ML之KMeans：利用KMeans算法对Boston房价数据集(两特征+归一化)进行二聚类分析

╰+攻爆jí腚メ 2022-12-24 05:51 161阅读 0赞

**目录**

利用KMeans算法对Boston房价数据集(两特征+归一化)进行二聚类分析

设计思路

输出结果

核心代码

--------------------

**相关文章**  
[ML之KMeans：利用KMeans算法对Boston房价数据集(两特征+归一化)进行二聚类分析][ML_KMeans_KMeans_Boston]  
[ML之KMeans：利用KMeans算法对Boston房价数据集(两特征+归一化)进行二聚类分析实现][ML_KMeans_KMeans_Boston 1]

# 利用KMeans算法对Boston房价数据集(两特征+归一化)进行二聚类分析 #

## 设计思路 ##

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQxMTg1ODY4_size_16_color_FFFFFF_t_70][]

## 输出结果 ##

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQxMTg1ODY4_size_16_color_FFFFFF_t_70 1][]

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   0.331126
       LotFrontage  GarageArea
    0     0.207668    0.386460
    1     0.255591    0.324401
    2     0.217252    0.428773
    3     0.191693    0.452750
    4     0.268371    0.589563
                         Id  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]

## 核心代码 ##

class KMeans Found at: sklearn.cluster._kmeans
    
    class KMeans(TransformerMixin, ClusterMixin, BaseEstimator):
        """K-Means clustering.
        
        Read more in the :ref:`User Guide <k_means>`.
        
        Parameters
        ----------
        
        n_clusters : int, default=8
        The number of clusters to form as well as the number of
        centroids to generate.
        
        init : {'k-means++', 'random', ndarray, callable}, default='k-
         means++'
        Method for initialization:
        
        'k-means++' : selects initial cluster centers for k-mean
        clustering in a smart way to speed up convergence. See 
         section
        Notes in k_init for more details.
        
        'random': choose `n_clusters` observations (rows) at 
         random from data
        for 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 a
        random state and return an initialization.
        
        n_init : int, default=10
        Number of time the k-means algorithm will be run with 
         different
        centroid seeds. The final results will be the best output of
        n_init consecutive runs in terms of inertia.
        
        max_iter : int, default=300
        Maximum number of iterations of the k-means algorithm 
         for a
        single run.
        
        tol : float, default=1e-4
        Relative tolerance with regards to Frobenius norm of the 
         difference
        in the cluster centers of two consecutive iterations to 
         declare
        convergence.
        It's not advised to set `tol=0` since convergence might 
         never be
        declared 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 > 12
        million. This corresponds to about 100MB overhead per 
         job using
        double precision.
        
        True : always precompute distances.
        
        False : never precompute distances.
        
        .. deprecated:: 0.23
        'precompute_distances' was deprecated in version 0.22 
         and will be
        removed in 0.25. It has no effect.
        
        verbose : int, default=0
        Verbosity mode.
        
        random_state : int, RandomState instance, default=None
        Determines random number generation for centroid 
         initialization. Use
        an int to make the randomness deterministic.
        See :term:`Glossary <random_state>`.
        
        copy_x : bool, default=True
        When pre-computing distances it is more numerically 
         accurate to center
        the data first. If copy_x is True (default), then the original 
         data is
        not modified. If False, the original data is modified, and put 
         back
        before the function returns, but small numerical 
         differences may be
        introduced by subtracting and then adding the data mean. 
         Note that if
        the original data is not C-contiguous, a copy will be made 
         even if
        copy_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=None
        The number of OpenMP threads to use for the 
         computation. Parallelism is
        sample-wise on the main cython loop which assigns each 
         sample to its
        closest center.
        
        ``None`` or ``-1`` means using all processors.
        
        .. deprecated:: 0.23
        ``n_jobs`` was deprecated in version 0.23 and will be 
         removed in
        0.25.
        
        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-
         defined
        clusters, by using the triangle inequality. However it's 
         more memory
        intensive due to the allocation of an extra array of shape
        (n_samples, n_clusters).
        
        For now "auto" (kept for backward compatibiliy) chooses 
         "elkan" but it
        might change in the future for a better heuristic.
        
        .. versionchanged:: 0.18
        Added Elkan algorithm
        
        Attributes
        ----------
        cluster_centers_ : ndarray of shape (n_clusters, n_features)
        Coordinates of cluster centers. If the algorithm stops 
         before fully
        converging (see ``tol`` and ``max_iter``), these will not be
        consistent with ``labels_``.
        
        labels_ : ndarray of shape (n_samples,)
        Labels of each point
        
        inertia_ : float
        Sum of squared distances of samples to their closest 
         cluster center.
        
        n_iter_ : int
        Number of iterations run.
        
        See also
        --------
        
        MiniBatchKMeans
        Alternative online implementation that does incremental 
         updates
        of the centers positions using mini-batches.
        For large scale learning (say n_samples > 10k) 
         MiniBatchKMeans is
        probably 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 of
        samples and T is the number of iteration.
        
        The worst case complexity is given by O(n^(k+2/p)) with
        n = 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 
         fastest
        clustering algorithms available), but it falls in local minima. 
         That's why
        it 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 each
        cluster. Also, the estimator will reassign ``labels_`` after the 
         last
        iteration to make ``labels_`` consistent with ``predict`` on 
         the training
        set.
        
        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_args
        def __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_clusters
            self.init = init
            self.max_iter = max_iter
            self.tol = tol
            self.precompute_distances = precompute_distances
            self.n_init = n_init
            self.verbose = verbose
            self.random_state = random_state
            self.copy_x = copy_x
            self.n_jobs = n_jobs
            self.algorithm = algorithm
        
        def _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.shape
            expected_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 X
        
        def 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 
                 data
                will be converted to C ordering, which will cause a 
                 memory
                copy if the given data is not C-contiguous.
                If a sparse matrix is passed, a copy will be made if it's 
                 not in
                CSR format.
    
            y : Ignored
                Not used, present here for API consistency by 
                 convention.
    
            sample_weight : array-like of shape (n_samples,), 
             default=None
                The weights for each observation in X. If None, all 
                 observations
                are assigned equal weight.
    
                .. versionadded:: 0.20
    
            Returns
            -------
            self
                Fitted 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_jobs
            else:
                self._n_threads = None
            self._n_threads = _openmp_effective_n_threads(self.
             _n_threads)
            n_init = self.n_init
            if 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 k
            if _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 array
            init = self.init
            if 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 computations
            if not sp.issparse(X):
                X_mean = X.mean(axis=0) # The copy was already 
                 done above
                X -= X_mean
                if hasattr(init, '__array__'):
                    init -= X_mean
            # precompute squared norms of data points
            x_squared_norms = row_norms(X, squared=True)
            best_labels, best_inertia, best_centers = None, None, 
             None
            algorithm = self.algorithm
            if 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_lloyd
            elif algorithm == "elkan":
                kmeans_single = _kmeans_single_elkan
            else:
                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 once
                labels, 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 far
                if best_inertia is None or inertia < best_inertia:
                    best_labels = labels.copy()
                    best_centers = centers.copy()
                    best_inertia = inertia
                    best_n_iter = n_iter_
            
            if not sp.issparse(X):
                if not self.copy_x:
                    X += X_mean
                best_centers += X_mean
            distinct_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_centers
            self.labels_ = best_labels
            self.inertia_ = best_inertia
            self.n_iter_ = best_n_iter
            return self
        
        def 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 by
            predict(X).
    
            Parameters
            ----------
            X : {array-like, sparse matrix} of shape (n_samples, 
             n_features)
                New data to transform.
    
            y : Ignored
                Not used, present here for API consistency by 
                 convention.
    
            sample_weight : array-like of shape (n_samples,), 
             default=None
                The weights for each observation in X. If None, all 
                 observations
                are 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 : Ignored
                Not used, present here for API consistency by 
                 convention.
    
            sample_weight : array-like of shape (n_samples,), 
             default=None
                The weights for each observation in X. If None, all 
                 observations
                are 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 
             cluster
            centers.  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 
             called
            the code book and each value returned by `predict` is 
             the index of
            the 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=None
                The weights for each observation in X. If None, all 
                 observations
                are 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 : Ignored
                Not used, present here for API consistency by 
                 convention.
    
            sample_weight : array-like of shape (n_samples,), 
             default=None
                The weights for each observation in X. If None, all 
                 observations
                are assigned equal weight.
    
            Returns
            -------
            score : float
                Opposite 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]

[ML_KMeans_KMeans_Boston]: https://yunyaniu.blog.csdn.net/article/details/110210520
[ML_KMeans_KMeans_Boston 1]: https://yunyaniu.blog.csdn.net/article/details/110248845
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