基于MLxtend绘制分类模型的决策边界

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皮大大

发布于 2024-06-06 11:16:23

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发布于 2024-06-06 11:16:23

文章被收录于专栏：机器学习/数据可视化机器学习/数据可视化

公众号：尤而小屋编辑：Peter 作者：Peter

大家好，我是Peter~

继续更新机器学习扩展包MLxtend的文章。本文介绍如何使用MLxtend来绘制与分类模型相关的决策边界decision_regions。

导入库

导入相关用于数据处理和建模的库：

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 EnsembleVoteClassifier  # 从mlxtend导入集成投票表决分类算法
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')

1维决策边界（Decision regions in 1D）

X,y = iris_data()
X[:3]  # names = ['sepal length', 'sepal width','petal length', 'petal width']

array([[5.1, 3.5, 1.4, 0.2],
           [4.9, 3. , 1.4, 0.2],
           [4.7, 3.2, 1.3, 0.2]])

X = X[:,2]  # 只取第二个特征
# X = X[:,None]  # 转成2维数组；下同
X = X.reshape(-1,1)
X[:5]

array([[1.4],
       [1.4],
       [1.3],
       [1.5],
       [1.4]])

建立模型：

svm = SVC(C=0.5,kernel="linear")
svm.fit(X,y)

绘制决策边界图形：

plot_decision_regions(X,y,clf=svm,legend=2)

plt.xlabel("sepal width")
plt.title("SVM on Iris Datasets based on 1D")
plt.show()

2维决策边界（Decision regions in 2D）

X,y = iris_data()
X = X[:,:2]  # 选择两个特征用于建模和可视化
X[:10]

输出结果为：

array([[5.1, 3.5],
     [4.9, 3. ],
     [4.7, 3.2],
     [4.6, 3.1],
     [5. , 3.6],
     [5.4, 3.9],
     [4.6, 3.4],
     [5. , 3.4],
     [4.4, 2.9],
     [4.9, 3.1]])

建立模型：

svm = SVC(C=0.5,kernel="linear")
svm.fit(X,y)

绘制决策边界图形：

plot_decision_regions(X,y,clf=svm,legend=2)

plt.xlabel("sepal length")
plt.ylabel("sepal width")
plt.title("SVM on Iris Datasets based on 2D")
plt.show()

多模型决策边界（Decision Region Grids）

# 导入4个分类模型
from sklearn.linear_model import LogisticRegression
from sklearn.naive_bayes import GaussianNB 
from sklearn.ensemble import RandomForestClassifier
from sklearn.svm import SVC

import numpy as np

import matplotlib.pyplot as plt
import matplotlib.gridspec as gridspec
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 mlxtend.data import iris_data # 内置数据集
from mlxtend.plotting import plot_decision_regions

4个模型的初始化：

clf1 = LogisticRegression(random_state=1,solver='newton-cg',multi_class='multinomial')
clf2 = RandomForestClassifier(random_state=1, n_estimators=100)
clf3 = GaussianNB()
clf4 = SVC(gamma='auto')

导入数据集：

X,y = iris_data()
X = X[:,:2]  # 选择2个特征建模

4个模型的迭代训练与可视化：

gs = gridspec.GridSpec(2,2)  # 2*2的网格面

fig = plt.figure(figsize=(10,8))

labels = ['Logistic Regression', 'Random Forest', 'Naive Bayes', 'SVM']

for clf,lab,grd in zip([clf1, clf2, clf3, clf4],
                      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, legend=2)
    plt.title(lab)
    
plt.show()

高亮测试数据集Highlighting test data

from mlxtend.plotting import plot_decision_regions
from mlxtend.data import iris_data # 内置数据集
from mlxtend.plotting import plot_decision_regions

import matplotlib.pyplot as plt
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

from sklearn.svm import SVC
from sklearn.model_selection import train_test_split

导入数据集并切分：

X,y = iris_data()
X = X[:,:2]  # 选择前2个特征建模

# 切分数据集
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.33, random_state=0)

模型训练：

svm =SVC(C=0.5, kernel="linear")
svm.fit(X_train, y_train)

plot_decision_regions(X, 
                      y, 
                      clf=svm, 
                      legend=2, 
                      X_highlight=X_test
                     )

plt.xlabel('sepal length')
plt.ylabel('petal length')
plt.title('SVM on Iris with Highlighting Test Data Points')
plt.show()

评估分类器在非线性问题的表现Evaluating Classifier Behavior on Non-Linear Problems

import matplotlib.pyplot as plt
import matplotlib.gridspec as gridspec

import itertools
from mlxtend.plotting import plot_decision_regions
import numpy as np

from sklearn.linear_model import LogisticRegression
from sklearn.naive_bayes import GaussianNB 
from sklearn.ensemble import RandomForestClassifier
from sklearn.svm import SVC

# 定义4个模型
clf1 = LogisticRegression(random_state=1, solver='lbfgs')
clf2 = RandomForestClassifier(n_estimators=100, random_state=1)
clf3 = GaussianNB()
clf4 = SVC(gamma='auto')

XOR问题

X = np.random.randn(300, 2)  # 300*2；符合正态分布的数组
X[:5]

array([[-1.96399101, -0.13610581],
         [-1.4832503 , -0.01927823],
         [-2.32101114,  0.09310347],
         [ 1.85377755,  0.08739847],
         [-1.26535948,  0.75706403]])

# np.logical_xor用于计算两个布尔数组之间的逐元素逻辑异或。当两个输入数组中的元素相同，为False；当不同时，结果为True。

y = np.array(np.logical_xor(X[:, 0] > 0, X[:, 1] > 0),  # 两个特征的是否都大于0；使用异或的结果
             dtype=int)

y[:10]  # 0-表示False，1-表示True

array([0, 0, 1, 0, 1, 1, 1, 0, 1, 0])

gs = gridspec.GridSpec(2, 2)  # 创建2*2的网格布局

fig = plt.figure(figsize=(10,8))  # 图像大小
labels = ['Logistic Regression', 'Random Forest', 'Naive Bayes', 'SVM']  # 模型名称

for clf, lab, grd in zip([clf1, clf2, clf3, clf4], # 模型clf + 名称lab + 位置grd（00,01,10,11）
                         labels,
                         itertools.product([0, 1], repeat=2)):

    clf.fit(X, y)  # 模型拟合
    ax = plt.subplot(gs[grd[0], grd[1]])  # grd[0]-row  grd[1]-column
    fig = plot_decision_regions(X=X, y=y, clf=clf, legend=2)  # 绘制决策边界
    plt.title(lab)  # 模型名称
    
plt.show()

半月数据集的分类Half-Moons

make_moons是Scikit-learn库中的一个函数，用于生成具有两个弯月形状的数据集。它通常用于测试分类算法在非线性可分数据上的性能。

该函数的基本用法如下：

from sklearn.datasets import make_moons

X, y = make_moons(n_samples=100, noise=0.1, random_state=42)

其中，n_samples参数指定生成的数据点数量，noise参数指定数据的噪声水平（0表示无噪声，越大表示噪声越多），random_state参数用于设置随机数生成器的种子以确保结果的可重复性。

from sklearn.datasets import make_moons
X, y = make_moons(n_samples=100, random_state=123) # 生成弯月数据集

gs = gridspec.GridSpec(2, 2)

fig = plt.figure(figsize=(10,8))

labels = ['Logistic Regression', 'Random Forest', 'Naive Bayes', 'SVM']
for clf, lab, grd in zip([clf1, clf2, clf3, clf4],
                         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, legend=2)
    plt.title(lab)

plt.show()

同心圆数据的分类Concentric Circles

from sklearn.datasets import make_circles  

# 生成同心圆数据集
X, y = make_circles(n_samples=1000, random_state=123, noise=0.1, factor=0.2)

gs = gridspec.GridSpec(2, 2)

fig = plt.figure(figsize=(10,8))

labels = ['Logistic Regression', 'Random Forest', 'Naive Bayes', 'SVM']
for clf, lab, grd in zip([clf1, clf2, clf3, clf4],
                         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, legend=2)
    plt.title(lab)

plt.show()

基于子图的分类决策边界

import matplotlib.pyplot as plt
from mlxtend.plotting import plot_decision_regions
from mlxtend.data import iris_data # 内置数据集

from sklearn.linear_model import LogisticRegression
from sklearn.naive_bayes import GaussianNB 
from sklearn import datasets
import numpy as np


X,y = iris_data()
X = X[:,2]
X = np.array(X).reshape(-1,1)

建立两个模型并训练：

clf1 = LogisticRegression(
    random_state=1,
    solver='lbfgs',
    multi_class='multinomial')

clf2 = GaussianNB()
clf1.fit(X, y)
clf2.fit(X, y)

创建图形对象fig和ax绘图对象：

fig, axes = plt.subplots(1,2,figsize=(10,3))  # 创建1*2的图形

fig = plot_decision_regions(X=X, y=y, clf=clf1, ax=axes[0], legend=2) 
fig = plot_decision_regions(X=X, y=y, clf=clf2, ax=axes[1], legend=1)

plt.show()

基于多特征的决策边界

from mlxtend.plotting import plot_decision_regions
import matplotlib.pyplot as plt
from sklearn import datasets
from sklearn.svm import SVC

X, y = datasets.make_blobs(
    n_samples=600, # 样本数
    n_features=3,  # 特征数
    centers=[[2, 2, -2],[-2, -2, 2]], # 聚类中心
    cluster_std=[2, 2],  # 聚类方差
    random_state=2  # 随机种子
)

建立SVM模型并训练：

svm = SVC(gamma="auto")
svm.fit(X,y)

fig, ax = plt.subplots()

value = 1.5
width = 0.75

plot_decision_regions(
    X,
    y,
    clf=svm,
    # Filler values must be provided when X has more than 2 training features.
    # 多个特征该参数必须有
    filler_feature_values={2: value},  
    filler_feature_ranges={2: width},
    legend=2,
    ax=ax
    )

ax.set_xlabel("Feature1")
ax.set_ylabel("Feature2")
ax.set_title("Feature3={}".format(value))

fig.suptitle("SVM on make_blobs")

plt.show()

决策边界的网格切片

from mlxtend.plotting import plot_decision_regions
import matplotlib.pyplot as plt
from sklearn import datasets
from sklearn.svm import SVC

X, y = datasets.make_blobs(
    n_samples=600, # 样本数
    n_features=3,  # 特征数
    centers=[[2, 2, -2],[-2, -2, 2]], # 聚类中心
    cluster_std=[2, 2],  # 聚类方差
    random_state=2  # 随机种子
)

# 模型训练
svm = SVC(gamma="auto")
svm.fit(X,y)

fig, axarr = plt.subplots(2, 2, figsize=(10,8), sharex=True, sharey=True)
values = [-4.0, -1.0, 1.0, 4.0]
width = 0.75

for value, ax in zip(values, axarr.flat):
    plot_decision_regions(X,
                          y,
                          clf=svm,
                          filler_feature_values={2: value},
                          filler_feature_ranges={2: width},
                          legend=2,
                          ax=ax)
    ax.set_xlabel("Feature1")
    ax.set_ylabel("Feature2")
    ax.set_title("Feature3={}".format(value))
    
fig.suptitle('SVM on make_blobs')
plt.show()

自定义绘图风格

from mlxtend.plotting import plot_decision_regions
from mlxtend.data import iris_data # 内置数据集
from mlxtend.plotting import plot_decision_regions
import matplotlib.pyplot as plt
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
from sklearn.svm import SVC
from sklearn.model_selection import train_test_split

# 导入和切分数据
X,y = iris_data()
X = X[:,:2]  # 选择前2个特征建模
# 切分数据集
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.33, random_state=0)

建立模型和训练：

svm = SVC(C=0.5, kernel='linear')
svm.fit(X_train, y_train)

自定义绘图风格：

scatter_kwargs = {'s': 120, 'edgecolor': None, 'alpha': 0.7}
contourf_kwargs = {'alpha': 0.2}
scatter_highlight_kwargs = {'s': 120, 'label': 'Test data', 'alpha': 0.7}

# 绘制决策边界
plot_decision_regions(X, 
                      y, 
                      clf=svm, 
                      legend=2,
                      X_highlight=X_test, #  高亮数据
                      scatter_kwargs=scatter_kwargs,
                      contourf_kwargs=contourf_kwargs,
                      scatter_highlight_kwargs=scatter_highlight_kwargs)

# 添加坐标轴标注
plt.xlabel('sepal length')
plt.ylabel('petal length')
plt.title('SVM on Iris')
plt.show()

自定义图例legend

from mlxtend.plotting import plot_decision_regions
from mlxtend.data import iris_data # 内置数据集
from mlxtend.plotting import plot_decision_regions
import matplotlib.pyplot as plt
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
from sklearn.svm import SVC
from sklearn.model_selection import train_test_split

# 导入和切分数据
X,y = iris_data()
X = X[:,:2]  # 选择前2个特征建模
# 切分数据集
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.33, random_state=0)
svm = SVC(C=0.5, kernel='linear')
svm.fit(X_train, y_train)

修改图例：

ax = plot_decision_regions(X,y,clf=svm, legend=0)

plt.xlabel('sepal length')
plt.ylabel('petal length')
plt.title('SVM on Iris')

# 自定义图例
handles, labels = ax.get_legend_handles_labels()
ax.legend(handles, 
          ['class square','class triangle','class circle'], 
           framealpha=0.3, 
          scatterpoints=1)

plt.show()

基于缩放因子的决策边界可视化zoom factors

from mlxtend.plotting import plot_decision_regions
from mlxtend.data import iris_data # 内置数据集
from mlxtend.plotting import plot_decision_regions
import matplotlib.pyplot as plt
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
from sklearn.svm import SVC
from sklearn.model_selection import train_test_split

X,y = iris_data()
X = X[:,:2]  
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.33, random_state=0)
svm = SVC(C=0.5, kernel='linear')
svm.fit(X_train, y_train)

1、默认的缩放因子zoom_factor=1.0：

plot_decision_regions(X, y, clf=svm, zoom_factor=1.)
plt.show()

2、使用不同的缩放因子：

plot_decision_regions(X, y, clf=svm, zoom_factor=0.1)
plt.show()

plot_decision_regions(X, y, clf=svm, zoom_factor=2)
plt.xlim(5, 6)
plt.ylim(2, 5)
plt.show()

使用Onehot编码输出的分类器onehot-encoded outputs (Keras)

定义了一个名为Onehot2Int的类，该类用于将模型预测的one-hot编码结果转换为整数

import matplotlib.pyplot as plt
import numpy as np
np.random.seed(123)

import keras
from keras.models import Sequential
from keras.layers import Dense
from keras.utils import to_categorical

from mlxtend.data import iris_data
from mlxtend.preprocessing import standardize
from mlxtend.plotting import plot_decision_regions

class Onehot2Int(object):
    
    # 参数为model；表示需要转换预测结果的模型
    def __init__(self, model):  
        self.model = model
    
    # X表示输入
    def predict(self, X):
        y_pred = self.model.predict(X)  # 预测
        return np.argmax(y_pred, axis=1) # 找到每行中最大值的索引，即one-hot编码中1的位置，返回这些索引组成的数组

数据预处理：

X, y = iris_data()
X = X[:, [2, 3]]

X = standardize(X)  # 标准化
y_onehot = to_categorical(y) # 独热编码

建立网络模型：

model = Sequential()
model.add(Dense(8, 
                input_shape=(2,), 
                activation='relu', 
                kernel_initializer='he_uniform'))

model.add(Dense(4, 
                activation='relu', 
                kernel_initializer='he_uniform'))

model.add(Dense(3, activation='softmax'))

模型编译和训练：

model.compile(loss="categorical_crossentropy", 
             optimizer=keras.optimizers.Adam(lr=0.005), 
             metrics=['accuracy'])

history = model.fit(X, 
                    y_onehot, 
                    epochs=10,
                    batch_size=5, 
                    verbose=1, 
                    validation_split=0.1)

    Epoch 1/10
    27/27 [==============================] - 0s 7ms/step - loss: 0.9506 - accuracy: 0.6074 - val_loss: 1.0899 - val_accuracy: 0.0000e+00
    Epoch 2/10
    27/27 [==============================] - 0s 2ms/step - loss: 0.7453 - accuracy: 0.6963 - val_loss: 1.0886 - val_accuracy: 0.0000e+00
    Epoch 3/10
    27/27 [==============================] - 0s 1ms/step - loss: 0.6098 - accuracy: 0.7185 - val_loss: 1.0572 - val_accuracy: 0.0000e+00
    Epoch 4/10
    27/27 [==============================] - 0s 2ms/step - loss: 0.5159 - accuracy: 0.7333 - val_loss: 1.0118 - val_accuracy: 0.0000e+00
    Epoch 5/10
    27/27 [==============================] - 0s 1ms/step - loss: 0.4379 - accuracy: 0.7630 - val_loss: 0.9585 - val_accuracy: 0.8000
    Epoch 6/10
    27/27 [==============================] - 0s 2ms/step - loss: 0.3784 - accuracy: 0.8815 - val_loss: 0.8806 - val_accuracy: 0.9333
    Epoch 7/10
    27/27 [==============================] - 0s 1ms/step - loss: 0.3378 - accuracy: 0.9407 - val_loss: 0.8155 - val_accuracy: 1.0000
    Epoch 8/10
    27/27 [==============================] - 0s 2ms/step - loss: 0.3130 - accuracy: 0.9481 - val_loss: 0.7535 - val_accuracy: 1.0000
    Epoch 9/10
    27/27 [==============================] - 0s 2ms/step - loss: 0.2893 - accuracy: 0.9259 - val_loss: 0.6859 - val_accuracy: 1.0000
    Epoch 10/10
    27/27 [==============================] - 0s 2ms/step - loss: 0.2695 - accuracy: 0.9481 - val_loss: 0.6258 - val_accuracy: 1.0000

model_no_ohe = Onehot2Int(model)  # 将现有模型转成one-hot处理后的模型

# 绘制决策边界
plot_decision_regions(X, y, clf=model_no_ohe)
plt.show()  

9600/9600 [==============================] - 5s 555us/step