机器学习分类模型决策边界，MLxtend轻松绘制！

原创

皮大大

发布于 2024-07-12 15:37:36

910

发布于 2024-07-12 15:37:36

文章被收录于专栏：机器学习/数据可视化

公众号：尤而小屋编辑：Peter 作者：Peter

大家好，我是Peter~

今天给大家介绍如何基于MLxtend扩展包绘制5种机器学习分类模型的决策边界。

自适应神经元二分类器Adative Linear Neuron Classifier
逻辑回归分类器LogisticRegression
多层感知机分类器MultillayerPerceptron
集成投票分类器EnsembleVoteClassifier
堆叠分类器StackingClassifier

导入库

import numpy as np
import pandas as pd

import matplotlib
import matplotlib.pyplot as plt
import matplotlib.gridspec as gridspec
from matplotlib import cm
plt.rcParams['font.sans-serif']=['SimHei'] #用来正常显示中文标签
plt.rcParams['axes.unicode_minus'] = False #用来正常显示负号

import itertools 

from sklearn import datasets
from sklearn.linear_model import LogisticRegression # 逻辑回归分类
from sklearn.svm import SVC  # SVC
from sklearn.ensemble import RandomForestClassifier  # 随机森林分类
from mlxtend.classifier import Adaline, EnsembleVoteClassifier    # 从mlxtend导入多个模型
from mlxtend.data import iris_data # 内置数据集
from mlxtend.plotting import plot_decision_regions  # 绘制决策边界

import warnings
warnings.filterwarnings('ignore')

自适应神经元分类器Adaline（Adaptive Linear Neuron Classifier）

X,y = iris_data()
X = X[:, [0,3]]
X = X[0:100]
y = y[0:100]

X[:5]

array([[5.1, 0.2],
       [4.9, 0.2],
       [4.7, 0.2],
       [4.6, 0.2],
       [5. , 0.2]])

y[:10]

array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0])

数据标准化过程：

X[:,0] = (X[:,0] - X[:,0].mean()) / X[:,0].std()
X[:,1] = (X[:,1] - X[:,1].mean()) / X[:,0].std()

ada = Adaline(epochs=30, eta=0.01, minibatches=None, random_seed=1)  # closed form
ada.fit(X,y)

plot_decision_regions(X,y,clf=ada)
plt.title("Adaline-Closed form for Classifier")
plt.show()

ada = Adaline(epochs=30, eta=0.01, minibatches=1, random_seed=1,print_progress=3) # gradient descent
ada.fit(X,y)

plot_decision_regions(X,y,clf=ada)
plt.title("Adaline-Gradient Descent for Classifier")
plt.show()

plt.plot(range(len(ada.cost_)), ada.cost_)
plt.xlabel('Iterations')
plt.ylabel('Cost')

Iteration: 30/30 | Cost 3.81 | Elapsed: 0:00:00 | ETA: 0:00:0000

Text(0, 0.5, 'Cost')

ada = Adaline(epochs=15, 
          eta=0.02, 
          minibatches=len(y),  # SGD learning 
          random_seed=1,
          print_progress=3) 
ada.fit(X,y)

plot_decision_regions(X,y,clf=ada)
plt.title("Adaline-Stochastic Gradient Descent for Classifier")
plt.show()

plt.plot(range(len(ada.cost_)), ada.cost_)
plt.xlabel('Iterations')
plt.ylabel('Cost')

Iteration: 15/15 | Cost 3.85 | Elapsed: 0:00:00 | ETA: 0:00:0000

Text(0, 0.5, 'Cost')

逻辑回归LogisticRegression（二分类器）

https://rasbt.github.io/mlxtend/user_guide/classifier/LogisticRegression/

from mlxtend.data import iris_data
from mlxtend.plotting import plot_decision_regions
from mlxtend.classifier import LogisticRegression
import matplotlib.pyplot as plt

# 生成数据
X, y = iris_data()
X = X[:, [0, 3]] 
X = X[0:100] 
y = y[0:100] 

# 数据标准化
X[:,0] = (X[:,0] - X[:,0].mean()) / X[:,0].std()
X[:,1] = (X[:,1] - X[:,1].mean()) / X[:,1].std()

lr = LogisticRegression(
    eta=0.1, 
    l2_lambda=0.0, 
    epochs=100,
    minibatches=1, # 梯度下降 (GD)  默认是1
    #minibatches=5, # SGD with Minibatches
    #minibatches=len(y),  # 随机梯度下降（SGD）
    random_seed=1,
    print_progress=3)

lr.fit(X, y)

plot_decision_regions(X, y, clf=lr)
plt.title('Logistic Regression - Gradient Descent')
plt.show()

plt.plot(range(len(lr.cost_)), lr.cost_)  
plt.xlabel('Iterations')
plt.ylabel('Cost')
plt.show()

Iteration: 100/100 | Cost 0.32 | Elapsed: 0:00:00 | ETA: 0:00:00

模型预测的最终类别及对应概率：

lr.predict(X)[:3]

array([0, 0, 0])

lr.predict_proba(X)[-3:]

array([0.99997968, 0.99339873, 0.99992707])

多层感知机分类器MultilayerPerceptron-MLP

MLP模型：https://rasbt.github.io/mlxtend/user_guide/classifier/MultiLayerPerceptron/
感知机模型：https://rasbt.github.io/mlxtend/user_guide/classifier/Perceptron/

from mlxtend.classifier import MultiLayerPerceptron as MLP
# from mlxtend.classifier import Perceptron   也可以使用感知机

基于MLP的iris数据分类

from mlxtend.data import iris_data
X, y = iris_data()
X = X[:, [0, 3]]    

# 数据标准化
X_std = (X - X.mean(axis=0)) / X.std(axis=0)

建立MLP模型：

mlp = MLP(  # 或者Perceptron模型
    hidden_layers=[50],
    l1=0.0,
    l2=0.0,
    epochs=150,
    eta=0.05,
    momentum=0.1,
    decrease_const=0.0,
    minibatches=1,  # Gradient Descent
    #minibatches=len(y),  # Stochastic Gradient Descent 
    random_seed=1,
    print_progress=3
)

mlp.fit(X_std, y)

Iteration: 150/150 | Cost 0.06 | Elapsed: 0:00:00 | ETA: 0:00:000

<mlxtend.classifier.multilayerperceptron.MultiLayerPerceptron at 0x2565add0c90>

绘制分类模型决策边界：

from mlxtend.plotting import plot_decision_regions
import matplotlib.pyplot as plt

fig = plot_decision_regions(X=X_std, y=y, clf=mlp, legend=2)
plt.title('Multi-Layer-Perceptron w. 50 hidden layer (logistic sigmoid)')
plt.show()

绘制模型损失变化趋势：

import matplotlib.pyplot as plt
plt.plot(range(len(mlp.cost_)), mlp.cost_)
plt.ylabel('Cost')
plt.xlabel('Epochs')
plt.show()

print('Accuracy: %.2f%%' % (100 * mlp.score(X_std, y))) 

Accuracy: 96.67%

10% MINIST Subset数据集分类

from mlxtend.data import mnist_data
from mlxtend.preprocessing import shuffle_arrays_unison

X, y = mnist_data()
X, y = shuffle_arrays_unison((X, y), random_seed=1)  # 打乱数据
X_train, y_train = X[:500], y[:500]  # 取出前10%的数据
X_test, y_test = X[500:], y[500:]

1、显示某个具体的图片：

import matplotlib.pyplot as plt

def plot_digit(X,y,idx):
    img = X[idx].reshape(28,28)
    plt.imshow(img, cmap="Greys", interpolation="nearest")
    plt.title("True Label: %d" % y[idx])
    plt.show()
    
plot_digit(X,y,2800)

2、数据标准化

from mlxtend.preprocessing import standardize

# 训练集归一化；返回参数params
X_train_std, params = standardize(X_train, columns=range(X_train.shape[1]),return_params=True)

用训练集返回的参数对测试集进行归一化：

X_test_std = standardize(X_test, columns=range(X_test.shape[1]), params=params)

3、建立MLP模型

mlp = MLP(
    hidden_layers=[150], 
    l2=0.00, 
    l1=0.0, 
    epochs=100, 
    eta=0.005, 
    momentum=0.0,
    decrease_const=0.0,
    minibatches=100, 
    random_seed=1,
    print_progress=3
)

mlp.fit(X_train_std, y_train)

Iteration: 100/100 | Cost 0.01 | Elapsed: 0:00:13 | ETA: 0:00:00

<mlxtend.classifier.multilayerperceptron.MultiLayerPerceptron at 0x2565ae37c90>

4、模型损失可视化

import matplotlib.pyplot as plt
plt.plot(range(len(mlp.cost_)), mlp.cost_)
plt.ylabel('Cost')
plt.xlabel('Epochs')
plt.show()

5、模型准确率评估

print('Train Accuracy: %.2f%%' % (100 * mlp.score(X_train_std, y_train)))
print('Test Accuracy: %.2f%%' % (100 * mlp.score(X_test_std, y_test)))

Train Accuracy: 100.00%
Test Accuracy: 84.62%

集成投票分类器EnsembleVoteClassifier（多分类投票表决）

使用不同分类模型解决分类预测

from sklearn import model_selection
from sklearn.linear_model import LogisticRegression
from sklearn.naive_bayes import GaussianNB 
from sklearn.ensemble import RandomForestClassifier
import numpy as np

from sklearn import datasets

iris = datasets.load_iris()
X, y = iris.data[:, 1:3], iris.target

1、建立不同的分类模型：

clf1 = LogisticRegression(random_state=1)
clf2 = RandomForestClassifier(random_state=1)
clf3 = GaussianNB()

labels = ["LR","RandomForest","Naive Bayes"]

for clf, label in zip([clf1, clf2, clf3], labels):
    scores = model_selection.cross_val_score(clf,X,y,cv=5,scoring="accuracy")
    print("Accuracy: %0.2f (+/- %0.2f) [%s]" % (scores.mean(), scores.std(), label))

Accuracy: 0.95 (+/- 0.04) [LR]
Accuracy: 0.94 (+/- 0.04) [RandomForest]
Accuracy: 0.91 (+/- 0.04) [Naive Bayes]

2、创建集成投票表决分类器模型实例：

from mlxtend.classifier import EnsembleVoteClassifier  # 集成投票表决分类器
eclf = EnsembleVoteClassifier(clfs=[clf1, clf2, clf3], weights=[1,1,1])

# 基于集成模型的预测

labels = ["LR","RandomForest","Naive Bayes","EnsembleVote"]

for clf, label in zip([clf1, clf2, clf3, eclf], labels):
    scores = model_selection.cross_val_score(clf,X,y,cv=5,scoring="accuracy")
    print("Accuracy: %0.2f (+/- %0.2f) [%s]" % (scores.mean(), scores.std(), label))

Accuracy: 0.95 (+/- 0.04) [LR]
Accuracy: 0.94 (+/- 0.04) [RandomForest]
Accuracy: 0.91 (+/- 0.04) [Naive Bayes]
Accuracy: 0.95 (+/- 0.04) [EnsembleVote]

3、绘制决策边界：

import matplotlib.pyplot as plt
from mlxtend.plotting import plot_decision_regions
import matplotlib.gridspec as gridspec
import itertools

gs = gridspec.GridSpec(2,2)
fig = plt.figure(figsize=(10,8))

labels = ["LR","RandomForest","Naive Bayes","EnsembleVote"]
for clf, lab, grd in zip([clf1, clf2, clf3, eclf],
                  labels,
                  itertools.product([0,1], repeat=2)):
    clf.fit(X,y)
    ax = plt.subplot(gs[grd[0], grd[1]])
    fig = plot_decision_regions(X=X, y=y, clf=clf)
    plt.title(lab)

使用不同分类模型预测网格搜索GridSearch

# 导入数据
from sklearn import datasets
iris = datasets.load_iris()
X, y = iris.data, iris.target

# 创建不同的模型
clf1 = LogisticRegression(random_state=1)
clf2 = RandomForestClassifier(random_state=1)
clf3 = GaussianNB()
eclf = EnsembleVoteClassifier(clfs=[clf1,clf1, clf2, clf3], voting='soft')  # 同一个模型多次出现

# 实施网格搜索
from sklearn.model_selection import GridSearchCV

# 参数组合
params = {"logisticregression-1__C":[1.0, 100.0],  # 参数组合使用自然数递增方式
       "logisticregression-2__C":[1.0, 100.0], 
       "randomforestclassifier__n_estimators": [20,200]}

grid = GridSearchCV(estimator=eclf, param_grid=params, cv=5)
grid.fit(X,y)

cv_keys = ("mean_test_score", "std_test_score", "params")

for r, _ in enumerate(grid.cv_results_["mean_test_score"]):
    print("%0.3f +/- %0.2f %r"
          %(grid.cv_results_[cv_keys[0]][r],
            grid.cv_results_[cv_keys[1]][r] / 2.0,
            grid.cv_results_[cv_keys[2]][r]))

    0.953 +/- 0.01 {'logisticregression-1__C': 1.0, 'logisticregression-2__C': 1.0, 'randomforestclassifier__n_estimators': 20}
    0.960 +/- 0.01 {'logisticregression-1__C': 1.0, 'logisticregression-2__C': 1.0, 'randomforestclassifier__n_estimators': 200}
    0.960 +/- 0.01 {'logisticregression-1__C': 1.0, 'logisticregression-2__C': 100.0, 'randomforestclassifier__n_estimators': 20}
    0.960 +/- 0.01 {'logisticregression-1__C': 1.0, 'logisticregression-2__C': 100.0, 'randomforestclassifier__n_estimators': 200}
    0.960 +/- 0.01 {'logisticregression-1__C': 100.0, 'logisticregression-2__C': 1.0, 'randomforestclassifier__n_estimators': 20}
    0.960 +/- 0.01 {'logisticregression-1__C': 100.0, 'logisticregression-2__C': 1.0, 'randomforestclassifier__n_estimators': 200}
    0.960 +/- 0.01 {'logisticregression-1__C': 100.0, 'logisticregression-2__C': 100.0, 'randomforestclassifier__n_estimators': 20}
    0.960 +/- 0.01 {'logisticregression-1__C': 100.0, 'logisticregression-2__C': 100.0, 'randomforestclassifier__n_estimators': 200}
```python

grid.best_params_  # 最佳参数组合

{'logisticregression-1__C': 1.0,
     'logisticregression-2__C': 1.0,
     'randomforestclassifier__n_estimators': 200}

不同特征子集训练多数投票分类器

# 生成数据

from sklearn import datasets
iris = datasets.load_iris()
X, y = iris.data[:, :], iris.target

from sklearn.model_selection import GridSearchCV
from sklearn.linear_model import LogisticRegression
from sklearn.naive_bayes import GaussianNB 
from sklearn.ensemble import RandomForestClassifier
from mlxtend.classifier import EnsembleVoteClassifier 
from sklearn.pipeline import Pipeline
from mlxtend.feature_selection import SequentialFeatureSelector  # 序惯特征选择

clf1 = LogisticRegression(random_state=1)
clf2 = RandomForestClassifier(random_state=1)
clf3 = GaussianNB()

创建特征选择的管道：

sfs1 = SequentialFeatureSelector(
    clf1,
    k_features=4,
    forward=True,
    floating=False,
    scoring="accuracy",
    verbose=0,
    cv=0
)

clf1_pipe = Pipeline([
    ("sfs", sfs1),
    ("logreg", clf1)
])

创建集成投票表决分类器模型：

eclf = EnsembleVoteClassifier(clfs=[clf1_pipe, clf2, clf3],voting="soft")

创建参数组合：

params = {
    'pipeline__sfs__k_features': [1, 2, 3],
    'pipeline__logreg__C': [1.0, 100.0],
    'randomforestclassifier__n_estimators': [20, 200]
}

grid = GridSearchCV(estimator=eclf, param_grid=params, cv=5)
grid.fit(X,y)

cv_keys = ('mean_test_score', 'std_test_score', 'params')

for r, _ in enumerate(grid.cv_results_['mean_test_score']):
    print("%0.3f +/- %0.2f %r"
          % (grid.cv_results_[cv_keys[0]][r],
             grid.cv_results_[cv_keys[1]][r] / 2.0,
             grid.cv_results_[cv_keys[2]][r]))

    0.947 +/- 0.02 {'pipeline__logreg__C': 1.0, 'pipeline__sfs__k_features': 1, 'randomforestclassifier__n_estimators': 20}
    0.947 +/- 0.02 {'pipeline__logreg__C': 1.0, 'pipeline__sfs__k_features': 1, 'randomforestclassifier__n_estimators': 200}
    0.947 +/- 0.02 {'pipeline__logreg__C': 1.0, 'pipeline__sfs__k_features': 2, 'randomforestclassifier__n_estimators': 20}
    0.960 +/- 0.01 {'pipeline__logreg__C': 1.0, 'pipeline__sfs__k_features': 2, 'randomforestclassifier__n_estimators': 200}
    0.953 +/- 0.01 {'pipeline__logreg__C': 1.0, 'pipeline__sfs__k_features': 3, 'randomforestclassifier__n_estimators': 20}
    0.960 +/- 0.01 {'pipeline__logreg__C': 1.0, 'pipeline__sfs__k_features': 3, 'randomforestclassifier__n_estimators': 200}
    0.953 +/- 0.01 {'pipeline__logreg__C': 100.0, 'pipeline__sfs__k_features': 1, 'randomforestclassifier__n_estimators': 20}
    0.953 +/- 0.01 {'pipeline__logreg__C': 100.0, 'pipeline__sfs__k_features': 1, 'randomforestclassifier__n_estimators': 200}
    0.960 +/- 0.01 {'pipeline__logreg__C': 100.0, 'pipeline__sfs__k_features': 2, 'randomforestclassifier__n_estimators': 20}
    0.960 +/- 0.01 {'pipeline__logreg__C': 100.0, 'pipeline__sfs__k_features': 2, 'randomforestclassifier__n_estimators': 200}
    0.960 +/- 0.01 {'pipeline__logreg__C': 100.0, 'pipeline__sfs__k_features': 3, 'randomforestclassifier__n_estimators': 20}
    0.960 +/- 0.01 {'pipeline__logreg__C': 100.0, 'pipeline__sfs__k_features': 3, 'randomforestclassifier__n_estimators': 200}

最佳参数组合：

grid.best_params_

{'pipeline__logreg__C': 1.0,
'pipeline__sfs__k_features': 2,
'randomforestclassifier__n_estimators': 200}

使用最佳的参数组合再次进行预测：

eclf = eclf.set_params(**grid.best_params_)  # 解析参数组合
eclf.fit(X, y).predict(X[[1, 51, 149]])

array([0, 1, 2])

使用预训练模型

# 生成数据
from sklearn import datasets
iris = datasets.load_iris()
X, y = iris.data[:, :], iris.target

# 不同分类模型
from sklearn import model_selection
from sklearn.linear_model import LogisticRegression
from sklearn.naive_bayes import GaussianNB 
from sklearn.ensemble import RandomForestClassifier
import numpy as np

clf1 = LogisticRegression(random_state=1)
clf2 = RandomForestClassifier(random_state=1)
clf3 = GaussianNB()

for clf in (clf1, clf2, clf3):
    clf.fit(X, y)

from mlxtend.classifier import EnsembleVoteClassifier
import copy

eclf = EnsembleVoteClassifier(clfs=[clf1, clf2, clf3], weights=[1,1,1], fit_base_estimators=False)
labels = ['Logistic Regression', 'Random Forest', 'Naive Bayes', 'Ensemble']
eclf.fit(X, y)
print('accuracy:', np.mean(y == eclf.predict(X)))

accuracy: 0.98

不同特征子集上的集成分类器使用

from sklearn.pipeline import make_pipeline
from mlxtend.feature_selection import ColumnSelector  # 特征选择

pipe1 = make_pipeline(ColumnSelector(cols=(0,2)))
pipe2 = make_pipeline(ColumnSelector(cols=(0,1,3)))

eclf = EnsembleVoteClassifier(clfs=[pipe1, pipe2])
eclf.fit(X,y)

堆叠分类器StackingClassifier

https://rasbt.github.io/mlxtend/user_guide/classifier/StackingClassifier/

Simple Stacked Classification

import numpy as np
from sklearn import model_selection
from sklearn.linear_model import LogisticRegression
from sklearn.neighbors import KNeighborsClassifier
from sklearn.naive_bayes import GaussianNB 
from sklearn.ensemble import RandomForestClassifier
from mlxtend.classifier import StackingClassifier

import warnings
warnings.simplefilter('ignore')

1、导入数据

from sklearn import datasets
iris = datasets.load_iris()
X, y = iris.data[:, 1:3], iris.target

clf1 = KNeighborsClassifier(n_neighbors=1)
clf2 = RandomForestClassifier(random_state=1)
clf3 = GaussianNB()
lr = LogisticRegression()

2、建立Stacking模型，使用LogisticRegression作为基模型：

sclf = StackingClassifier(
    classifiers=[clf1, clf2, clf3],
    use_probas=True,
    average_probas=False, # 是否使用概率作为Meta-Features
    meta_classifier=lr  # 元模型
)

3、模型训练

for clf, label in zip([clf1, clf2, clf3, sclf], 
               ['KNN', 'Random Forest', 'Naive Bayes','StackingClassifier']):
    # 模型训练与评估
    scores = model_selection.cross_val_score(clf, X, y, cv=3, scoring='accuracy')
    print("Accuracy: %0.2f (+/- %0.2f) [%s]" % (scores.mean(), scores.std(), label))

Accuracy: 0.91 (+/- 0.01) [KNN]
Accuracy: 0.95 (+/- 0.01) [Random Forest]
Accuracy: 0.91 (+/- 0.02) [Naive Bayes]
Accuracy: nan (+/- nan) [StackingClassifier]

4、绘制决策边界

import matplotlib.pyplot as plt
from mlxtend.plotting import plot_decision_regions
import matplotlib.gridspec as gridspec
import itertools

gs = gridspec.GridSpec(2, 2)
fig = plt.figure(figsize=(10,8))

for clf, lab, grd in zip([clf1, clf2, clf3, sclf], 
                  ['KNN','Random Forest','Naive Bayes','StackingClassifier'],
                  itertools.product([0, 1], repeat=2)):
    
    clf.fit(X, y)   # 模型训练
    ax = plt.subplot(gs[grd[0], grd[1]])
    fig = plot_decision_regions(X=X, y=y, clf=clf)
    plt.title(lab)

Stacked Classifier&GridSearch

将堆叠分类器和网格搜索结合起来：

from sklearn.linear_model import LogisticRegression
from sklearn.neighbors import KNeighborsClassifier
from sklearn.naive_bayes import GaussianNB 
from sklearn.ensemble import RandomForestClassifier
from sklearn.model_selection import GridSearchCV
from mlxtend.classifier import StackingClassifier

1、创建模型

clf1 = KNeighborsClassifier(n_neighbors=1)
clf2 = RandomForestClassifier(random_state=1)
clf3 = GaussianNB()
lr = LogisticRegression()  # meta模型

# 堆叠分类器
sclf = StackingClassifier(classifiers=[clf1, clf2, clf3], meta_classifier=lr)

2、参数的网格搜索

params = {
    'kneighborsclassifier__n_neighbors': [1, 5],
    'randomforestclassifier__n_estimators': [10, 50],
    'meta_classifier__C': [0.1, 10.0]
}

3、模型训练

grid = GridSearchCV(estimator=sclf,param_grid=params,cv=5,refit=True)
grid.fit(X, y)

4、获取参数组合及得分：

cv_keys = ('mean_test_score', 'std_test_score', 'params')

for r, _ in enumerate(grid.cv_results_['mean_test_score']):
    print("%0.3f +/- %0.2f %r"
          % (grid.cv_results_[cv_keys[0]][r],
             grid.cv_results_[cv_keys[1]][r] / 2.0,
             grid.cv_results_[cv_keys[2]][r]))

print('Best parameters: %s' % grid.best_params_)
print('Accuracy: %.2f' % grid.best_score_)

    0.933 +/- 0.03 {'kneighborsclassifier__n_neighbors': 1, 'meta_classifier__C': 0.1, 'randomforestclassifier__n_estimators': 10}
    0.947 +/- 0.02 {'kneighborsclassifier__n_neighbors': 1, 'meta_classifier__C': 0.1, 'randomforestclassifier__n_estimators': 50}
    0.927 +/- 0.03 {'kneighborsclassifier__n_neighbors': 1, 'meta_classifier__C': 10.0, 'randomforestclassifier__n_estimators': 10}
    0.947 +/- 0.02 {'kneighborsclassifier__n_neighbors': 1, 'meta_classifier__C': 10.0, 'randomforestclassifier__n_estimators': 50}
    0.947 +/- 0.02 {'kneighborsclassifier__n_neighbors': 5, 'meta_classifier__C': 0.1, 'randomforestclassifier__n_estimators': 10}
    0.947 +/- 0.02 {'kneighborsclassifier__n_neighbors': 5, 'meta_classifier__C': 0.1, 'randomforestclassifier__n_estimators': 50}
    0.933 +/- 0.02 {'kneighborsclassifier__n_neighbors': 5, 'meta_classifier__C': 10.0, 'randomforestclassifier__n_estimators': 10}
    0.940 +/- 0.02 {'kneighborsclassifier__n_neighbors': 5, 'meta_classifier__C': 10.0, 'randomforestclassifier__n_estimators': 50}
    Best parameters: {'kneighborsclassifier__n_neighbors': 1, 'meta_classifier__C': 0.1, 'randomforestclassifier__n_estimators': 50}
    Accuracy: 0.95

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