机械学习将鸢尾花的特征值和特征向量进行组合
import pandas as pd #第一步数据读取 data = pd.read_csv('IrisData.csv') data.columns = ['sepal_len','sepal_wid','petal_len','petal_wid','classes'] #第二步提取特征 X = data[['sepal_len','sepal_wid','petal_len','petal_wid']].values y = data['classes'].values feature_names = ['sepal_len','sepal_wid','petal_len','petal_wid'] label_names = data['classes'].unique() #第三步对每一个特征的样 品类别做直方图 for feature in range(len(feature_names)): plt.subplot(2,2,feature+1) for label in label_names: plt.hist(X[y==label,feature],bins=10,alpha=0.5,label=label) plt.legend(loc='best') plt.show() #第四步对特征进行标准化操作 from sklearn.preprocessing import StandardScaler std_feature = StandardScaler().fit_transform(X) # 第五步 对特征去除均值，并构造协方差矩阵，也可以使用np. conv进行构造 mean_fea = std_feature.mean(axis=0) cov_matrix = (std_feature - mean_fea).T.dot(std_feature-mean_fea) #第六步使用np.1inalg.eig求出协方差矩阵的特征值和特征向量 eig_val,eig_vector = np.linalg.eig(cov_matrix) #第七步:我们将特征值和特征向量进行组合 eig_paries = [(eig_val[j],eig_vector[:,j]) for j in range(len(eig_val))] eig_vector_two = np.vstack([eig_paries[0][1],eig_paries[1][1]]) print(eig_vector_two) trans_std_X = std_feature.dot(eig_vector_two.T)
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鸢尾花数据
sepal length,sepal width,petal length,petal width,Species 5.1,3.5,1.4,0.2,Setosa 4.9,3,1.4,0.2,Setosa 4.7,3.2,1.3,0.2,Setosa 4.6,3.1,1.5,0.2,Setosa 5,3.6,1.4,0.2,Setosa 5.4,3.9,1.7,0.4,Setosa 4.6,3.4,1.4,0.3,Setosa 5,3.4,1.5,0.2,Setosa 4.4,2.9,1.4,0.2,Setosa 4.9,3.1,1.5,0.1,Setosa 5.4,3.7,1.5,0.2,Setosa 4.8,3.4,1.6,0.2,Setosa 4.8,3,1.4,0.1,Setosa 4.3,3,1.1,0.1,Setosa 5.8,4,1.2,0.2,Setosa 5.7,4.4,1.5,0.4,Setosa 5.4,3.9,1.3,0.4,Setosa 5.1,3.5,1.4,0.3,Setosa 5.7,3.8,1.7,0.3,Setosa 5.1,3.8,1.5,0.3,Setosa 5.4,3.4,1.7,0.2,Setosa 5.1,3.7,1.5,0.4,Setosa 4.6,3.6,1,0.2,Setosa 5.1,3.3,1.7,0.5,Setosa 4.8,3.4,1.9,0.2,Setosa 5,3,1.6,0.2,Setosa 5,3.4,1.6,0.4,Setosa 5.2,3.5,1.5,0.2,Setosa 5.2,3.4,1.4,0.2,Setosa 4.7,3.2,1.6,0.2,Setosa 4.8,3.1,1.6,0.2,Setosa 5.4,3.4,1.5,0.4,Setosa 5.2,4.1,1.5,0.1,Setosa 5.5,4.2,1.4,0.2,Setosa 4.9,3.1,1.5,0.2,Setosa 5,3.2,1.2,0.2,Setosa 5.5,3.5,1.3,0.2,Setosa 4.9,3.6,1.4,0.1,Setosa 4.4,3,1.3,0.2,Setosa 5.1,3.4,1.5,0.2,Setosa 5,3.5,1.3,0.3,Setosa 4.5,2.3,1.3,0.3,Setosa 4.4,3.2,1.3,0.2,Setosa 5,3.5,1.6,0.6,Setosa 5.1,3.8,1.9,0.4,Setosa 4.8,3,1.4,0.3,Setosa 5.1,3.8,1.6,0.2,Setosa 4.6,3.2,1.4,0.2,Setosa 5.3,3.7,1.5,0.2,Setosa 5,3.3,1.4,0.2,Setosa 7,3.2,4.7,1.4,Versicolour 6.4,3.2,4.5,1.5,Versicolour 6.9,3.1,4.9,1.5,Versicolour 5.5,2.3,4,1.3,Versicolour 6.5,2.8,4.6,1.5,Versicolour 5.7,2.8,4.5,1.3,Versicolour 6.3,3.3,4.7,1.6,Versicolour 4.9,2.4,3.3,1,Versicolour 6.6,2.9,4.6,1.3,Versicolour 5.2,2.7,3.9,1.4,Versicolour 5,2,3.5,1,Versicolour 5.9,3,4.2,1.5,Versicolour 6,2.2,4,1,Versicolour 6.1,2.9,4.7,1.4,Versicolour 5.6,2.9,3.6,1.3,Versicolour 6.7,3.1,4.4,1.4,Versicolour 5.6,3,4.5,1.5,Versicolour 5.8,2.7,4.1,1,Versicolour 6.2,2.2,4.5,1.5,Versicolour 5.6,2.5,3.9,1.1,Versicolour 5.9,3.2,4.8,1.8,Versicolour 6.1,2.8,4,1.3,Versicolour 6.3,2.5,4.9,1.5,Versicolour 6.1,2.8,4.7,1.2,Versicolour 6.4,2.9,4.3,1.3,Versicolour 6.6,3,4.4,1.4,Versicolour 6.8,2.8,4.8,1.4,Versicolour 6.7,3,5,1.7,Versicolour 6,2.9,4.5,1.5,Versicolour 5.7,2.6,3.5,1,Versicolour 5.5,2.4,3.8,1.1,Versicolour 5.5,2.4,3.7,1,Versicolour 5.8,2.7,3.9,1.2,Versicolour 6,2.7,5.1,1.6,Versicolour 5.4,3,4.5,1.5,Versicolour 6,3.4,4.5,1.6,Versicolour 6.7,3.1,4.7,1.5,Versicolour 6.3,2.3,4.4,1.3,Versicolour 5.6,3,4.1,1.3,Versicolour 5.5,2.5,4,1.3,Versicolour 5.5,2.6,4.4,1.2,Versicolour 6.1,3,4.6,1.4,Versicolour 5.8,2.6,4,1.2,Versicolour 5,2.3,3.3,1,Versicolour 5.6,2.7,4.2,1.3,Versicolour 5.7,3,4.2,1.2,Versicolour 5.7,2.9,4.2,1.3,Versicolour 6.2,2.9,4.3,1.3,Versicolour 5.1,2.5,3,1.1,Versicolour 5.7,2.8,4.1,1.3,Versicolour 6.3,3.3,6,2.5,Virginica 5.8,2.7,5.1,1.9,Virginica 7.1,3,5.9,2.1,Virginica 6.3,2.9,5.6,1.8,Virginica 6.5,3,5.8,2.2,Virginica 7.6,3,6.6,2.1,Virginica 4.9,2.5,4.5,1.7,Virginica 7.3,2.9,6.3,1.8,Virginica 6.7,2.5,5.8,1.8,Virginica 7.2,3.6,6.1,2.5,Virginica 6.5,3.2,5.1,2,Virginica 6.4,2.7,5.3,1.9,Virginica 6.8,3,5.5,2.1,Virginica 5.7,2.5,5,2,Virginica 5.8,2.8,5.1,2.4,Virginica 6.4,3.2,5.3,2.3,Virginica 6.5,3,5.5,1.8,Virginica 7.7,3.8,6.7,2.2,Virginica 7.7,2.6,6.9,2.3,Virginica 6,2.2,5,1.5,Virginica 6.9,3.2,5.7,2.3,Virginica 5.6,2.8,4.9,2,Virginica 7.7,2.8,6.7,2,Virginica 6.3,2.7,4.9,1.8,Virginica 6.7,3.3,5.7,2.1,Virginica 7.2,3.2,6,1.8,Virginica 6.2,2.8,4.8,1.8,Virginica 6.1,3,4.9,1.8,Virginica 6.4,2.8,5.6,2.1,Virginica 7.2,3,5.8,1.6,Virginica 7.4,2.8,6.1,1.9,Virginica 7.9,3.8,6.4,2,Virginica 6.4,2.8,5.6,2.2,Virginica 6.3,2.8,5.1,1.5,Virginica 6.1,2.6,5.6,1.4,Virginica 7.7,3,6.1,2.3,Virginica 6.3,3.4,5.6,2.4,Virginica 6.4,3.1,5.5,1.8,Virginica 6,3,4.8,1.8,Virginica 6.9,3.1,5.4,2.1,Virginica 6.7,3.1,5.6,2.4,Virginica 6.9,3.1,5.1,2.3,Virginica 5.8,2.7,5.1,1.9,Virginica 6.8,3.2,5.9,2.3,Virginica 6.7,3.3,5.7,2.5,Virginica 6.7,3,5.2,2.3,Virginica 6.3,2.5,5,1.9,Virginica 6.5,3,5.2,2,Virginica 6.2,3.4,5.4,2.3,Virginica 5.9,3,5.1,1.8,Virginica
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A是方阵,齐次方程组 的所有的解就是A对应于特征值λ=0的特征向量。
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