ó ‡ˆ\c@ sdZddlmZddlZddlZddlZddlmZddl m Z ddl m Z m Z dd lmZdd lmZmZd dee dd „Zd dee d „Zdd ee dd„Zde dd„Zde fd„ƒYZdS(sn Robust location and covariance estimators. Here are implemented estimators that are resistant to outliers. iÿÿÿÿ(tdivisionN(tlinalg(tchi2i(tempirical_covariancetEmpiricalCovariancei(t fast_logdet(tcheck_random_statet check_arrayic C sFtj|ƒ}t|ƒ}t||d|d|d|d|d|ƒS(s)C_step procedure described in [Rouseeuw1984]_ aiming at computing MCD. Parameters ---------- X : array-like, shape (n_samples, n_features) Data set in which we look for the n_support observations whose scatter matrix has minimum determinant. n_support : int, > n_samples / 2 Number of observations to compute the robust estimates of location and covariance from. remaining_iterations : int, optional Number of iterations to perform. According to [Rouseeuw1999]_, two iterations are sufficient to get close to the minimum, and we never need more than 30 to reach convergence. initial_estimates : 2-tuple, optional Initial estimates of location and shape from which to run the c_step procedure: - initial_estimates[0]: an initial location estimate - initial_estimates[1]: an initial covariance estimate verbose : boolean, optional Verbose mode. cov_computation_method : callable, default empirical_covariance The function which will be used to compute the covariance. Must return shape (n_features, n_features) random_state : int, RandomState instance or None, optional (default=None) If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by `np.random`. Returns ------- location : array-like, shape (n_features,) Robust location estimates. covariance : array-like, shape (n_features, n_features) Robust covariance estimates. support : array-like, shape (n_samples,) A mask for the `n_support` observations whose scatter matrix has minimum determinant. References ---------- .. [Rouseeuw1999] A Fast Algorithm for the Minimum Covariance Determinant Estimator, 1999, American Statistical Association and the American Society for Quality, TECHNOMETRICS tremaining_iterationstinitial_estimatestverbosetcov_computation_methodt random_state(tnptasarrayRt_c_step(tXt n_supportRR R R R ((sClib/python2.7/site-packages/sklearn/covariance/robust_covariance.pytc_steps ;  cC s |j\}}tj} tj|dtƒ} |dkrSt| |j|ƒ| log(previous_det) (%.15f > %.15f). You may want to try with a higher value of support_fraction (current value: %.3f).s$Maximum number of iterations reached(tshapeR tinftzerostbooltNonetTruet permutationRtpinvhtdottsumtargsorttmeanRtisinftallclosetwarningstwarntRuntimeWarning(RRR RR R R t n_samplest n_featurestdisttsupporttlocationt covariancet precisiont X_centeredt X_supporttdett previous_dettprevious_locationtprevious_covariancetprevious_supportt previous_disttresults((sClib/python2.7/site-packages/sklearn/covariance/robust_covariance.pyRasl          "   *    cC sÆt|ƒ}|j\}} t|tjƒr6t} nKt|tƒret} |} | djd}ntd|t |ƒfƒ‚g} | sÕx¬t |ƒD]4} | j t ||d|d|d|d|ƒƒqšWngxdt |ƒD]V} | d| | d| f}| j t ||d|d|d|d|d|ƒƒqâWt | Œ\}}}}}tj|ƒ| }tj|ƒ|}tj|ƒ|}tj|ƒ|}tj|ƒ|}||||fS( s) Finds the best pure subset of observations to compute MCD from it. The purpose of this function is to find the best sets of n_support observations with respect to a minimization of their covariance matrix determinant. Equivalently, it removes n_samples-n_support observations to construct what we call a pure data set (i.e. not containing outliers). The list of the observations of the pure data set is referred to as the `support`. Starting from a random support, the pure data set is found by the c_step procedure introduced by Rousseeuw and Van Driessen in [RV]_. Parameters ---------- X : array-like, shape (n_samples, n_features) Data (sub)set in which we look for the n_support purest observations. n_support : int, [(n + p + 1)/2] < n_support < n The number of samples the pure data set must contain. n_trials : int, nb_trials > 0 or 2-tuple Number of different initial sets of observations from which to run the algorithm. Instead of giving a number of trials to perform, one can provide a list of initial estimates that will be used to iteratively run c_step procedures. In this case: - n_trials[0]: array-like, shape (n_trials, n_features) is the list of `n_trials` initial location estimates - n_trials[1]: array-like, shape (n_trials, n_features, n_features) is the list of `n_trials` initial covariances estimates select : int, int > 0 Number of best candidates results to return. n_iter : int, nb_iter > 0 Maximum number of iterations for the c_step procedure. (2 is enough to be close to the final solution. "Never" exceeds 20). verbose : boolean, default False Control the output verbosity. cov_computation_method : callable, default empirical_covariance The function which will be used to compute the covariance. Must return shape (n_features, n_features) random_state : int, RandomState instance or None, optional (default=None) If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by `np.random`. See Also --------- c_step Returns ------- best_locations : array-like, shape (select, n_features) The `select` location estimates computed from the `select` best supports found in the data set (`X`). best_covariances : array-like, shape (select, n_features, n_features) The `select` covariance estimates computed from the `select` best supports found in the data set (`X`). best_supports : array-like, shape (select, n_samples) The `select` best supports found in the data set (`X`). References ---------- .. [RV] A Fast Algorithm for the Minimum Covariance Determinant Estimator, 1999, American Statistical Association and the American Society for Quality, TECHNOMETRICS isEInvalid 'n_trials' parameter, expected tuple or integer, got %s (%s)RR R R iR (RRt isinstancetnumberstIntegraltFalsettupleRt TypeErrorttypetrangetappendRtzipR RR(RRtn_trialstselecttn_iterR R R R&R'trun_from_estimatestestimates_listt all_estimatestjR t all_locs_subt all_covs_subt all_dets_subtall_supports_subt all_ds_subt index_besttbest_locationstbest_covariancest best_supportstbest_ds((sClib/python2.7/site-packages/sklearn/covariance/robust_covariance.pytselect_candidates¸s@P    c0 C sît|ƒ}t|ddddƒ}|j\}}|dkrcttjd||dƒƒ}nt||ƒ}|dkr1||kr¥tjtj|ƒƒ}||||| }tj |tj |ƒkƒd} d||| || j ƒ} tj |dt ƒ} || } t| tjtj| ƒdƒ| `. Parameters ---------- X : array-like, shape (n_samples, n_features) The data matrix, with p features and n samples. support_fraction : float, 0 < support_fraction < 1 The proportion of points to be included in the support of the raw MCD estimate. Default is None, which implies that the minimum value of support_fraction will be used within the algorithm: `[n_sample + n_features + 1] / 2`. cov_computation_method : callable, default empirical_covariance The function which will be used to compute the covariance. Must return shape (n_features, n_features) random_state : int, RandomState instance or None, optional (default=None) If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by `np.random`. Notes ----- The FastMCD algorithm has been introduced by Rousseuw and Van Driessen in "A Fast Algorithm for the Minimum Covariance Determinant Estimator, 1999, American Statistical Association and the American Society for Quality, TECHNOMETRICS". The principle is to compute robust estimates and random subsets before pooling them into a larger subsets, and finally into the full data set. Depending on the size of the initial sample, we have one, two or three such computation levels. Note that only raw estimates are returned. If one is interested in the correction and reweighting steps described in [RouseeuwVan]_, see the MinCovDet object. References ---------- .. [RouseeuwVan] A Fast Algorithm for the Minimum Covariance Determinant Estimator, 1999, American Statistical Association and the American Society for Quality, TECHNOMETRICS .. [Butler1993] R. W. Butler, P. L. Davies and M. Jhun, Asymptotics For The Minimum Covariance Determinant Estimator, The Annals of Statistics, 1993, Vol. 21, No. 3, 1385-1400 Returns ------- location : array-like, shape (n_features,) Robust location of the data. covariance : array-like, shape (n_features, n_features) Robust covariance of the features. support : array-like, type boolean, shape (n_samples,) A mask of the observations that have been used to compute the robust location and covariance estimates of the data set. tensure_min_samplesit estimatortfast_mcdgà?iiRRiôi,i RARBR R iÜR@iN( RRRRtintR tceiltsorttraveltwheretminR RRRRtabsRtvartarrayRRRRtonesRtfloattmaxt MemoryErrorR=RQtarange(0Rtsupport_fractionR R R&R'RtX_sortedtdifft halves_startR*R)R-R+R,R(t n_subsetstn_samples_subsetstsamples_shuffleth_subsett n_trials_tott n_best_subR@t n_best_tottall_best_locationstall_best_covariancestit low_boundt high_boundtcurrent_subsettbest_locations_subtbest_covariances_subt_t subset_slicetn_samples_mergedth_mergedt n_best_mergedt selectiontlocations_mergedtcovariances_mergedtsupports_mergedtdtlocations_fulltcovariances_fullt supports_fulltn_besttlocations_besttcovariances_best((sClib/python2.7/site-packages/sklearn/covariance/robust_covariance.pyRT4sÎC  $  " #"% %                                  t MinCovDetcB sMeZdZeeƒZeeddd„Z dd„Z d„Z d„Z RS(s5Minimum Covariance Determinant (MCD): robust estimator of covariance. The Minimum Covariance Determinant covariance estimator is to be applied on Gaussian-distributed data, but could still be relevant on data drawn from a unimodal, symmetric distribution. It is not meant to be used with multi-modal data (the algorithm used to fit a MinCovDet object is likely to fail in such a case). One should consider projection pursuit methods to deal with multi-modal datasets. Read more in the :ref:`User Guide `. Parameters ---------- store_precision : bool Specify if the estimated precision is stored. assume_centered : bool If True, the support of the robust location and the covariance estimates is computed, and a covariance estimate is recomputed from it, without centering the data. Useful to work with data whose mean is significantly equal to zero but is not exactly zero. If False, the robust location and covariance are directly computed with the FastMCD algorithm without additional treatment. support_fraction : float, 0 < support_fraction < 1 The proportion of points to be included in the support of the raw MCD estimate. Default is None, which implies that the minimum value of support_fraction will be used within the algorithm: [n_sample + n_features + 1] / 2 random_state : int, RandomState instance or None, optional (default=None) If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by `np.random`. Attributes ---------- raw_location_ : array-like, shape (n_features,) The raw robust estimated location before correction and re-weighting. raw_covariance_ : array-like, shape (n_features, n_features) The raw robust estimated covariance before correction and re-weighting. raw_support_ : array-like, shape (n_samples,) A mask of the observations that have been used to compute the raw robust estimates of location and shape, before correction and re-weighting. location_ : array-like, shape (n_features,) Estimated robust location covariance_ : array-like, shape (n_features, n_features) Estimated robust covariance matrix precision_ : array-like, shape (n_features, n_features) Estimated pseudo inverse matrix. (stored only if store_precision is True) support_ : array-like, shape (n_samples,) A mask of the observations that have been used to compute the robust estimates of location and shape. dist_ : array-like, shape (n_samples,) Mahalanobis distances of the training set (on which `fit` is called) observations. Examples -------- >>> import numpy as np >>> from sklearn.covariance import MinCovDet >>> from sklearn.datasets import make_gaussian_quantiles >>> real_cov = np.array([[.8, .3], ... [.3, .4]]) >>> np.random.seed(0) >>> X = np.random.multivariate_normal(mean=[0, 0], ... cov=real_cov, ... size=500) >>> cov = MinCovDet(random_state=0).fit(X) >>> cov.covariance_ # doctest: +ELLIPSIS array([[0.7411..., 0.2535...], [0.2535..., 0.3053...]]) >>> cov.location_ array([0.0813... , 0.0427...]) References ---------- .. [Rouseeuw1984] `P. J. Rousseeuw. Least median of squares regression. J. Am Stat Ass, 79:871, 1984.` .. [Rousseeuw] `A Fast Algorithm for the Minimum Covariance Determinant Estimator, 1999, American Statistical Association and the American Society for Quality, TECHNOMETRICS` .. [ButlerDavies] `R. W. Butler, P. L. Davies and M. Jhun, Asymptotics For The Minimum Covariance Determinant Estimator, The Annals of Statistics, 1993, Vol. 21, No. 3, 1385-1400` cC s(||_||_||_||_dS(N(tstore_precisiontassume_centeredRcR (tselfR‡RˆRcR ((sClib/python2.7/site-packages/sklearn/covariance/robust_covariance.pyt__init__is   c C s_t|ddddƒ}t|jƒ}|j\}}tjtj|j|ƒƒdkj ƒ|krvt j dƒnt |d|j d|jd |ƒ\}}}} |jr tj|ƒ}|j||d tƒ}tj|ƒ} tj tj|| ƒ|d ƒ} n||_||_||_||_||_| |_|j|ƒ|j|ƒ|S( s¡Fits a Minimum Covariance Determinant with the FastMCD algorithm. Parameters ---------- X : array-like, shape = [n_samples, n_features] Training data, where n_samples is the number of samples and n_features is the number of features. y not used, present for API consistence purpose. Returns ------- self : object RRiRSR†g:Œ0âŽyE>sAThe covariance matrix associated to your dataset is not full rankRcR R Rˆi(RRR RRtsvdvalsR RtTRR#R$RTRct_nonrobust_covarianceRˆRRRt raw_location_traw_covariance_t raw_support_t location_tsupport_tdist_tcorrect_covariancetreweight_covariance( R‰RtyR R&R't raw_locationtraw_covariancet raw_supporttraw_distR,((sClib/python2.7/site-packages/sklearn/covariance/robust_covariance.pytfitps00   %        cC st|jƒ}tj|jƒ}||krQtj|jdƒrQtdƒ‚ntj|jƒt |j dƒj dƒ}|j|}|j|_|S(sNApply a correction to raw Minimum Covariance Determinant estimates. Correction using the empirical correction factor suggested by Rousseeuw and Van Driessen in [RVD]_. Parameters ---------- data : array-like, shape (n_samples, n_features) The data matrix, with p features and n samples. The data set must be the one which was used to compute the raw estimates. References ---------- .. [RVD] `A Fast Algorithm for the Minimum Covariance Determinant Estimator, 1999, American Statistical Association and the American Society for Quality, TECHNOMETRICS` Returns ------- covariance_corrected : array-like, shape (n_features, n_features) Corrected robust covariance estimate. isYThe covariance matrix of the support data is equal to 0, try to increase support_fractionigà?( tlenR“R RR’R"Rt ValueErrortmedianRRtisf(R‰tdataR&Rt correctiontcovariance_corrected((sClib/python2.7/site-packages/sklearn/covariance/robust_covariance.pyR”¡s!, c C sú|j\}}|jt|ƒjdƒk}|jrHtj|ƒ}n||jdƒ}|j||d|jƒ}tj|dt ƒ}t ||<|j |ƒ||_ ||_ ||j }tjtj||jƒƒ|dƒ|_|||fS(sRe-weight raw Minimum Covariance Determinant estimates. Re-weight observations using Rousseeuw's method (equivalent to deleting outlying observations from the data set before computing location and covariance estimates) described in [RVDriessen]_. Parameters ---------- data : array-like, shape (n_samples, n_features) The data matrix, with p features and n samples. The data set must be the one which was used to compute the raw estimates. References ---------- .. [RVDriessen] `A Fast Algorithm for the Minimum Covariance Determinant Estimator, 1999, American Statistical Association and the American Society for Quality, TECHNOMETRICS` Returns ------- location_reweighted : array-like, shape (n_features, ) Re-weighted robust location estimate. covariance_reweighted : array-like, shape (n_features, n_features) Re-weighted robust covariance estimate. support_reweighted : array-like, type boolean, shape (n_samples,) A mask of the observations that have been used to compute the re-weighted robust location and covariance estimates. gš™™™™™™?iRˆRi(RR“RRŸRˆR RR RRRt_set_covarianceR‘R’RRt get_precision( R‰R R&R'tmasktlocation_reweightedtcovariance_reweightedtsupport_reweightedR-((sClib/python2.7/site-packages/sklearn/covariance/robust_covariance.pyR•Ès #      %N( t__name__t __module__t__doc__t staticmethodRRRR9RRŠR›R”R•(((sClib/python2.7/site-packages/sklearn/covariance/robust_covariance.pyR†sd  1 '(R«t __future__RR#R7tnumpyR tscipyRt scipy.statsRtRRt utils.extmathRtutilsRRRR9RRRQRTR†(((sClib/python2.7/site-packages/sklearn/covariance/robust_covariance.pyts.     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