.sample_steps):
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factor = np.sqrt(step / np.cosh(np.pi * j * self.sample_interval))
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X_new.append(factor * np.cos(j * log_step))
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X_new.append(factor * np.sin(j * log_step))
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return np.hstack(X_new)
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