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kernel_approximation.cpython-35.pyc
��(X8F � @ s d Z d d l Z d d l Z d d l j Z d d l m Z d d l m Z d d l m Z d d l m Z m Z m Z d d l m Z d d l m Z d d l m Z Gd d � d e e � Z Gd d � d e e � Z Gd d � d e e � Z Gd d � d e e � Z d S)z The :mod:`sklearn.kernel_approximation` module implements several approximate kernel feature maps base on Fourier transforms. � N)�svd� )� BaseEstimator)�TransformerMixin)� check_array�check_random_state�as_float_array)�safe_sparse_dot)�check_is_fitted)�pairwise_kernelsc @ sI e Z d Z d Z d d d d d � Z d d d � Z d d d � Z d S) � RBFSamplera� Approximates feature map of an RBF kernel by Monte Carlo approximation of its Fourier transform. It implements a variant of Random Kitchen Sinks.[1] Read more in the :ref:`User Guide <rbf_kernel_approx>`. Parameters ---------- gamma : float Parameter of RBF kernel: exp(-gamma * x^2) n_components : int Number of Monte Carlo samples per original feature. Equals the dimensionality of the computed feature space. random_state : {int, RandomState}, optional If int, random_state is the seed used by the random number generator; if RandomState instance, random_state is the random number generator. Notes ----- See "Random Features for Large-Scale Kernel Machines" by A. Rahimi and Benjamin Recht. [1] "Weighted Sums of Random Kitchen Sinks: Replacing minimization with randomization in learning" by A. Rahimi and Benjamin Recht. (http://people.eecs.berkeley.edu/~brecht/papers/08.rah.rec.nips.pdf) g �?�d Nc C s | | _ | | _ | | _ d S)N)�gamma� n_components� random_state)�selfr r r � r �/kernel_approximation.py�__init__8 s zRBFSampler.__init__c C s� t | d d �} t | j � } | j d } t j d | j � | j d | | j f � | _ | j d d t j d | j �| _ | S)a� Fit the model with X. Samples random projection according to n_features. Parameters ---------- X : {array-like, sparse matrix}, shape (n_samples, n_features) Training data, where n_samples in the number of samples and n_features is the number of features. Returns ------- self : object Returns the transformer. � accept_sparse�csrr � �sizer ) r r r �shape�np�sqrtr Znormalr �random_weights_�uniform�pi�random_offset_)r �X�yr � n_featuresr r r �fit= s zRBFSampler.fitc C su t | d � t | d d �} t | | j � } | | j 7} t j | | � | t j d � t j | j � 9} | S)ap Apply the approximate feature map to X. Parameters ---------- X : {array-like, sparse matrix}, shape (n_samples, n_features) New data, where n_samples in the number of samples and n_features is the number of features. Returns ------- X_new : array-like, shape (n_samples, n_components) r r r g @) r r r r r r �cosr r )r r r! � projectionr r r � transformY s #zRBFSampler.transform)�__name__� __module__� __qualname__�__doc__r r# r& r r r r r s r c @ sI e Z d Z d Z d d d d d � Z d d d � Z d d d � Z d S) �SkewedChi2Samplera. Approximates feature map of the "skewed chi-squared" kernel by Monte Carlo approximation of its Fourier transform. Read more in the :ref:`User Guide <skewed_chi_kernel_approx>`. Parameters ---------- skewedness : float "skewedness" parameter of the kernel. Needs to be cross-validated. n_components : int number of Monte Carlo samples per original feature. Equals the dimensionality of the computed feature space. random_state : {int, RandomState}, optional If int, random_state is the seed used by the random number generator; if RandomState instance, random_state is the random number generator. References ---------- See "Random Fourier Approximations for Skewed Multiplicative Histogram Kernels" by Fuxin Li, Catalin Ionescu and Cristian Sminchisescu. See also -------- AdditiveChi2Sampler : A different approach for approximating an additive variant of the chi squared kernel. sklearn.metrics.pairwise.chi2_kernel : The exact chi squared kernel. g �?r Nc C s | | _ | | _ | | _ d S)N)� skewednessr r )r r, r r r r r r � s zSkewedChi2Sampler.__init__c C s� t | � } t | j � } | j d } | j d | | j f � } d t j t j t j t j d | � � | _ | j d d t j d | j �| _ | S)a� Fit the model with X. Samples random projection according to n_features. Parameters ---------- X : array-like, shape (n_samples, n_features) Training data, where n_samples in the number of samples and n_features is the number of features. Returns ------- self : object Returns the transformer. r r g �?g @r r ) r r r r r r r r �log�tanr r )r r r! r r" r r r r r# � s 1zSkewedChi2Sampler.fitc C s� t | d � t | d d �} t | d d �} | d k j � rO t d � � | | j 7} t j | | � t | | j � } | | j 7} t j | | � | t j d � t j | j � 9} | S)a_ Apply the approximate feature map to X. Parameters ---------- X : array-like, shape (n_samples, n_features) New data, where n_samples in the number of samples and n_features is the number of features. Returns ------- X_new : array-like, shape (n_samples, n_components) r �copyTFr z,X may not contain entries smaller than zero.g @)r r r �any� ValueErrorr, r r- r r r r$ r r )r r r! r% r r r r& � s #zSkewedChi2Sampler.transform)r' r( r) r* r r# r& r r r r r+ p s r+ c @ s^ e Z d Z d Z d d d d � Z d d d � Z d d d � Z d d � Z d d � Z d S)�AdditiveChi2Samplera} 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 {1,2,3}. 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 r Nc C s | | _ | | _ d S)N)� sample_steps�sample_interval)r r3 r4 r r r r � s z AdditiveChi2Sampler.__init__c C s� t | d d �} | j d k r� | j d k r< d | _ q� | j d k rW d | _ q� | j d k rr d | _ q� t d � � n | j | _ | S) zSet parameters.r r Nr g�������?r g �?� g�������?zHIf sample_steps is not in [1, 2, 3], you need to provide sample_interval)r r4 r3 �sample_interval_r1 )r r r! r r r r# s zAdditiveChi2Sampler.fitc C s� d } t | d d | �t | d d �} t j | � } | rI | j n | d k j � rg t d � � | rv | j n | j } | | � S)a� Apply approximate feature map to X. Parameters ---------- X : {array-like, sparse matrix}, shape = (n_samples, n_features) Returns ------- X_new : {array, sparse matrix}, shape = (n_samples, n_features * (2*sample_steps + 1)) Whether the return value is an array of sparse matrix depends on the type of the input X. zO%(name)s is not fitted. Call fit to set the parameters before calling transformr6 �msgr r r z"Entries of X must be non-negative.) r r �spZissparse�datar0 r1 �_transform_sparse�_transform_dense)r r r! r7 �sparseZtransfr r r r& s ! z AdditiveChi2Sampler.transformc C s1 | d k } | | } t j | � } t j | | j � | | <| g } | j t j | � } d | | j } x� t d | j � D]� } t j | t j t j | | j � � } t j | � } | t j | | � | | <| j | � t j | � } | t j | | � | | <| j | � q� Wt j | � S)Ng r r ) r Z zeros_liker r6 r- �ranger3 �coshr r$ �append�sin�hstack) r r Znon_zeroZX_nz�X_step�X_new� log_step_nz�step_nz�j� factor_nzr r r r; 2 s" ! z$AdditiveChi2Sampler._transform_densec C s� | j j � } | j j � } t j | j | j � } t j | | | f d | j d | j d d �} | g } | j t j | j � } d | j | j } x� t d | j � D]� } t j | t j t j | | j � � } | t j | | � } t j | | | f d | j d | j d d �} | j | � | t j | | � } t j | | | f d | j d | j d d �} | j | � q� Wt j | � S)Nr �dtyper/ Fr r )�indicesr/ �indptrr r r9 r6 r8 Z csr_matrixr rH r- r= r3 r> r r$ r? r@ rA ) r r rI rJ Z data_steprB rC rD rE rF rG r r r r: L s( ! z%AdditiveChi2Sampler._transform_sparse) r' r( r) r* r r# r& r; r: r r r r r2 � s - r2 c @ s^ e Z d Z d Z d d d d d d d d d � Z d d d � Z d d � Z d d � Z d S)�Nystroema Approximate a kernel map using a subset of the training data. Constructs an approximate feature map for an arbitrary kernel using a subset of the data as basis. Read more in the :ref:`User Guide <nystroem_kernel_approx>`. Parameters ---------- kernel : string or callable, default="rbf" Kernel map to be approximated. A callable should accept two arguments and the keyword arguments passed to this object as kernel_params, and should return a floating point number. n_components : int Number of features to construct. How many data points will be used to construct the mapping. gamma : float, default=None Gamma parameter for the RBF, polynomial, exponential chi2 and sigmoid kernels. Interpretation of the default value is left to the kernel; see the documentation for sklearn.metrics.pairwise. Ignored by other kernels. degree : float, default=3 Degree of the polynomial kernel. Ignored by other kernels. coef0 : float, default=1 Zero coefficient for polynomial and sigmoid kernels. Ignored by other kernels. kernel_params : mapping of string to any, optional Additional parameters (keyword arguments) for kernel function passed as callable object. random_state : {int, RandomState}, optional If int, random_state is the seed used by the random number generator; if RandomState instance, random_state is the random number generator. Attributes ---------- components_ : array, shape (n_components, n_features) Subset of training points used to construct the feature map. component_indices_ : array, shape (n_components) Indices of ``components_`` in the training set. normalization_ : array, shape (n_components, n_components) Normalization matrix needed for embedding. Square root of the kernel matrix on ``components_``. References ---------- * Williams, C.K.I. and Seeger, M. "Using the Nystroem method to speed up kernel machines", Advances in neural information processing systems 2001 * T. Yang, Y. Li, M. Mahdavi, R. Jin and Z. Zhou "Nystroem Method vs Random Fourier Features: A Theoretical and Empirical Comparison", Advances in Neural Information Processing Systems 2012 See also -------- RBFSampler : An approximation to the RBF kernel using random Fourier features. sklearn.metrics.pairwise.kernel_metrics : List of built-in kernels. ZrbfNr r5 r c C sC | | _ | | _ | | _ | | _ | | _ | | _ | | _ d S)N)�kernelr �coef0�degree� kernel_paramsr r )r rL r rM rN rO r r r r r r � s zNystroem.__init__c C s t | d d �} t | j � } | j d } | j | k rS | } t j d � n | j } t | | � } | j | � } | d | � } | | } t | d | j d d | j � �} t | � \ } } } t j | d � } t j | d t j | � | � | _ | | _ | | _ | S) a Fit estimator to data. Samples a subset of training points, computes kernel on these and computes normalization matrix. Parameters ---------- X : array-like, shape=(n_samples, n_feature) Training data. r r r z�n_components > n_samples. This is not possible. n_components was set to n_samples, which results in inefficient evaluation of the full kernel.N�metric� filter_paramsTg�-���q=g �?)r r r r r �warnings�warn�minZ permutationr rL �_get_kernel_paramsr r Zmaximum�dotr �normalization_� components_Zcomponent_indices_) r r r! ZrndZ n_samplesr ZindsZ basis_indsZbasisZ basis_kernel�U�S�Vr r r r# � s( & z Nystroem.fitc C se t | d � t | d d �} | j � } t | | j d | j d d | �} t j | | j j � S)a� Apply feature map to X. Computes an approximate feature map using the kernel between some training points and X. Parameters ---------- X : array-like, shape=(n_samples, n_features) Data to transform. Returns ------- X_transformed : array, shape=(n_samples, n_components) Transformed data. rX r r rP rQ T) r r rU r rX rL r rV rW �T)r r rO Zembeddedr r r r& � s zNystroem.transformc C sU | j } | d k r i } t | j � sQ | j | d <| j | d <| j | d <| S)Nr rN rM )rO �callablerL r rN rM )r Zparamsr r r rU s zNystroem._get_kernel_params)r' r( r) r* r r# r& rU r r r r rK i s H * rK )r* rR Znumpyr Z scipy.sparser< r8 Z scipy.linalgr �baser r Zutilsr r r Z utils.extmathr Zutils.validationr Zmetrics.pairwiser r r+ r2 rK r r r r �<module> s X^�
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kernel_approximation.cpython-35.opt-1.pyc
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