机器学习之对鸢尾花数据集和月亮数据集，分别采用线性LDA、k
一、采用线性LDA算法进行二分类可视化分析
1、鸢尾花数据集import numpy as np import matplotlib.pyplot as plt from sklearn.datasets.samples_generator import make_classification class LDA(): def Train(self, X, y): """X为训练数据集，y为训练label""" X1 = np.array([X[i] for i in range(len(X)) if y[i] == 0]) X2 = np.array([X[i] for i in range(len(X)) if y[i] == 1]) # 求中心点 mju1 = np.mean(X1, axis=0) # mju1是ndrray类型 mju2 = np.mean(X2, axis=0) # dot(a, b, out=None) 计算矩阵乘法 cov1 = np.dot((X1 - mju1).T, (X1 - mju1)) cov2 = np.dot((X2 - mju2).T, (X2 - mju2)) Sw = cov1 + cov2 # 计算w w = np.dot(np.mat(Sw).I, (mju1 - mju2).reshape((len(mju1), 1))) # 记录训练结果 self.mju1 = mju1 # 第1类的分类中心 self.cov1 = cov1 self.mju2 = mju2 # 第2类的分类中心 self.cov2 = cov2 self.Sw = Sw # 类内散度矩阵 self.w = w # 判别权重矩阵 def Test(self, X, y): """X为测试数据集，y为测试label""" # 分类结果 y_new = np.dot((X), self.w) # 计算fisher线性判别式 nums = len(y) c1 = np.dot((self.mju1 - self.mju2).reshape(1, (len(self.mju1))), np.mat(self.Sw).I) c2 = np.dot(c1, (self.mju1 + self.mju2).reshape((len(self.mju1), 1))) c = 1/2 * c2 # 2个分类的中心 h = y_new - c # 判别 y_hat = [] for i in range(nums): if h[i] >= 0: y_hat.append(0) else: y_hat.append(1) # 计算分类精度 count = 0 for i in range(nums): if y_hat[i] == y[i]: count += 1 precise = count / nums # 显示信息 print("测试样本数量:", nums) print("预测正确样本的数量:", count) print("测试准确度:", precise) return precise if '__main__' == __name__: # 产生分类数据 n_samples = 500 X, y = make_classification(n_samples=n_samples, n_features=2, n_redundant=0, n_classes=2,n_informative=1, n_clusters_per_class=1, class_sep=0.5, random_state=10) # LDA线性判别分析(二分类) lda = LDA() # 60% 用作训练，40%用作测试 Xtrain = X[:299, :] Ytrain = y[:299] Xtest = X[300:, :] Ytest = y[300:] lda.Train(Xtrain, Ytrain) precise = lda.Test(Xtest, Ytest) # 原始数据 plt.scatter(X[:, 0], X[:, 1], marker='o', c=y) plt.xlabel("x1") plt.ylabel("x2") plt.title("Test precise:" + str(precise)) plt.show()
1234567891011121314151617181920212223242526272829303132333435363738394041424344454647484950515253545556575859606162636465666768697071727374运行结果：
import numpy as np import matplotlib.pyplot as plt from sklearn.datasets import make_moons class LDA(): def Train(self, X, y): """X为训练数据集，y为训练label""" X1 = np.array([X[i] for i in range(len(X)) if y[i] == 0]) X2 = np.array([X[i] for i in range(len(X)) if y[i] == 1]) # 求中心点 mju1 = np.mean(X1, axis=0) # mju1是ndrray类型 mju2 = np.mean(X2, axis=0) # dot(a, b, out=None) 计算矩阵乘法 cov1 = np.dot((X1 - mju1).T, (X1 - mju1)) cov2 = np.dot((X2 - mju2).T, (X2 - mju2)) Sw = cov1 + cov2 # 计算w w = np.dot(np.mat(Sw).I, (mju1 - mju2).reshape((len(mju1), 1))) # 记录训练结果 self.mju1 = mju1 # 第1类的分类中心 self.cov1 = cov1 self.mju2 = mju2 # 第1类的分类中心 self.cov2 = cov2 self.Sw = Sw # 类内散度矩阵 self.w = w # 判别权重矩阵 def Test(self, X, y): """X为测试数据集，y为测试label""" # 分类结果 y_new = np.dot((X), self.w) # 计算fisher线性判别式 nums = len(y) c1 = np.dot((self.mju1 - self.mju2).reshape(1, (len(self.mju1))), np.mat(self.Sw).I) c2 = np.dot(c1, (self.mju1 + self.mju2).reshape((len(self.mju1), 1))) c = 1/2 * c2 # 2个分类的中心 h = y_new - c # 判别 y_hat = [] for i in range(nums): if h[i] >= 0: y_hat.append(0) else: y_hat.append(1) # 计算分类精度 count = 0 for i in range(nums): if y_hat[i] == y[i]: count += 1 precise = count / (nums+0.000001) # 显示信息 print("测试样本数量:", nums) print("预测正确样本的数量:", count) print("测试准确度:", precise) return precise if '__main__' == __name__: # 产生分类数据 X, y = make_moons(n_samples=100, noise=0.15, random_state=42) # LDA线性判别分析(二分类) lda = LDA() # 60% 用作训练，40%用作测试 Xtrain = X[:60, :] Ytrain = y[:60] Xtest = X[40:, :] Ytest = y[40:] lda.Train(Xtrain, Ytrain) precise = lda.Test(Xtest, Ytest) # 原始数据 plt.scatter(X[:, 0], X[:, 1], marker='o', c=y) plt.xlabel("x1") plt.ylabel("x2") plt.title("Test precise:" + str(precise)) plt.show()
12345678910111213141516171819202122232425262728293031323334353637383940414243444546474849505152535455565758596061626364656667686970运行结果：
二、采用k-means算法进行二分类可视化分析
1、鸢尾花数据集#鸢尾花数据集的K-means分类 from sklearn import datasets import matplotlib.pyplot as plt from sklearn.cluster import KMeans #加载数据集，是一个字典类似Java中的map lris_df = datasets.load_iris() #挑选出前两个维度作为x轴和y轴，你也可以选择其他维度 x_axis = lris_df.data[:,0] y_axis = lris_df.data[:,2] #这里已经知道了分2类，其他分类这里的参数需要调试 model = KMeans(n_clusters=2) #训练模型 model.fit(lris_df.data) #选取行标为100的那条数据，进行预测 prddicted_label= model.predict([[6.3, 3.3, 6, 2.5]]) #预测全部150条数据 all_predictions = model.predict(lris_df.data) #打印出来对150条数据的聚类散点图 plt.scatter(x_axis, y_axis, c=all_predictions) plt.show()
12345678910111213141516171819202122232425262728运行结果：
import matplotlib.pyplot as plt import numpy as np from sklearn.cluster import KMeans from sklearn.datasets import make_moons X, y = make_moons(n_samples=100, noise=0.15, random_state=42) estimator = KMeans(n_clusters=5)#构造聚类器 estimator.fit(X)#聚类 label_pred = estimator.labels_ #获取聚类标签 #绘制k-means结果 x0 = X[label_pred == 0] x1 = X[label_pred == 1] x2 = X[label_pred == 2] x3 = X[label_pred == 3] plt.scatter(x0[:, 0], x0[:, 1], c = "red", marker='o', label='label0') plt.scatter(x1[:, 0], x1[:, 1], c = "green", marker='*', label='label1') #plt.scatter(x2[:, 0], x2[:, 1], c = "blue", marker='+', label='label2') #plt.scatter(x3[:, 0], x3[:, 1], c = "yellow", marker='o', label='label3') plt.xlabel('petal length') plt.ylabel('petal width') plt.legend(loc=2) plt.show()
123456789101112131415161718192021运行结果：
三、采用SVM算法进行二分类可视化分析
1、鸢尾花数据集from sklearn.svm import SVC from sklearn import datasets import matplotlib.pyplot as plt import numpy as np iris = datasets.load_iris() X = iris["data"][:, (2, 3)] # 花瓣长度与花瓣宽度 petal length, petal width y = iris["target"] setosa_or_versicolor = (y == 0) | (y == 1) X = X[setosa_or_versicolor] y = y[setosa_or_versicolor] # SVM Classifier model svm_clf = SVC(kernel="linear", C=float("inf")) svm_clf.fit(X, y) def plot_svc_decision_boundary(svm_clf, xmin, xmax): # 获取决策边界的w和b w = svm_clf.coef_[0] b = svm_clf.intercept_[0] # At the decision boundary, w0*x0 + w1*x1 + b = 0 # => x1 = -w0/w1 * x0 - b/w1 x0 = np.linspace(xmin, xmax, 200) # 画中间的粗线 decision_boundary = -w[0]/w[1] * x0 - b/w[1] # 计算间隔 margin = 1/w[1] gutter_up = decision_boundary + margin gutter_down = decision_boundary - margin # 获取支持向量 svs = svm_clf.support_vectors_ plt.scatter(svs[:, 0], svs[:, 1], s=180, facecolors='#FFAAAA') plt.plot(x0, decision_boundary, "k-", linewidth=2) plt.plot(x0, gutter_up, "k--", linewidth=2) plt.plot(x0, gutter_down, "k--", linewidth=2) plt.title("大间隔分类", fontsize=16) plt.rcParams['font.sans-serif']=['SimHei'] #显示中文标签 plt.rcParams['axes.unicode_minus']=False plot_svc_decision_boundary(svm_clf, 0, 5.5) plt.plot(X[:, 0][y==1], X[:, 1][y==1], "bs") plt.plot(X[:, 0][y==0], X[:, 1][y==0], "yo") plt.xlabel("Petal length", fontsize=14) plt.axis([0, 5.5, 0, 2]) plt.show()
1234567891011121314151617181920212223242526272829303132333435363738394041运行结果：
import matplotlib.pyplot as plt from sklearn.pipeline import Pipeline import numpy as np import matplotlib as mpl from sklearn.datasets import make_moons from sklearn.preprocessing import PolynomialFeatures from sklearn.preprocessing import StandardScaler from sklearn.svm import LinearSVC # 为了显示中文 mpl.rcParams['font.sans-serif'] = [u'SimHei'] mpl.rcParams['axes.unicode_minus'] = False 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()
12345678910111213141516171819202122结果：
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_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()
123456789101112131415161718192021222324结果：
from sklearn.svm import SVC gamma1, gamma2 = 0.1, 5 C1, C2 = 0.001, 1000 hyperparams = (gamma1, C1), (gamma1, C2) svm_clfs = [] for gamma, C in hyperparams: rbf_kernel_svm_clf = Pipeline([ ("scaler", StandardScaler()), ("svm_clf", SVC(kernel="rbf", gamma=gamma, C=C)) ]) rbf_kernel_svm_clf.fit(X, y) svm_clfs.append(rbf_kernel_svm_clf) plt.figure(figsize=(11, 7)) for i, svm_clf in enumerate(svm_clfs): plt.subplot(221 + i) plot_predictions(svm_clf, [-1.5, 2.5, -1, 1.5]) plot_dataset(X, y, [-1.5, 2.5, -1, 1.5]) gamma, C = hyperparams[i] plt.title(r"$gamma = {}, C = {}$".format(gamma, C), fontsize=16) plt.tight_layout() plt.show()
123456789101112131415161718192021结果：
四、SVM算法优缺点
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
参考文献
参考地址
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