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一、鸢尾花数据集分类

鸢尾花数据集以鸢尾花的特征作为数据来源，数据集包含150个数据集，有4维，分为3类（setosa、versicolour、virginica），每类50个数据，每个数据包含4个属性，花萼长度、宽度和花瓣长度、宽度

软件及使用方法请查看上一篇文章

1. 选择分类
   代码：

from sklearn import datasetsimport matplotlib.pyplot as pltimport numpy as npimport math#prepare the datairis = datasets.load_iris()X = iris.datay = iris.targetnames = iris.feature_nameslabels = iris.target_namesy_c = np.unique(y)"""visualize the distributions of the four different features in 1-dimensional histograms"""fig, axes = plt.subplots(2, 2, figsize=(12, 6))for ax, column in zip(axes.ravel(), range(X.shape[1])):  # set bin sizes  min_b = math.floor(np.min(X[:, column]))  max_b = math.ceil(np.max(X[:, column]))  bins = np.linspace(min_b, max_b, 25)  # plotting the histograms  for i, color in zip(y_c, ('blue', 'red', 'green')):      ax.hist(X[y == i, column], color=color, label='class %s' % labels[i],              bins=bins, alpha=0.5, )  ylims = ax.get_ylim()  # plot annotation  l = ax.legend(loc='upper right', fancybox=True, fontsize=8)  l.get_frame().set_alpha(0.5)  ax.set_ylim([0, max(ylims) + 2])  ax.set_xlabel(names[column])  ax.set_title('Iris histogram feature %s' % str(column + 1))  # hide axis ticks  ax.tick_params(axis='both', which='both', bottom=False, top=False, left=False, right=False,                 labelbottom=True, labelleft=True)  # remove axis spines  ax.spines['top'].set_visible(False)  ax.spines["right"].set_visible(False)  ax.spines["bottom"].set_visible(False)  ax.spines["left"].set_visible(False)axes[0][0].set_ylabel('count')axes[1][0].set_ylabel('count')fig.tight_layout()plt.show()

2. 鸢尾花 数据集的Fisher分类
   代码

np.set_printoptions(precision=4) mean_vector = []  # 类别的平均值for i in y_c:    mean_vector.append(np.mean(X[y == i], axis=0))    print('Mean Vector class %s:%s\n' % (i, mean_vector[i]))S_W = np.zeros((X.shape[1], X.shape[1]))for i in y_c:    Xi = X[y == i] - mean_vector[i]    S_W += np.mat(Xi).T * np.mat(Xi)print('S_W:\n', S_W)S_B = np.zeros((X.shape[1], X.shape[1]))mu = np.mean(X, axis=0)  # 所有样本平均值for i in y_c:    Ni = len(X[y == i])    S_B += Ni * np.mat(mean_vector[i] - mu).T * np.mat(mean_vector[i] - mu)print('S_B:\n', S_B) eigvals, eigvecs = np.linalg.eig(np.linalg.inv(S_W) * S_B)  # 求特征值，特征向量np.testing.assert_array_almost_equal(np.mat(np.linalg.inv(S_W) * S_B) * np.mat(eigvecs[:, 0].reshape(4, 1)),                                     eigvals[0] * np.mat(eigvecs[:, 0].reshape(4, 1)), decimal=6, err_msg='',                                     verbose=True)# sorting the eigenvectors by decreasing eigenvalueseig_pairs = [(np.abs(eigvals[i]), eigvecs[:, i]) for i in range(len(eigvals))]eig_pairs = sorted(eig_pairs, key=lambda k: k[0], reverse=True)W = np.hstack((eig_pairs[0][1].reshape(4, 1), eig_pairs[1][1].reshape(4, 1)))   X_trans = X.dot(W)assert X_trans.shape == (150, 2) plt.figure(figsize=(8, 4))plt.subplot(121)plt.scatter(X_trans[y == 0, 0], X_trans[y == 0, 1], c='r')plt.scatter(X_trans[y == 1, 0], X_trans[y == 1, 1], c='g')plt.scatter(X_trans[y == 2, 0], X_trans[y == 2, 1], c='b')plt.title('my LDA')plt.xlabel('LD1')plt.ylabel('LD2')plt.legend(labels, loc='best', fancybox=True)

3. 判断准确率
   代码

import pandas as pdimport numpy as npimport matplotlib.pyplot as plt %matplotlib inlinedf = pd.read_csv(r'http://archive.ics.uci.edu/ml/machine-learning-databases/iris/iris.data',header = None)Iris1=df.values[0:50,0:4]Iris2=df.values[50:100,0:4]Iris3=df.values[100:150,0:4]m1=np.mean(Iris1,axis=0)m2=np.mean(Iris2,axis=0)m3=np.mean(Iris3,axis=0)s1=np.zeros((4,4))s2=np.zeros((4,4))s3=np.zeros((4,4))for i in range(0,30,1):    a=Iris1[i,:]-m1    a=np.array([a])    b=a.T    s1=s1+np.dot(b,a)    for i in range(0,30,1):    c=Iris2[i,:]-m2    c=np.array([c])    d=c.T    s2=s2+np.dot(d,c)     #s2=s2+np.dot((Iris2[i,:]-m2).T,(Iris2[i,:]-m2))for i in range(0,30,1):    a=Iris3[i,:]-m3    a=np.array([a])    b=a.T    s3=s3+np.dot(b,a) sw12=s1+s2sw13=s1+s3sw23=s2+s3#投影方向a=np.array([m1-m2])sw12=np.array(sw12,dtype='float')sw13=np.array(sw13,dtype='float')sw23=np.array(sw23,dtype='float')#判别函数以及T#需要先将m1-m2转化成矩阵才能进行求其转置矩阵a=m1-m2a=np.array([a])a=a.Tb=m1-m3b=np.array([b])b=b.Tc=m2-m3c=np.array([c])c=c.Tw12=(np.dot(np.linalg.inv(sw12),a)).Tw13=(np.dot(np.linalg.inv(sw13),b)).Tw23=(np.dot(np.linalg.inv(sw23),c)).T#print(m1+m2) #1x4维度  invsw12 4x4维度  m1-m2 4x1维度T12=-0.5*(np.dot(np.dot((m1+m2),np.linalg.inv(sw12)),a))T13=-0.5*(np.dot(np.dot((m1+m3),np.linalg.inv(sw13)),b))T23=-0.5*(np.dot(np.dot((m2+m3),np.linalg.inv(sw23)),c))kind1=0kind2=0kind3=0newiris1=[]newiris2=[]newiris3=[]for i in range(30,49):    x=Iris1[i,:]    x=np.array([x])    g12=np.dot(w12,x.T)+T12    g13=np.dot(w13,x.T)+T13    g23=np.dot(w23,x.T)+T23    if g12>0 and g13>0:        newiris1.extend(x)        kind1=kind1+1    elif g12<0 and g23>0:        newiris2.extend(x)    elif g13<0 and g23<0 :        newiris3.extend(x)#print(newiris1)for i in range(30,49):    x=Iris2[i,:]    x=np.array([x])    g12=np.dot(w12,x.T)+T12    g13=np.dot(w13,x.T)+T13    g23=np.dot(w23,x.T)+T23    if g12>0 and g13>0:        newiris1.extend(x)    elif g12<0 and g23>0:               newiris2.extend(x)        kind2=kind2+1    elif g13<0 and g23<0 :        newiris3.extend(x)for i in range(30,50):    x=Iris3[i,:]    x=np.array([x])    g12=np.dot(w12,x.T)+T12    g13=np.dot(w13,x.T)+T13    g23=np.dot(w23,x.T)+T23    if g12>0 and g13>0:        newiris1.extend(x)    elif g12<0 and g23>0:             newiris2.extend(x)    elif g13<0 and g23<0 :        newiris3.extend(x)        kind3=kind3+1#花瓣与花萼的长度散点图plt.scatter(df.values[:50, 3], df.values[:50, 1], color='red', marker='o', label='setosa')plt.scatter(df.values[50:100, 3], df.values[50: 100, 1], color='blue', marker='x', label='versicolor')plt.scatter(df.values[100:150, 3], df.values[100: 150, 1], color='green', label='virginica')plt.xlabel('petal length')plt.ylabel('sepal length')plt.title("花瓣与花萼长度的散点图")plt.rcParams['font.sans-serif']=['SimHei'] #显示中文标签plt.rcParams['axes.unicode_minus']=Falseplt.legend(loc='upper left')plt.show()#花瓣与花萼的宽度度散点图plt.scatter(df.values[:50, 4], df.values[:50, 2], color='red', marker='o', label='setosa')plt.scatter(df.values[50:100, 4], df.values[50: 100, 2], color='blue', marker='x', label='versicolor')plt.scatter(df.values[100:150, 4], df.values[100: 150, 2], color='green', label='virginica')plt.xlabel('petal width')plt.ylabel('sepal width')plt.title("花瓣与花萼宽度的散点图")plt.legend(loc='upper left')plt.show()correct=(kind1+kind2+kind3)/60print("样本类内离散度矩阵S1：",s1,'\n')print("样本类内离散度矩阵S2：",s2,'\n')print("样本类内离散度矩阵S3：",s3,'\n')print('-----------------------------------------------------------------------------------------------')print("总体类内离散度矩阵Sw12：",sw12,'\n')print("总体类内离散度矩阵Sw13：",sw13,'\n')print("总体类内离散度矩阵Sw23：",sw23,'\n')print('-----------------------------------------------------------------------------------------------')print('判断出来的综合正确率：',correct*100,'%')

二、可视化显示

在PC上安装seaborn库

pip install seaborn

鸢尾花数据集文件

upload到jupyter里

用python对“Iris-”字符进行分割

import numpy as npimport pandas as pdimport seaborn as snsimport matplotlib.pyplot as pltdf_Iris = pd.read_csv('Iris.csv')#对数据进行分割df_Iris['Species']= df_Iris.Species.apply(lambda x: x.split('-')[1])df_Iris.Species.unique()

2.1散点图

#sns初始化sns.set()#设置散点图x轴与y轴以及data参数sns.relplot(x='SepalLengthCm', y='SepalWidthCm', data = df_Iris)plt.title('SepalLengthCm and SepalWidthCm data analysize')

#hue表示按照Species对数据进行分类, 而style表示每个类别的标签系列格式不一致.sns.relplot(x='SepalLengthCm', y='SepalWidthCm', hue='Species', style='Species', data=df_Iris )plt.title('SepalLengthCm and SepalWidthCm data by Species')

#花瓣长度与宽度分布散点图sns.relplot(x='PetalLengthCm', y='PetalWidthCm', hue='Species', style='Species', data=df_Iris )plt.title('PetalLengthCm and PetalWidthCm data by Species')

#花萼与花瓣长度分布散点图sns.relplot(x='SepalLengthCm', y='PetalLengthCm', hue='Species', style='Species', data=df_Iris )plt.title('SepalLengthCm and PetalLengthCm data by Species')

#花萼与花瓣宽度分布散点图sns.relplot(x='SepalWidthCm', y='PetalWidthCm', hue='Species', style='Species', data=df_Iris )plt.title('SepalWidthCm and PetalWidthCm data by Species')

#花萼的长度与花瓣的宽度分布散点图sns.relplot(x='SepalLengthCm', y='PetalWidthCm', hue='Species', style='Species', data=df_Iris )plt.title('SepalLengthCm and PetalWidthCm data by Species')

#花萼的宽度与花瓣的长度分布散点图sns.relplot(x='SepalWidthCm', y='PetalLengthCm', hue='Species', style='Species', data=df_Iris )plt.title('SepalWidthCm and PetalLengthCm data by Species')

2.2直方图

sns.distplot(df_Iris.SepalLengthCm,bins=8, hist=True, kde=False)

sns.distplot(df_Iris.SepalWidthCm,bins=13, hist=True, kde=False)

sns.distplot(df_Iris.PetalLengthCm, bins=5, hist=True, kde=False)

sns.distplot(df_Iris.PetalWidthCm, bins=5, hist=True, kde=False)

2.3 pairplot

sns.pairplot(df_Iris, hue='Species')plt.savefig('pairplot.png')plt.show()

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