本次学习从机器学习的典例数据：鸢尾花数据集出发。
Iris dataset可以从sklearn直接引入，也可以从http://archive.ics.uci.edu/ml/datasets/Iris获取。
实验环境
- python3环境
- 使用到的库
from sklearn import datasets
from matplotlib import pyplot as plt
import numpy as np
数据的可视化
- 从sklearn引入数据集
iris = datasets.load_iris()
features = iris['data']
feature_names = iris['feature_names']
target = iris['target']
- 画出每个类别的数据集，代码中以sepal length 和sepal width为例
for t, marker, c in zip(range(3), ">ox", "rgb"):
#我们划出每个类别，各自采用不通颜色标识
plt.scatter(features[target == t, 0],
features[target == t, 1],
marker=marker,
c=c)
plt.xlabel('sepal length')
plt.ylabel('sepal width')
plt.show()
Figure_1.png
- 画出每个类别的数据集
def scatter_plot(dim1,dim2):
for t, marker, c in zip(range(3), ">ox", "rgb"):
#我们划出每个类别，各自采用不通颜色标识
plt.scatter(features[target == t, dim1],
features[target == t, dim2],
marker=marker,
c=c)
dim_desc={0:'sepal length',1:'sepal width',2:'petal length',3:'petal width'}
plt.xlabel(dim_desc.get(dim1))
plt.ylabel(dim_desc.get(dim2))
#plt.show()
#用subplot构建6个子图
count = 0
for j in range(3):
for k in range(1, 4):
if(k>j):
plt.subplot(231+count)
scatter_plot(j, k)
count=count+1
plt.show()#注意plt.show()的位置
Figure_1.png
根据可视化的图形，显而易见，山鸢尾花可以由花瓣长度很明显的区分出来。
分类
- 山鸢尾花区分开来
plength = features[:, 2]
#用numpy操作，来获取setosa的特征,花瓣长度，是一维矩阵
is_setosa = (target == 0) #布尔型一维矩阵
#print(is_setosa)
#print((is_setosa.shape))
#print(plength.shape)
#布尔型索引
setosa_plength = plength[is_setosa]
other_plength = plength[~is_setosa]
max_setosa = setosa_plength.max()
min_non_setosa = other_plength.min()
print('Maximum of setosa:{0}. '.format(max_setosa))
print('Minmum of others:{0}.'.format(min_non_setosa))
- 筛出另外两个花种
# #筛出非setosa的花种
features = features[~is_setosa]
labels = target[~is_setosa]
# #rint(labels)
#
#
virginica = (labels == 2)
#print(virginica)
#
# #print(virginica)
print(features.shape)
best_acc = -1.0
for fi in range(features.shape[1]):
thresh = features[:, fi].copy()
#thresh.sort()
#print(thresh)
for t in thresh:
#print('t is',t)
pred = (features[:, fi] > t)
#print(pred)
#print(pred == virginica)
acc = (pred == virginica).mean()
#print('acc=', acc)
if acc > best_acc:
best_acc = acc
best_fi = fi
best_t = t
print('Best Accuracy:', best_acc)
print('Best Feature Index', fi)
print('Best Threshold', t)
#这里我们首先对每一维度进行排序，然后从该维度中取出任一值作为阈值的一个假设，再计算这个假设的Boolean序列和实际的标签Boolean序列的一致情况，求平均，即得到了准确率。经过所有的循环，最终得到的阈值和所对应的维度。
#最后，我们得到了最佳模型针对第四维花瓣的宽度petal width，我们就可以得到这个决策边界decision boundary。
这里得出的分界是以某个参数的界限值为标准的
得出准确率最高是0.96 但是这里我们的训练数据和测试数据并没有分开来。
- 交叉验证
去一法，从训练集中拿出一个样本，并在缺少这个样本的数据上训练一个模型，然后看模型能否对这个样本正确分类：
def learn_model(features,labels):
best_acc = -1.0
for fi in range(features.shape[1]):
thresh = features[:, fi].copy()
# thresh.sort()
#print(thresh)
for t in thresh:
# print('t is',t)
pred = (features[:, fi] > t)
# print(pred)
# print(pred == virginica)
acc = (pred == labels).mean()
# print('acc=', acc)
if acc > best_acc:
best_acc = acc
best_fi = fi
best_t = t
print('Best Accuracy:', best_acc)
print('Best Feature Index', fi)
print('Best Threshold', t)
return {'accuracy':best_acc, 'Feature Index':best_fi, 'Threshold':best_t}
def apply_model(features,labels,model):
t = model['Threshold']
pred = (features[:, fi] > t)
acc = (pred == labels).mean()
return pred
error = 0.0
for ei in range(len(features)):
#选择除了ei以外的所有位置：
training = np.ones(len(features), bool)
training[ei] = False
testing = ~training
model = learn_model(features[training],virginica[training])
predictions = apply_model(features[testing],virginica[testing],model)
error += np.sum(predictions != virginica[testing])
print(error)