ML之KMeans：利用KMeans算法對Boston房價數(shù)據(jù)集(兩特征+歸一化)進(jìn)行二聚類分析

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目錄

利用KMeans算法對Boston房價數(shù)據(jù)集(兩特征+歸一化)進(jìn)行二聚類分析

設(shè)計思路

輸出結(jié)果

核心代碼

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相關(guān)文章
ML之KMeans：利用KMeans算法對Boston房價數(shù)據(jù)集(兩特征+歸一化)進(jìn)行二聚類分析
ML之KMeans：利用KMeans算法對Boston房價數(shù)據(jù)集(兩特征+歸一化)進(jìn)行二聚類分析實現(xiàn)
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利用KMeans算法對Boston房價數(shù)據(jù)集(兩特征+歸一化)進(jìn)行二聚類分析

設(shè)計思路

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輸出結(jié)果

train_boston_data.shape (1460, 81)Id MSSubClass MSZoning ... SaleType SaleCondition SalePrice 0 1 60 RL ... WD Normal 208500 1 2 20 RL ... WD Normal 181500 2 3 60 RL ... WD Normal 223500 3 4 70 RL ... WD Abnorml 140000 4 5 60 RL ... WD Normal 250000[5 rows x 81 columns] train_t.head() LotFrontage GarageArea SalePrice 0 65.0 548 208500 1 80.0 460 181500 2 68.0 608 223500 3 60.0 642 140000 4 84.0 836 250000 after scale,train_t.head() LotFrontage GarageArea SalePrice 0 0.207668 0.386460 0.276159 1 0.255591 0.324401 0.240397 2 0.217252 0.428773 0.296026 3 0.191693 0.452750 0.185430 4 0.268371 0.589563 0.331126LotFrontage GarageArea 0 0.207668 0.386460 1 0.255591 0.324401 2 0.217252 0.428773 3 0.191693 0.452750 4 0.268371 0.589563Id MSSubClass LotFrontage ... MoSold YrSold SalePrice Id 1.000000 0.011156 -0.010601 ... 0.021172 0.000712 -0.021917 MSSubClass 0.011156 1.000000 -0.386347 ... -0.013585 -0.021407 -0.084284 LotFrontage -0.010601 -0.386347 1.000000 ... 0.011200 0.007450 0.351799 LotArea -0.033226 -0.139781 0.426095 ... 0.001205 -0.014261 0.263843 OverallQual -0.028365 0.032628 0.251646 ... 0.070815 -0.027347 0.790982 OverallCond 0.012609 -0.059316 -0.059213 ... -0.003511 0.043950 -0.077856 YearBuilt -0.012713 0.027850 0.123349 ... 0.012398 -0.013618 0.522897 YearRemodAdd -0.021998 0.040581 0.088866 ... 0.021490 0.035743 0.507101 MasVnrArea -0.050298 0.022936 0.193458 ... -0.005965 -0.008201 0.477493 BsmtFinSF1 -0.005024 -0.069836 0.233633 ... -0.015727 0.014359 0.386420 BsmtFinSF2 -0.005968 -0.065649 0.049900 ... -0.015211 0.031706 -0.011378 BsmtUnfSF -0.007940 -0.140759 0.132644 ... 0.034888 -0.041258 0.214479 TotalBsmtSF -0.015415 -0.238518 0.392075 ... 0.013196 -0.014969 0.613581 1stFlrSF 0.010496 -0.251758 0.457181 ... 0.031372 -0.013604 0.605852 2ndFlrSF 0.005590 0.307886 0.080177 ... 0.035164 -0.028700 0.319334 LowQualFinSF -0.044230 0.046474 0.038469 ... -0.022174 -0.028921 -0.025606 GrLivArea 0.008273 0.074853 0.402797 ... 0.050240 -0.036526 0.708624 BsmtFullBath 0.002289 0.003491 0.100949 ... -0.025361 0.067049 0.227122 BsmtHalfBath -0.020155 -0.002333 -0.007234 ... 0.032873 -0.046524 -0.016844 FullBath 0.005587 0.131608 0.198769 ... 0.055872 -0.019669 0.560664 HalfBath 0.006784 0.177354 0.053532 ... -0.009050 -0.010269 0.284108 BedroomAbvGr 0.037719 -0.023438 0.263170 ... 0.046544 -0.036014 0.168213 KitchenAbvGr 0.002951 0.281721 -0.006069 ... 0.026589 0.031687 -0.135907 TotRmsAbvGrd 0.027239 0.040380 0.352096 ... 0.036907 -0.034516 0.533723 Fireplaces -0.019772 -0.045569 0.266639 ... 0.046357 -0.024096 0.466929 GarageYrBlt 0.000072 0.085072 0.070250 ... 0.005337 -0.001014 0.486362 GarageCars 0.016570 -0.040110 0.285691 ... 0.040522 -0.039117 0.640409 GarageArea 0.017634 -0.098672 0.344997 ... 0.027974 -0.027378 0.623431 WoodDeckSF -0.029643 -0.012579 0.088521 ... 0.021011 0.022270 0.324413 OpenPorchSF -0.000477 -0.006100 0.151972 ... 0.071255 -0.057619 0.315856 EnclosedPorch 0.002889 -0.012037 0.010700 ... -0.028887 -0.009916 -0.128578 3SsnPorch -0.046635 -0.043825 0.070029 ... 0.029474 0.018645 0.044584 ScreenPorch 0.001330 -0.026030 0.041383 ... 0.023217 0.010694 0.111447 PoolArea 0.057044 0.008283 0.206167 ... -0.033737 -0.059689 0.092404 MiscVal -0.006242 -0.007683 0.003368 ... -0.006495 0.004906 -0.021190 MoSold 0.021172 -0.013585 0.011200 ... 1.000000 -0.145721 0.046432 YrSold 0.000712 -0.021407 0.007450 ... -0.145721 1.000000 -0.028923 SalePrice -0.021917 -0.084284 0.351799 ... 0.046432 -0.028923 1.000000[38 rows x 38 columns] k_means_cluster_centers [[0.1938454 0.21080405][0.25140958 0.44595543]] k_means_labels_unique [0 1] 0 [1 1 1 ... 0 0 0] 0 [1 1 1 ... 0 0 0] [False False False ... True True True] 1 [1 1 1 ... 0 0 0] 1 [1 1 1 ... 0 0 0] [ True True True ... False False False]

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核心代碼

class KMeans Found at: sklearn.cluster._kmeansclass KMeans(TransformerMixin, ClusterMixin, BaseEstimator):"""K-Means clustering.Read more in the :ref:`User Guide <k_means>`.Parameters----------n_clusters : int, default=8The number of clusters to form as well as the number ofcentroids to generate.init : {'k-means++', 'random', ndarray, callable}, default='k-means++'Method for initialization:'k-means++' : selects initial cluster centers for k-meanclustering in a smart way to speed up convergence. See sectionNotes in k_init for more details.'random': choose `n_clusters` observations (rows) at random from datafor the initial centroids.If an ndarray is passed, it should be of shape (n_clusters, n_features)and gives the initial centers.If a callable is passed, it should take arguments X, n_clusters and arandom state and return an initialization.n_init : int, default=10Number of time the k-means algorithm will be run with differentcentroid seeds. The final results will be the best output ofn_init consecutive runs in terms of inertia.max_iter : int, default=300Maximum number of iterations of the k-means algorithm for asingle run.tol : float, default=1e-4Relative tolerance with regards to Frobenius norm of the differencein the cluster centers of two consecutive iterations to declareconvergence.It's not advised to set `tol=0` since convergence might never bedeclared due to rounding errors. Use a very small number instead.precompute_distances : {'auto', True, False}, default='auto'Precompute distances (faster but takes more memory).'auto' : do not precompute distances if n_samples * n_clusters > 12million. This corresponds to about 100MB overhead per job usingdouble precision.True : always precompute distances.False : never precompute distances... deprecated:: 0.23'precompute_distances' was deprecated in version 0.22 and will beremoved in 0.25. It has no effect.verbose : int, default=0Verbosity mode.random_state : int, RandomState instance, default=NoneDetermines random number generation for centroid initialization. Usean int to make the randomness deterministic.See :term:`Glossary <random_state>`.copy_x : bool, default=TrueWhen pre-computing distances it is more numerically accurate to centerthe data first. If copy_x is True (default), then the original data isnot modified. If False, the original data is modified, and put backbefore the function returns, but small numerical differences may beintroduced by subtracting and then adding the data mean. Note that ifthe original data is not C-contiguous, a copy will be made even ifcopy_x is False. If the original data is sparse, but not in CSR format,a copy will be made even if copy_x is False.n_jobs : int, default=NoneThe number of OpenMP threads to use for the computation. Parallelism issample-wise on the main cython loop which assigns each sample to itsclosest center.``None`` or ``-1`` means using all processors... deprecated:: 0.23``n_jobs`` was deprecated in version 0.23 and will be removed in0.25.algorithm : {"auto", "full", "elkan"}, default="auto"K-means algorithm to use. The classical EM-style algorithm is "full".The "elkan" variation is more efficient on data with well-definedclusters, by using the triangle inequality. However it's more memoryintensive due to the allocation of an extra array of shape(n_samples, n_clusters).For now "auto" (kept for backward compatibiliy) chooses "elkan" but itmight change in the future for a better heuristic... versionchanged:: 0.18Added Elkan algorithmAttributes----------cluster_centers_ : ndarray of shape (n_clusters, n_features)Coordinates of cluster centers. If the algorithm stops before fullyconverging (see ``tol`` and ``max_iter``), these will not beconsistent with ``labels_``.labels_ : ndarray of shape (n_samples,)Labels of each pointinertia_ : floatSum of squared distances of samples to their closest cluster center.n_iter_ : intNumber of iterations run.See also--------MiniBatchKMeansAlternative online implementation that does incremental updatesof the centers positions using mini-batches.For large scale learning (say n_samples > 10k) MiniBatchKMeans isprobably much faster than the default batch implementation.Notes-----The k-means problem is solved using either Lloyd's or Elkan's algorithm.The average complexity is given by O(k n T), were n is the number ofsamples and T is the number of iteration.The worst case complexity is given by O(n^(k+2/p)) withn = n_samples, p = n_features. (D. Arthur and S. Vassilvitskii,'How slow is the k-means method?' SoCG2006)In practice, the k-means algorithm is very fast (one of the fastestclustering algorithms available), but it falls in local minima. That's whyit can be useful to restart it several times.If the algorithm stops before fully converging (because of ``tol`` or``max_iter``), ``labels_`` and ``cluster_centers_`` will not be consistent,i.e. the ``cluster_centers_`` will not be the means of the points in eachcluster. Also, the estimator will reassign ``labels_`` after the lastiteration to make ``labels_`` consistent with ``predict`` on the trainingset.Examples-------->>> from sklearn.cluster import KMeans>>> import numpy as np>>> X = np.array([[1, 2], [1, 4], [1, 0],... [10, 2], [10, 4], [10, 0]])>>> kmeans = KMeans(n_clusters=2, random_state=0).fit(X)>>> kmeans.labels_array([1, 1, 1, 0, 0, 0], dtype=int32)>>> kmeans.predict([[0, 0], [12, 3]])array([1, 0], dtype=int32)>>> kmeans.cluster_centers_array([[10., 2.],[ 1., 2.]])"""@_deprecate_positional_argsdef __init__(self, n_clusters=8, *, init='k-means++', n_init=10, max_iter=300, tol=1e-4, precompute_distances='deprecated', verbose=0, random_state=None, copy_x=True, n_jobs='deprecated', algorithm='auto'):self.n_clusters = n_clustersself.init = initself.max_iter = max_iterself.tol = tolself.precompute_distances = precompute_distancesself.n_init = n_initself.verbose = verboseself.random_state = random_stateself.copy_x = copy_xself.n_jobs = n_jobsself.algorithm = algorithmdef _check_test_data(self, X):X = check_array(X, accept_sparse='csr', dtype=[np.float64, np.float32], order='C', accept_large_sparse=False)n_samples, n_features = X.shapeexpected_n_features = self.cluster_centers_.shape[1]if not n_features == expected_n_features:raise ValueError("Incorrect number of features. ""Got %d features, expected %d" % (n_features, expected_n_features))return Xdef fit(self, X, y=None, sample_weight=None):"""Compute k-means clustering.Parameters----------X : {array-like, sparse matrix} of shape (n_samples, n_features)Training instances to cluster. It must be noted that the datawill be converted to C ordering, which will cause a memorycopy if the given data is not C-contiguous.If a sparse matrix is passed, a copy will be made if it's not inCSR format.y : IgnoredNot used, present here for API consistency by convention.sample_weight : array-like of shape (n_samples,), default=NoneThe weights for each observation in X. If None, all observationsare assigned equal weight... versionadded:: 0.20Returns-------selfFitted estimator."""random_state = check_random_state(self.random_state)if self.precompute_distances != 'deprecated':warnings.warn("'precompute_distances' was deprecated in version ""0.23 and will be removed in 0.25. It has no ""effect", FutureWarning)if self.n_jobs != 'deprecated':warnings.warn("'n_jobs' was deprecated in version 0.23 and will be"" removed in 0.25.", FutureWarning)self._n_threads = self.n_jobselse:self._n_threads = Noneself._n_threads = _openmp_effective_n_threads(self._n_threads)n_init = self.n_initif n_init <= 0:raise ValueError("Invalid number of initializations."" n_init=%d must be bigger than zero." % n_init)if self.max_iter <= 0:raise ValueError('Number of iterations should be a positive number,'' got %d instead' % self.max_iter)X = self._validate_data(X, accept_sparse='csr', dtype=[np.float64, np.float32], order='C', copy=self.copy_x, accept_large_sparse=False)# verify that the number of samples given is larger than kif _num_samples(X) < self.n_clusters:raise ValueError("n_samples=%d should be >= n_clusters=%d" % (_num_samples(X), self.n_clusters))tol = _tolerance(X, self.tol)# Validate init arrayinit = self.initif hasattr(init, '__array__'):init = check_array(init, dtype=X.dtype.type, copy=True, order='C')_validate_center_shape(X, self.n_clusters, init)if n_init != 1:warnings.warn('Explicit initial center position passed: ''performing only one init in k-means instead of n_init=%d' % n_init, RuntimeWarning, stacklevel=2)n_init = 1 # subtract of mean of x for more accurate distance computationsif not sp.issparse(X):X_mean = X.mean(axis=0) # The copy was already done aboveX -= X_meanif hasattr(init, '__array__'):init -= X_mean# precompute squared norms of data pointsx_squared_norms = row_norms(X, squared=True)best_labels, best_inertia, best_centers = None, None, Nonealgorithm = self.algorithmif algorithm == "elkan" and self.n_clusters == 1:warnings.warn("algorithm='elkan' doesn't make sense for a single ""cluster. Using 'full' instead.", RuntimeWarning)algorithm = "full"if algorithm == "auto":algorithm = "full" if self.n_clusters == 1 else "elkan"if algorithm == "full":kmeans_single = _kmeans_single_lloydelif algorithm == "elkan":kmeans_single = _kmeans_single_elkanelse:raise ValueError("Algorithm must be 'auto', 'full' or 'elkan', got"" {}".format(str(algorithm))) # seeds for the initializations of the kmeans runs.seeds = random_state.randint(np.iinfo(np.int32).max, size=n_init)for seed in seeds:# run a k-means oncelabels, inertia, centers, n_iter_ = kmeans_single(X, sample_weight, self.n_clusters, max_iter=self.max_iter, init=init, verbose=self.verbose, tol=tol, x_squared_norms=x_squared_norms, random_state=seed, n_threads=self._n_threads)# determine if these results are the best so farif best_inertia is None or inertia < best_inertia:best_labels = labels.copy()best_centers = centers.copy()best_inertia = inertiabest_n_iter = n_iter_if not sp.issparse(X):if not self.copy_x:X += X_meanbest_centers += X_meandistinct_clusters = len(set(best_labels))if distinct_clusters < self.n_clusters:warnings.warn("Number of distinct clusters ({}) found smaller than ""n_clusters ({}). Possibly due to duplicate points ""in X.".format(distinct_clusters, self.n_clusters), ConvergenceWarning, stacklevel=2)self.cluster_centers_ = best_centersself.labels_ = best_labelsself.inertia_ = best_inertiaself.n_iter_ = best_n_iterreturn selfdef fit_predict(self, X, y=None, sample_weight=None):"""Compute cluster centers and predict cluster index for each sample.Convenience method; equivalent to calling fit(X) followed bypredict(X).Parameters----------X : {array-like, sparse matrix} of shape (n_samples, n_features)New data to transform.y : IgnoredNot used, present here for API consistency by convention.sample_weight : array-like of shape (n_samples,), default=NoneThe weights for each observation in X. If None, all observationsare assigned equal weight.Returns-------labels : ndarray of shape (n_samples,)Index of the cluster each sample belongs to."""return self.fit(X, sample_weight=sample_weight).labels_def fit_transform(self, X, y=None, sample_weight=None):"""Compute clustering and transform X to cluster-distance space.Equivalent to fit(X).transform(X), but more efficiently implemented.Parameters----------X : {array-like, sparse matrix} of shape (n_samples, n_features)New data to transform.y : IgnoredNot used, present here for API consistency by convention.sample_weight : array-like of shape (n_samples,), default=NoneThe weights for each observation in X. If None, all observationsare assigned equal weight.Returns-------X_new : array of shape (n_samples, n_clusters)X transformed in the new space."""# Currently, this just skips a copy of the data if it is not in# np.array or CSR format already.# XXX This skips _check_test_data, which may change the dtype;# we should refactor the input validation.return self.fit(X, sample_weight=sample_weight)._transform(X)def transform(self, X):"""Transform X to a cluster-distance space.In the new space, each dimension is the distance to the clustercenters. Note that even if X is sparse, the array returned by`transform` will typically be dense.Parameters----------X : {array-like, sparse matrix} of shape (n_samples, n_features)New data to transform.Returns-------X_new : ndarray of shape (n_samples, n_clusters)X transformed in the new space."""check_is_fitted(self)X = self._check_test_data(X)return self._transform(X)def _transform(self, X):"""guts of transform method; no input validation"""return euclidean_distances(X, self.cluster_centers_)def predict(self, X, sample_weight=None):"""Predict the closest cluster each sample in X belongs to.In the vector quantization literature, `cluster_centers_` is calledthe code book and each value returned by `predict` is the index ofthe closest code in the code book.Parameters----------X : {array-like, sparse matrix} of shape (n_samples, n_features)New data to predict.sample_weight : array-like of shape (n_samples,), default=NoneThe weights for each observation in X. If None, all observationsare assigned equal weight.Returns-------labels : ndarray of shape (n_samples,)Index of the cluster each sample belongs to."""check_is_fitted(self)X = self._check_test_data(X)x_squared_norms = row_norms(X, squared=True)return _labels_inertia(X, sample_weight, x_squared_norms, self.cluster_centers_, self._n_threads)[0]def score(self, X, y=None, sample_weight=None):"""Opposite of the value of X on the K-means objective.Parameters----------X : {array-like, sparse matrix} of shape (n_samples, n_features)New data.y : IgnoredNot used, present here for API consistency by convention.sample_weight : array-like of shape (n_samples,), default=NoneThe weights for each observation in X. If None, all observationsare assigned equal weight.Returns-------score : floatOpposite of the value of X on the K-means objective."""check_is_fitted(self)X = self._check_test_data(X)x_squared_norms = row_norms(X, squared=True)return -_labels_inertia(X, sample_weight, x_squared_norms, self.cluster_centers_)[1]

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