Approximate feature map for additive chi2 kernel.
Uses sampling the fourier transform of the kernel characteristic at regular intervals.
Since the kernel that is to be approximated is additive, the components of the input vectors can be treated separately. Each entry in the original space is transformed into 2*sample_steps+1 features, where sample_steps is a parameter of the method. Typical values of sample_steps include 1, 2 and 3.
Optimal choices for the sampling interval for certain data ranges can be computed (see the reference). The default values should be reasonable.
Read more in the :ref:`User Guide <additive_chi_kernel_approx>`.
Parameters ---------- sample_steps : int, optional Gives the number of (complex) sampling points. sample_interval : float, optional Sampling interval. Must be specified when sample_steps not in
,2,3
.
Attributes ---------- sample_interval_ : float Stored sampling interval. Specified as a parameter if sample_steps not in
,2,3
.
Examples -------- >>> from sklearn.datasets import load_digits >>> from sklearn.linear_model import SGDClassifier >>> from sklearn.kernel_approximation import AdditiveChi2Sampler >>> X, y = load_digits(return_X_y=True) >>> chi2sampler = AdditiveChi2Sampler(sample_steps=2) >>> X_transformed = chi2sampler.fit_transform(X, y) >>> clf = SGDClassifier(max_iter=5, random_state=0, tol=1e-3) >>> clf.fit(X_transformed, y) SGDClassifier(max_iter=5, random_state=0) >>> clf.score(X_transformed, y) 0.9499...
Notes ----- This estimator approximates a slightly different version of the additive chi squared kernel then ``metric.additive_chi2`` computes.
See also -------- SkewedChi2Sampler : A Fourier-approximation to a non-additive variant of the chi squared kernel.
sklearn.metrics.pairwise.chi2_kernel : The exact chi squared kernel.
sklearn.metrics.pairwise.additive_chi2_kernel : The exact additive chi squared kernel.
References ---------- See `'Efficient additive kernels via explicit feature maps' <http://www.robots.ox.ac.uk/~vedaldi/assets/pubs/vedaldi11efficient.pdf>`_ A. Vedaldi and A. Zisserman, Pattern Analysis and Machine Intelligence, 2011