【人工智能与机器学习】对鸢尾花数据集和月亮数据集，分别采用线性LDA、k-means和SVM算法进行二分类可视化分析

什么是SVM？

SVM是一个很复杂的算法，不是一篇博文就能够讲完的，各位小伙伴可以看看知乎的解释：
https://www.zhihu.com/question/21094489.

什么是k-means算法

具体参考百度百科链接：
https://baike.baidu.com/item/K%E5%9D%87%E5%80%BC%E8%81%9A%E7%B1%BB%E7%AE%97%E6%B3%95/15779627?fromtitle=K-means&fromid=4934806&fr=aladdin.

什么是线性LDA

https://blog.csdn.net/ruthywei/article/details/83045288

SVM算法对两个数据集进行分类

鸢尾花数据集代码如下：

from sklearn.svm import SVC
from sklearn.datasets import load_iris
import matplotlib.pyplot as plt
import numpy as np
from sklearn.model_selection import train_test_split
from sklearn.model_selection import GridSearchCV
def plot_point2(dataArr, labelArr, Support_vector_index):
    for i in range(np.shape(dataArr)[0]):
        if labelArr[i] == 0:
            plt.scatter(dataArr[i][0], dataArr[i][1], c='b', s=20)
        elif labelArr[i] == 1:
            plt.scatter(dataArr[i][0], dataArr[i][1], c='y', s=20)
        else:
            plt.scatter(dataArr[i][0], dataArr[i][1], c='g', s=20)
    
    for j in Support_vector_index:
        plt.scatter(dataArr[j][0], dataArr[j][1], s=100, c='', alpha=0.5, linewidth=1.5, edgecolor='red')
    plt.show()
if __name__ == "__main__":
    iris = load_iris()
    x, y = iris.data, iris.target
    x = x[:, :2]
    X_train, X_test, y_train, y_test = train_test_split(x, y, test_size=0.3, random_state=0)
    clf = SVC(C=1, cache_size=200, class_weight=None, coef0=0.0,
                decision_function_shape='ovr', degree=3, gamma=0.1,
                kernel='linear', max_iter=-1, probability=False, random_state=None,
                shrinking=True, tol=0.001, verbose=False)
    # 调参选取最优参数
    # clf = GridSearchCV(SVC(), param_grid={"kernel": ['rbf', 'linear', 'poly', 'sigmoid'],
    #                                       "C": [0.1, 1, 10], "gamma": [1, 0.1, 0.01]}, cv=3)
    clf.fit(X_train, y_train)
 
    # print("The best parameters are %s with a score of %0.2f" % (clf.best_params_, clf.best_score_))
 
    predict_list = clf.predict(X_test)
 
    precition = clf.score(X_test, y_test)
    print("preciton is : ", precition * 100, "%")
 
    n_Support_vector = clf.n_support_
    print("vector num is : ", n_Support_vector)
    Support_vector_index = clf.support_
 
    x_min, x_max = x[:, 0].min() - 1, x[:, 0].max() + 1
    y_min, y_max = x[:, 1].min() - 1, x[:, 1].max() + 1
    h = 0.02
    xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))
    Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])
    Z = Z.reshape(xx.shape)
    plt.contourf(xx, yy, Z, cmap=plt.cm.Paired, alpha=0.8)
    plot_point2(x, y, Support_vector_index)

结果如下：

月亮数据集代码如下：

from sklearn.datasets import make_moons
from sklearn.pipeline import Pipeline
from sklearn.preprocessing import PolynomialFeatures
import numpy as np
from sklearn import datasets
from sklearn.preprocessing import StandardScaler
from sklearn.svm import LinearSVC
X, y = make_moons(n_samples=100, noise=0.15, random_state=42)
polynomial_svm_clf = Pipeline([
        # 将源数据 映射到 3阶多项式
        ("poly_features", PolynomialFeatures(degree=3)),
        # 标准化
        ("scaler", StandardScaler()),
        # SVC线性分类器
        ("svm_clf", LinearSVC(C=10, loss="hinge", random_state=42))
    ])
polynomial_svm_clf.fit(X, y)
def plot_dataset(X, y, axes):
    plt.plot(X[:, 0][y==0], X[:, 1][y==0], "bs")
    plt.plot(X[:, 0][y==1], X[:, 1][y==1], "g^")
    plt.axis(axes)
    plt.grid(True, which='both')
    plt.xlabel(r"$x_1$", fontsize=20)
    plt.ylabel(r"$x_2$", fontsize=20, rotation=0)
    plt.title("月亮数据",fontsize=20)
def plot_predictions(clf, axes):
    # 打表
    x0s = np.linspace(axes[0], axes[1], 100)
    x1s = np.linspace(axes[2], axes[3], 100)
    x0, x1 = np.meshgrid(x0s, x1s)
    X = np.c_[x0.ravel(), x1.ravel()]
    y_pred = clf.predict(X).reshape(x0.shape)
    y_decision = clf.decision_function(X).reshape(x0.shape)
#     print(y_pred)
#     print(y_decision)
    plt.contourf(x0, x1, y_pred, cmap=plt.cm.brg, alpha=0.2)
    plt.contourf(x0, x1, y_decision, cmap=plt.cm.brg, alpha=0.1)
plot_predictions(polynomial_svm_clf, [-1.5, 2.5, -1, 1.5])
plot_dataset(X, y, [-1.5, 2.5, -1, 1.5])
plt.show()

结果如下：

使用线性LDA算法对两个数据集进行分类

鸢尾花数据集的代码如下：

import numpy as np
import matplotlib.pyplot as plt
from sklearn import datasets
from sklearn.pipeline import Pipeline
from sklearn.preprocessing import StandardScaler
from sklearn.svm import LinearSVC

# 读取数据，并提取花瓣长度和宽度特征
iris = datasets.load_iris()
X = iris["data"][:, (2, 3)]  # petal length, petal width

plt.scatter(X[:49, 0], X[:49, 1], color='green', marker='o', label='setosa')
plt.scatter(X[49:99, 0], X[49: 99, 1], color='blue', marker='x', label='versicolor')
plt.xlabel('petal length')
plt.ylabel('petal width')
plt.legend(loc='upper left')
plt.title("鸢尾花数据",fontsize=20)
plt.show()

结果如图：

月亮数据集的代码如下：

from sklearn.datasets import make_moons
X, y = make_moons(n_samples=100, noise=0.15, random_state=42)

def plot_dataset(X, y, axes):
    plt.plot(X[:, 0][y==0], X[:, 1][y==0], "bs")
    plt.plot(X[:, 0][y==1], X[:, 1][y==1], "g^")
    plt.axis(axes)
    plt.grid(True, which='both')
    plt.xlabel(r"$x_1$", fontsize=20)
    plt.ylabel(r"$x_2$", fontsize=20, rotation=0)
    plt.title("月亮数据",fontsize=20)

plot_dataset(X, y, [-1.5, 2.5, -1, 1.5])
plt.show()

结果如下：

采用k-means算法对两个数据集进行分类

鸢尾花数据集的代码如下：

import numpy as np
import matplotlib.pyplot as plt
from sklearn import datasets
from sklearn.cluster import KMeans

# 读取数据，并提取花瓣长度和宽度特征
iris = datasets.load_iris()
X = iris["data"][:, (2, 3)]  # petal length, petal width
x_axis = iris["data"][:, (2)]

y_axis = iris["data"][:, (3)]
model = KMeans(n_clusters=2)

#训练模型
model.fit(X)
#选取行标为150的那条数据，进行预测
prddicted_label= model.predict([[71.67, 74]])
#预测全部数据

all_predictions = model.predict(X)
#all_predictions=np.array(all_predictions).reshape(-1,1)
#打印出来数据的聚类散点图
plt.scatter(x_axis,y_axis,c=all_predictions)
plt.show()

结果如下：

月亮数据集的代码如下：

import matplotlib.pyplot as plt
from sklearn.cluster import KMeans
from sklearn.datasets import make_moons
from sklearn.pipeline import Pipeline
import numpy as np
X,y=make_moons(n_samples=100,shuffle=True,noise=0.15,random_state=42)
clf = KMeans()
clf.fit(X,y)
predicted = clf.predict(X)   
plt.scatter(X[:,0], X[:,1], c=predicted, marker='s',s=100,cmap=plt.cm.Paired)    
plt.title("KMeans")    
plt.show() 

结果如下：

SVM算法的优点

算法优点：

（1）使用核函数可以向高维空间进行映射

（2）使用核函数可以解决非线性的分类

（3）分类思想很简单，就是将样本与决策面的间隔最大化

（4）分类效果较好

算法缺点：

（1）SVM算法对大规模训练样本难以实施

（2）用SVM解决多分类问题存在困难

（3）对缺失数据敏感，对参数和核函数的选择敏感　
　　　　　
资料参考：
https://www.cnblogs.com/lsm-boke/p/11761534.html

https://www.zhihu.com/question/21094489

https://baike.baidu.com/item/K%E5%9D%87%E5%80%BC%E8%81%9A%E7%B1%BB%E7%AE%97%E6%B3%95/15779627?fromtitle=K-means&fromid=4934806&fr=aladdin

https://blog.csdn.net/ruthywei/article/details/83045288/