B ud!]@sdZddlZddlmZmZddlZddlmZ ddl m Z m Z ddl mZddlmZddlmZdd lmZdd lmZd d d gZdddd ZddZddZdddZd ddZGddde e edZGdd d eZGdd d eZdS)!aRRandom Projection transformers. Random Projections are a simple and computationally efficient way to reduce the dimensionality of the data by trading a controlled amount of accuracy (as additional variance) for faster processing times and smaller model sizes. The dimensions and distribution of Random Projections matrices are controlled so as to preserve the pairwise distances between any two samples of the dataset. The main theoretical result behind the efficiency of random projection is the `Johnson-Lindenstrauss lemma (quoting Wikipedia) `_: In mathematics, the Johnson-Lindenstrauss lemma is a result concerning low-distortion embeddings of points from high-dimensional into low-dimensional Euclidean space. The lemma states that a small set of points in a high-dimensional space can be embedded into a space of much lower dimension in such a way that distances between the points are nearly preserved. The map used for the embedding is at least Lipschitz, and can even be taken to be an orthogonal projection. N)ABCMetaabstractmethod) BaseEstimatorTransformerMixin)check_random_state)safe_sparse_dot)sample_without_replacement)check_is_fitted)DataDimensionalityWarningSparseRandomProjectionGaussianRandomProjectionjohnson_lindenstrauss_min_dimg?)epscCst|}t|}t|dks0t|dkr= 4 log(n_samples) / (eps^2 / 2 - eps^3 / 3) Note that the number of dimensions is independent of the original number of features but instead depends on the size of the dataset: the larger the dataset, the higher is the minimal dimensionality of an eps-embedding. Read more in the :ref:`User Guide `. Parameters ---------- n_samples : int or array-like of int Number of samples that should be a integer greater than 0. If an array is given, it will compute a safe number of components array-wise. eps : float or ndarray of shape (n_components,), dtype=float, default=0.1 Maximum distortion rate in the range (0,1 ) as defined by the Johnson-Lindenstrauss lemma. If an array is given, it will compute a safe number of components array-wise. Returns ------- n_components : int or ndarray of int The minimal number of components to guarantee with good probability an eps-embedding with n_samples. Examples -------- >>> from sklearn.random_projection import johnson_lindenstrauss_min_dim >>> johnson_lindenstrauss_min_dim(1e6, eps=0.5) 663 >>> johnson_lindenstrauss_min_dim(1e6, eps=[0.5, 0.1, 0.01]) array([ 663, 11841, 1112658]) >>> johnson_lindenstrauss_min_dim([1e4, 1e5, 1e6], eps=0.1) array([ 7894, 9868, 11841]) References ---------- .. [1] https://en.wikipedia.org/wiki/Johnson%E2%80%93Lindenstrauss_lemma .. [2] Sanjoy Dasgupta and Anupam Gupta, 1999, "An elementary proof of the Johnson-Lindenstrauss Lemma." http://citeseer.ist.psu.edu/viewdoc/summary?doi=10.1.1.45.3654 grz1The JL bound is defined for eps in ]0, 1[, got %rrz?The JL bound is defined for n_samples greater than zero, got %r)npZasarrayany ValueErrorlogZastypeZint64) n_samplesr denominatorrf/work/yifan.wang/ringdown/master-ringdown-env/lib/python3.7/site-packages/sklearn/random_projection.pyr4sC   cCs8|dkrdt|}n|dks(|dkr4td||S)z.Factorize density check according to Li et al.autorrz)Expected density in range ]0, 1], got: %r)rsqrtr)density n_featuresrrr_check_densitys  rcCs,|dkrtd||dkr(td|dS)z9Factorize argument checking for random matrix generation.rz.n_components must be strictly positive, got %dz,n_features must be strictly positive, got %dN)r) n_componentsrrrr_check_input_sizes  r!cCs4t||t|}|jddt|||fd}|S)abGenerate a dense Gaussian random matrix. The components of the random matrix are drawn from N(0, 1.0 / n_components). Read more in the :ref:`User Guide `. Parameters ---------- n_components : int, Dimensionality of the target projection space. n_features : int, Dimensionality of the original source space. random_state : int, RandomState instance or None, default=None Controls the pseudo random number generator used to generate the matrix at fit time. Pass an int for reproducible output across multiple function calls. See :term:`Glossary `. Returns ------- components : ndarray of shape (n_components, n_features) The generated Gaussian random matrix. See Also -------- GaussianRandomProjection gg?)locscalesize)r!rnormalrr)r r random_staterng componentsrrr_gaussian_random_matrixs r)rc Cst||t||}t|}|dkrP|dd||fdd}dt||Sg}d}|g}xFt|D]:} |||} t|| |d} || || 7}||qhWt |}|jddt |ddd} t j | ||f||fd}td|t||SdS) aGeneralized Achlioptas random sparse matrix for random projection. Setting density to 1 / 3 will yield the original matrix by Dimitris Achlioptas while setting a lower value will yield the generalization by Ping Li et al. If we note :math:`s = 1 / density`, the components of the random matrix are drawn from: - -sqrt(s) / sqrt(n_components) with probability 1 / 2s - 0 with probability 1 - 1 / s - +sqrt(s) / sqrt(n_components) with probability 1 / 2s Read more in the :ref:`User Guide `. Parameters ---------- n_components : int, Dimensionality of the target projection space. n_features : int, Dimensionality of the original source space. density : float or 'auto', default='auto' Ratio of non-zero component in the random projection matrix in the range `(0, 1]` If density = 'auto', the value is set to the minimum density as recommended by Ping Li et al.: 1 / sqrt(n_features). Use density = 1 / 3.0 if you want to reproduce the results from Achlioptas, 2001. random_state : int, RandomState instance or None, default=None Controls the pseudo random number generator used to generate the matrix at fit time. Pass an int for reproducible output across multiple function calls. See :term:`Glossary `. Returns ------- components : {ndarray, sparse matrix} of shape (n_components, n_features) The generated Gaussian random matrix. Sparse matrix will be of CSR format. See Also -------- SparseRandomProjection References ---------- .. [1] Ping Li, T. Hastie and K. W. Church, 2006, "Very Sparse Random Projections". https://web.stanford.edu/~hastie/Papers/Ping/KDD06_rp.pdf .. [2] D. Achlioptas, 2001, "Database-friendly random projections", http://www.cs.ucsc.edu/~optas/papers/jl.pdf rg?rr)r&)r$)shapeN) r!rrZbinomialrrranger appendZ concatenater$spZ csr_matrix) r rrr&r'r(indicesoffsetZindptr_Z n_nonzero_iZ indices_idatarrr_sparse_random_matrixs*=      r2c@sFeZdZdZedddddddZed d Zdd d Zd dZdS)BaseRandomProjectionz~Base class for random projections. Warning: This class should not be used directly. Use derived classes instead. rg?FN)r dense_outputr&cCs||_||_||_||_dS)N)r rr4r&)selfr rr4r&rrr__init__,szBaseRandomProjection.__init__cCsdS)aGenerate the random projection matrix. Parameters ---------- n_components : int, Dimensionality of the target projection space. n_features : int, Dimensionality of the original source space. Returns ------- components : {ndarray, sparse matrix} of shape (n_components, n_features) The generated random matrix. Sparse matrix will be of CSR format. Nr)r5r rrrr_make_random_matrix5sz(BaseRandomProjection._make_random_matrixcCs|j|ddgd}|j\}}|jdkr|t||jd|_|jdkrXtd|j||jfq|j|krtd|j||j|fnB|jdkrtd |jn |j|krtd ||jft |j|_| |j||_ |j j|j|fkst d |S) aGenerate a sparse random projection matrix. Parameters ---------- X : {ndarray, sparse matrix} of shape (n_samples, n_features) Training set: only the shape is used to find optimal random matrix dimensions based on the theory referenced in the afore mentioned papers. y : Ignored Not used, present here for API consistency by convention. Returns ------- self : object BaseRandomProjection class instance. csrcsc) accept_sparser)rrrzIeps=%f and n_samples=%d lead to a target dimension of %d which is invalidzseps=%f and n_samples=%d lead to a target dimension of %d which is larger than the original space with n_features=%dz+n_components must be greater than 0, got %szThe number of components is higher than the number of features: n_features < n_components (%s < %s).The dimensionality of the problem will not be reduced.zLAn error has occurred the self.components_ matrix has not the proper shape.) _validate_datar*r rrZ n_components_rwarningswarnr r7 components_AssertionError)r5XyrrrrrfitIs4       zBaseRandomProjection.fitcCsht||j|ddgdd}|jd|jjdkrPtd|jd|jjdft||jj|jd}|S)aProject the data by using matrix product with the random matrix. Parameters ---------- X : {ndarray, sparse matrix} of shape (n_samples, n_features) The input data to project into a smaller dimensional space. Returns ------- X_new : {ndarray, sparse matrix} of shape (n_samples, n_components) Projected array. r8r9F)r:resetrz^Impossible to perform projection:X at fit stage had a different number of features. (%s != %s))r4)r r;r*r>rrTr4)r5r@ZX_newrrr transforms zBaseRandomProjection.transform)r)N) __name__ __module__ __qualname____doc__rr6r7rBrErrrrr3%s   Dr3) metaclasscs2eZdZdZd dddfdd Zdd ZZS) r a Reduce dimensionality through Gaussian random projection. The components of the random matrix are drawn from N(0, 1 / n_components). Read more in the :ref:`User Guide `. .. versionadded:: 0.13 Parameters ---------- n_components : int or 'auto', default='auto' Dimensionality of the target projection space. n_components can be automatically adjusted according to the number of samples in the dataset and the bound given by the Johnson-Lindenstrauss lemma. In that case the quality of the embedding is controlled by the ``eps`` parameter. It should be noted that Johnson-Lindenstrauss lemma can yield very conservative estimated of the required number of components as it makes no assumption on the structure of the dataset. eps : float, default=0.1 Parameter to control the quality of the embedding according to the Johnson-Lindenstrauss lemma when `n_components` is set to 'auto'. The value should be strictly positive. Smaller values lead to better embedding and higher number of dimensions (n_components) in the target projection space. random_state : int, RandomState instance or None, default=None Controls the pseudo random number generator used to generate the projection matrix at fit time. Pass an int for reproducible output across multiple function calls. See :term:`Glossary `. Attributes ---------- n_components_ : int Concrete number of components computed when n_components="auto". components_ : ndarray of shape (n_components, n_features) Random matrix used for the projection. n_features_in_ : int Number of features seen during :term:`fit`. .. versionadded:: 0.24 feature_names_in_ : ndarray of shape (`n_features_in_`,) Names of features seen during :term:`fit`. Defined only when `X` has feature names that are all strings. .. versionadded:: 1.0 See Also -------- SparseRandomProjection : Reduce dimensionality through sparse random projection. Examples -------- >>> import numpy as np >>> from sklearn.random_projection import GaussianRandomProjection >>> rng = np.random.RandomState(42) >>> X = rng.rand(25, 3000) >>> transformer = GaussianRandomProjection(random_state=rng) >>> X_new = transformer.fit_transform(X) >>> X_new.shape (25, 2759) rg?N)rr&cstj||d|ddS)NT)r rr4r&)superr6)r5r rr&) __class__rrr6s z!GaussianRandomProjection.__init__cCst|j}t|||dS)a Generate the random projection matrix. Parameters ---------- n_components : int, Dimensionality of the target projection space. n_features : int, Dimensionality of the original source space. Returns ------- components : {ndarray, sparse matrix} of shape (n_components, n_features) The generated random matrix. Sparse matrix will be of CSR format. )r&)rr&r))r5r rr&rrrr7s z,GaussianRandomProjection._make_random_matrix)r)rFrGrHrIr6r7 __classcell__rr)rLrr sGcs6eZdZdZd dddddfdd Zd d ZZS) r aeReduce dimensionality through sparse random projection. Sparse random matrix is an alternative to dense random projection matrix that guarantees similar embedding quality while being much more memory efficient and allowing faster computation of the projected data. If we note `s = 1 / density` the components of the random matrix are drawn from: - -sqrt(s) / sqrt(n_components) with probability 1 / 2s - 0 with probability 1 - 1 / s - +sqrt(s) / sqrt(n_components) with probability 1 / 2s Read more in the :ref:`User Guide `. .. versionadded:: 0.13 Parameters ---------- n_components : int or 'auto', default='auto' Dimensionality of the target projection space. n_components can be automatically adjusted according to the number of samples in the dataset and the bound given by the Johnson-Lindenstrauss lemma. In that case the quality of the embedding is controlled by the ``eps`` parameter. It should be noted that Johnson-Lindenstrauss lemma can yield very conservative estimated of the required number of components as it makes no assumption on the structure of the dataset. density : float or 'auto', default='auto' Ratio in the range (0, 1] of non-zero component in the random projection matrix. If density = 'auto', the value is set to the minimum density as recommended by Ping Li et al.: 1 / sqrt(n_features). Use density = 1 / 3.0 if you want to reproduce the results from Achlioptas, 2001. eps : float, default=0.1 Parameter to control the quality of the embedding according to the Johnson-Lindenstrauss lemma when n_components is set to 'auto'. This value should be strictly positive. Smaller values lead to better embedding and higher number of dimensions (n_components) in the target projection space. dense_output : bool, default=False If True, ensure that the output of the random projection is a dense numpy array even if the input and random projection matrix are both sparse. In practice, if the number of components is small the number of zero components in the projected data will be very small and it will be more CPU and memory efficient to use a dense representation. If False, the projected data uses a sparse representation if the input is sparse. random_state : int, RandomState instance or None, default=None Controls the pseudo random number generator used to generate the projection matrix at fit time. Pass an int for reproducible output across multiple function calls. See :term:`Glossary `. Attributes ---------- n_components_ : int Concrete number of components computed when n_components="auto". components_ : sparse matrix of shape (n_components, n_features) Random matrix used for the projection. Sparse matrix will be of CSR format. density_ : float in range 0.0 - 1.0 Concrete density computed from when density = "auto". n_features_in_ : int Number of features seen during :term:`fit`. .. versionadded:: 0.24 feature_names_in_ : ndarray of shape (`n_features_in_`,) Names of features seen during :term:`fit`. Defined only when `X` has feature names that are all strings. .. versionadded:: 1.0 See Also -------- GaussianRandomProjection : Reduce dimensionality through Gaussian random projection. References ---------- .. [1] Ping Li, T. Hastie and K. W. Church, 2006, "Very Sparse Random Projections". https://web.stanford.edu/~hastie/Papers/Ping/KDD06_rp.pdf .. [2] D. Achlioptas, 2001, "Database-friendly random projections", https://users.soe.ucsc.edu/~optas/papers/jl.pdf Examples -------- >>> import numpy as np >>> from sklearn.random_projection import SparseRandomProjection >>> rng = np.random.RandomState(42) >>> X = rng.rand(25, 3000) >>> transformer = SparseRandomProjection(random_state=rng) >>> X_new = transformer.fit_transform(X) >>> X_new.shape (25, 2759) >>> # very few components are non-zero >>> np.mean(transformer.components_ != 0) 0.0182... rg?FN)rrr4r&cstj||||d||_dS)N)r rr4r&)rKr6r)r5r rrr4r&)rLrrr6s zSparseRandomProjection.__init__cCs*t|j}t|j||_t|||j|dS)a Generate the random projection matrix Parameters ---------- n_components : int Dimensionality of the target projection space. n_features : int Dimensionality of the original source space. Returns ------- components : {ndarray, sparse matrix} of shape (n_components, n_features) The generated random matrix. Sparse matrix will be of CSR format. )rr&)rr&rrZdensity_r2)r5r rr&rrrr7s z*SparseRandomProjection._make_random_matrix)r)rFrGrHrIr6r7rMrr)rLrr sw )N)rN) rIr<abcrrnumpyrZ scipy.sparsesparser-baserrutilsrZ utils.extmathrZ utils.randomr Zutils.validationr exceptionsr __all__rrr!r)r2r3r r rrrrs,      S  ( bi