文章目錄
一、線性LDA
1.鳶尾花LDA
import numpy as np
import matplotlib.pyplot as plt
from sklearn import datasets
def LDA(X, y):
#根據y等於0或1分類
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])
len1 = len(X1)
len2 = len(X2)
mju1 = np.mean(X1, axis=0)#求中心點
mju2 = np.mean(X2, axis=0)
cov1 = np.dot((X1 - mju1).T, (X1 - mju1))
cov2=np.dot((X2 - mju2).T, (X2 - mju2))
Sw = cov1 + cov2
a=mju1-mju2
a=(np.array([a])).T
w=(np.dot(np.linalg.inv(Sw),a))
X1_new =func(X1, w)
X2_new = func(X2, w)
y1_new = [1 for i in range(len1)]
y2_new = [2 for i in range(len2)]
return X1_new,X2_new,y1_new,y2_new
def func(x, w):
return np.dot((x), w)
iris = datasets.load_iris()
X = iris["data"][:, (2, 3)] # 花瓣長度與花瓣寬度 petal length, petal width
y = iris["target"]
#print(y)
setosa_or_versicolor = (y == 0) | (y == 1)
X = X[setosa_or_versicolor]
y = y[setosa_or_versicolor]
#print(Sw)
x1_new, X2_new, y1_new, y2_new = LDA(X, y)
plt.xlabel('花瓣長度')
plt.ylabel('花瓣寬度')
plt.rcParams['font.sans-serif']=['SimHei'] #顯示中文標籤
plt.rcParams['axes.unicode_minus']=False
plt.scatter(X[:, 0], X[:, 1], marker='o', c=y)
plt.title("Iris_LDA")
plt.show()
2.月亮集LDA
def LDA(X, y):
#根據y等於0或1分類
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])
len1 = len(X1)
len2 = len(X2)
mju1 = np.mean(X1, axis=0)#求中心點
mju2 = np.mean(X2, axis=0)
cov1 = np.dot((X1 - mju1).T, (X1 - mju1))
cov2=np.dot((X2 - mju2).T, (X2 - mju2))
Sw = cov1 + cov2
a=mju1-mju2
a=(np.array([a])).T
w=(np.dot(np.linalg.inv(Sw),a))
X1_new =func(X1, w)
X2_new = func(X2, w)
y1_new = [1 for i in range(len1)]
y2_new = [2 for i in range(len2)]
def func(x, w):
return np.dot((x), w)
X, y = datasets.make_moons(n_samples=100, noise=0.15, random_state=42)
plt.scatter(X[:, 0], X[:, 1], marker='o', c=y)
plt.title("moon_LDA")
plt.show()
二、K-means
1.鳶尾花k-means
from sklearn import datasets
import matplotlib.pyplot as plt
from sklearn.cluster import KMeans
#加載數據集，是一個字典類似Java中的map
lris_df = datasets.load_iris()
#挑選出前兩個維度作爲x軸和y軸，你也可以選擇其他維度
x_axis = lris_df.data[:,0]
y_axis = lris_df.data[:,2]
model = KMeans(n_clusters=2)
#訓練模型
model.fit(lris_df.data)
#選取行標爲100的那條數據，進行預測
prddicted_label= model.predict([[6.3, 3.3, 6, 2.5]])
#預測全部150條數據
all_predictions = model.predict(lris_df.data)
#打印出來對150條數據的聚類散點圖
plt.scatter(x_axis, y_axis, c=all_predictions)
plt.title("Iris_KMeans")
plt.show()
2.月亮集k-means
#基於k-means算法對月亮數據集進行分類
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(n_clusters=2)
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("Moon_KMeans")
plt.show()
三、SVM
1.鳶尾花svm
from sklearn.svm import SVC
from sklearn import datasets
iris = datasets.load_iris()
X = iris["data"][:, (2, 3)] # 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):
# 獲取決策邊界的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)
# 畫中間的粗線
decision_boundary = -w[0]/w[1] * x0 - b/w[1]
# 計算間隔
margin = 1/w[1]
gutter_up = decision_boundary + margin
gutter_down = decision_boundary - margin
# 獲取支持向量
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)
# Bad models
x0 = np.linspace(0, 5.5, 200)
plt.figure(figsize=(12,2.7))
plt.axis([0, 5.5, 0, 2])
plt.subplot(122)
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.title("Iris_svm")
plt.show()
2.月亮集svm
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([
# 將源數據 映射到 3階多項式
("poly_features", PolynomialFeatures(degree=3)),
# 標準化
("scaler", StandardScaler()),
# SVC線性分類器
("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')
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.title("moon_svm")
plt.show()
四、SVM的優缺點
優點
1、使用核函數可以向高維空間進行映射
2、使用核函數可以解決非線性的分類
3、分類思想很簡單，就是將樣本與決策面的間隔最大化
4、分類效果較好
缺點
1、對大規模數據訓練比較困難
2、無法直接支持多分類，但是可以使用間接的方法來做
五、參考文章
https://blog.csdn.net/qq_45213986/article/details/106186415?fps=1&locationNum=2?ops_request_misc=&request_id=&biz_id=102&utm_term=python%E5%AE%9E%E7%8E%B0%E9%B8%A2%E5%B0%BE%E8%8A%B1LDA&utm_medium=distribute.pc_search_result.none-task-blog-2allsobaiduweb~default-1-106186415
https://blog.csdn.net/zrh_CSDN/article/details/80934248