头歌机器学习（2）
【代码】头歌机器学习（2）
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本文仅供机器学习参考
1、逻辑回归
1、逻辑回归核心思想
#encoding=utf8
#encoding=utf8
import numpy as np
def sigmoid(t):
'''
完成sigmoid函数计算
:param t: 负无穷到正无穷的实数
:return: 转换后的概率值
:可以考虑使用np.exp()函数
'''
#********** Begin **********#
return 1.0/(1+np.exp(-t))
#********** End **********#
2、逻辑回归的损失函数
3、梯度下降
## -*- coding: utf-8 -*-
import numpy as np
import warnings
warnings.filterwarnings("ignore")
def gradient_descent(initial_theta,eta=0.05,n_iters=1000,epslion=1e-8):
'''
梯度下降
:param initial_theta: 参数初始值，类型为float
:param eta: 学习率，类型为float
:param n_iters: 训练轮数，类型为int
:param epslion: 容忍误差范围，类型为float
:return: 训练后得到的参数
'''
# 请在此添加实现代码 #
#********** Begin *********#
theta = initial_theta
i_iter = 0
while i_iter < n_iters:
gradient = 2*(theta-3)
last_theta = theta
theta = theta - eta*gradient
if(abs(theta-last_theta)<epslion):
break
i_iter +=1
return theta
#********** End **********#
4、动手实现逻辑回归 - 癌细胞精准识别
# -*- coding: utf-8 -*-
import numpy as np
import warnings
warnings.filterwarnings("ignore")
def sigmoid(x):
'''
sigmoid函数
:param x: 转换前的输入
:return: 转换后的概率
'''
return 1/(1+np.exp(-x))
def fit(x,y,eta=1e-3,n_iters=10000):
'''
训练逻辑回归模型
:param x: 训练集特征数据，类型为ndarray
:param y: 训练集标签，类型为ndarray
:param eta: 学习率，类型为float
:param n_iters: 训练轮数，类型为int
:return: 模型参数，类型为ndarray
'''
# 请在此添加实现代码 #
#********** Begin *********#
theta = np.zeros(x.shape[1])
i_iter = 0
while i_iter < n_iters:
gradient = (sigmoid(x.dot(theta))-y).dot(x)
theta = theta -eta*gradient
i_iter += 1
return theta
#********** End **********#
5、手写数字识别
from sklearn.linear_model import LogisticRegression
def digit_predict(train_image, train_label, test_image):
'''
实现功能：训练模型并输出预测结果
:param train_sample: 包含多条训练样本的样本集，类型为ndarray,shape为[-1, 8, 8]
:param train_label: 包含多条训练样本标签的标签集，类型为ndarray
:param test_sample: 包含多条测试样本的测试集，类型为ndarry
:return: test_sample对应的预测标签
'''
#************* Begin ************#
# 训练集变形
flat_train_image = train_image.reshape((-1, 64))
# 训练集标准化
train_min = flat_train_image.min()
train_max = flat_train_image.max()
flat_train_image = (flat_train_image-train_min)/(train_max-train_min)
# 测试集变形
flat_test_image = test_image.reshape((-1, 64))
# 测试集标准化
test_min = flat_test_image.min()
test_max = flat_test_image.max()
flat_test_image = (flat_test_image - test_min) / (test_max - test_min)
# 训练--预测
rf = LogisticRegression(C=4.0)
rf.fit(flat_train_image, train_label)
return rf.predict(flat_test_image)
#************* End **************#
2、决策树
1、什么是决策树
2、信息熵与信息增益
import numpy as np
def calcInfoGain(feature, label, index):
'''
计算信息增益
:param feature:测试用例中字典里的feature，类型为ndarray
:param label:测试用例中字典里的label，类型为ndarray
:param index:测试用例中字典里的index，即feature部分特征列的索引。该索引指的是feature中第几个特征，如index:0表示使用第一个特征来计算信息增益。
:return:信息增益，类型float
'''
#*********** Begin ***********#
# 计算熵
def calcInfoEntropy(feature, label):
'''
计算信息熵
:param feature:数据集中的特征，类型为ndarray
:param label:数据集中的标签，类型为ndarray
:return:信息熵，类型float
'''
label_set = set(label)
result = 0
for l in label_set:
count = 0
for j in range(len(label)):
if label[j] == l:
count += 1
# 计算标签在数据集中出现的概率
p = count / len(label)
# 计算熵
result -= p * np.log2(p)
return result
# 计算条件熵
def calcHDA(feature, label, index, value):
'''
计算信息熵
:param feature:数据集中的特征，类型为ndarray
:param label:数据集中的标签，类型为ndarray
:param index:需要使用的特征列索引，类型为int
:param value:index所表示的特征列中需要考察的特征值，类型为int
:return:信息熵，类型float
'''
count = 0
# sub_feature和sub_label表示根据特征列和特征值分割出的子数据集中的特征和标签
sub_feature = []
sub_label = []
for i in range(len(feature)):
if feature[i][index] == value:
count += 1
sub_feature.append(feature[i])
sub_label.append(label[i])
pHA = count / len(feature)
e = calcInfoEntropy(sub_feature, sub_label)
return pHA * e
base_e = calcInfoEntropy(feature, label)
f = np.array(feature)
# 得到指定特征列的值的集合
f_set = set(f[:, index])
sum_HDA = 0
# 计算条件熵
for value in f_set:
sum_HDA += calcHDA(feature, label, index, value)
# 计算信息增益
return base_e - sum_HDA
#*********** End *************#3、使用ID3算法构建决策树
import numpy as np
class DecisionTree(object):
def __init__(self):
#决策树模型
self.tree = {}
def calcInfoGain(self, feature, label, index):
'''
计算信息增益
:param feature:测试用例中字典里的feature，类型为ndarray
:param label:测试用例中字典里的label，类型为ndarray
:param index:测试用例中字典里的index，即feature部分特征列的索引。该索引指的是feature中第几个特征，如index:0表示使用第一个特征来计算信息增益。
:return:信息增益，类型float
'''
# 计算熵
def calcInfoEntropy(label):
'''
计算信息熵
:param label:数据集中的标签，类型为ndarray
:return:信息熵，类型float
'''
label_set = set(label)
result = 0
for l in label_set:
count = 0
for j in range(len(label)):
if label[j] == l:
count += 1
# 计算标签在数据集中出现的概率
p = count / len(label)
# 计算熵
result -= p * np.log2(p)
return result
# 计算条件熵
def calcHDA(feature, label, index, value):
'''
计算信息熵
:param feature:数据集中的特征，类型为ndarray
:param label:数据集中的标签，类型为ndarray
:param index:需要使用的特征列索引，类型为int
:param value:index所表示的特征列中需要考察的特征值，类型为int
:return:信息熵，类型float
'''
count = 0
# sub_feature和sub_label表示根据特征列和特征值分割出的子数据集中的特征和标签
sub_feature = []
sub_label = []
for i in range(len(feature)):
if feature[i][index] == value:
count += 1
sub_feature.append(feature[i])
sub_label.append(label[i])
pHA = count / len(feature)
e = calcInfoEntropy(sub_label)
return pHA * e
base_e = calcInfoEntropy(label)
f = np.array(feature)
# 得到指定特征列的值的集合
f_set = set(f[:, index])
sum_HDA = 0
# 计算条件熵
for value in f_set:
sum_HDA += calcHDA(feature, label, index, value)
# 计算信息增益
return base_e - sum_HDA
# 获得信息增益最高的特征
def getBestFeature(self, feature, label):
max_infogain = 0
best_feature = 0
for i in range(len(feature[0])):
infogain = self.calcInfoGain(feature, label, i)
if infogain > max_infogain:
max_infogain = infogain
best_feature = i
return best_feature
def createTree(self, feature, label):
# 样本里都是同一个label没必要继续分叉了
if len(set(label)) == 1:
return label[0]
# 样本中只有一个特征或者所有样本的特征都一样的话就看哪个label的票数高
if len(feature[0]) == 1 or len(np.unique(feature, axis=0)) == 1:
vote = {}
for l in label:
if l in vote.keys():
vote[l] += 1
else:
vote[l] = 1
max_count = 0
vote_label = None
for k, v in vote.items():
if v > max_count:
max_count = v
vote_label = k
return vote_label
# 根据信息增益拿到特征的索引
best_feature = self.getBestFeature(feature, label)
tree = {best_feature: {}}
f = np.array(feature)
# 拿到bestfeature的所有特征值
f_set = set(f[:, best_feature])
# 构建对应特征值的子样本集sub_feature, sub_label
for v in f_set:
sub_feature = []
sub_label = []
for i in range(len(feature)):
if feature[i][best_feature] == v:
sub_feature.append(feature[i])
sub_label.append(label[i])
# 递归构建决策树
tree[best_feature][v] = self.createTree(sub_feature, sub_label)
return tree
def fit(self, feature, label):
'''
:param feature: 训练集数据，类型为ndarray
:param label:训练集标签，类型为ndarray
:return: None
'''
#************* Begin ************#
self.tree = self.createTree(feature, label)
#************* End **************#
def predict(self, feature):
'''
:param feature:测试集数据，类型为ndarray
:return:预测结果，如np.array([0, 1, 2, 2, 1, 0])
'''
#************* Begin ************#
result = []
def classify(tree, feature):
if not isinstance(tree, dict):
return tree
t_index, t_value = list(tree.items())[0]
f_value = feature[t_index]
if isinstance(t_value, dict):
classLabel = classify(tree[t_index][f_value], feature)
return classLabel
else:
return t_value
for f in feature:
result.append(classify(self.tree, f))
return np.array(result)
#************* End **************#4、信息增益率
import numpy as np
def calcInfoGain(feature, label, index):
'''
计算信息增益
:param feature:测试用例中字典里的feature，类型为ndarray
:param label:测试用例中字典里的label，类型为ndarray
:param index:测试用例中字典里的index，即feature部分特征列的索引。该索引指的是feature中第几个特征，如index:0表示使用第一个特征来计算信息增益。
:return:信息增益，类型float
'''
# 计算熵
def calcInfoEntropy(label):
'''
计算信息熵
:param label:数据集中的标签，类型为ndarray
:return:信息熵，类型float
'''
label_set = set(label)
result = 0
for l in label_set:
count = 0
for j in range(len(label)):
if label[j] == l:
count += 1
# 计算标签在数据集中出现的概率
p = count / len(label)
# 计算熵
result -= p * np.log2(p)
return result
# 计算条件熵
def calcHDA(feature, label, index, value):
'''
计算信息熵
:param feature:数据集中的特征，类型为ndarray
:param label:数据集中的标签，类型为ndarray
:param index:需要使用的特征列索引，类型为int
:param value:index所表示的特征列中需要考察的特征值，类型为int
:return:信息熵，类型float
'''
count = 0
# sub_label表示根据特征列和特征值分割出的子数据集中的标签
sub_label = []
for i in range(len(feature)):
if feature[i][index] == value:
count += 1
sub_label.append(label[i])
pHA = count / len(feature)
e = calcInfoEntropy(sub_label)
return pHA * e
base_e = calcInfoEntropy(label)
f = np.array(feature)
# 得到指定特征列的值的集合
f_set = set(f[:, index])
sum_HDA = 0
# 计算条件熵
for value in f_set:
sum_HDA += calcHDA(feature, label, index, value)
# 计算信息增益
return base_e - sum_HDA
def calcInfoGainRatio(feature, label, index):
'''
计算信息增益率
:param feature:测试用例中字典里的feature，类型为ndarray
:param label:测试用例中字典里的label，类型为ndarray
:param index:测试用例中字典里的index，即feature部分特征列的索引。该索引指的是feature中第几个特征，如index:0表示使用第一个特征来计算信息增益。
:return:信息增益率，类型float
'''
#********* Begin *********#
info_gain = calcInfoGain(feature, label, index)
unique_value = list(set(feature[:, index]))
IV = 0
for value in unique_value:
len_v = np.sum(feature[:, index] == value)
IV -= (len_v/len(feature))*np.log2((len_v/len(feature)))
return info_gain/IV
#********* End *********#5、基尼系数
import numpy as np
def calcGini(feature, label, index):
'''
计算基尼系数
:param feature:测试用例中字典里的feature，类型为ndarray
:param label:测试用例中字典里的label，类型为ndarray
:param index:测试用例中字典里的index，即feature部分特征列的索引。该索引指的是feature中第几个特征，如index:0表示使用第一个特征来计算信息增益。
:return:基尼系数，类型float
'''
#********* Begin *********#
def _gini(label):
unique_label = list(set(label))
gini = 1
for l in unique_label:
p = np.sum(label == l)/len(label)
gini -= p**2
return gini
unique_value = list(set(feature[:, index]))
gini = 0
for value in unique_value:
len_v = np.sum(feature[:, index] == value)
gini += (len_v/len(feature))*_gini(label[feature[:, index] == value])
return gini
#********* End *********#6、预剪枝与后剪枝
import numpy as np
from copy import deepcopy
class DecisionTree(object):
def __init__(self):
#决策树模型
self.tree = {}
def calcInfoGain(self, feature, label, index):
'''
计算信息增益
:param feature:测试用例中字典里的feature，类型为ndarray
:param label:测试用例中字典里的label，类型为ndarray
:param index:测试用例中字典里的index，即feature部分特征列的索引。该索引指的是feature中第几个特征，如index:0表示使用第一个特征来计算信息增益。
:return:信息增益，类型float
'''
# 计算熵
def calcInfoEntropy(feature, label):
'''
计算信息熵
:param feature:数据集中的特征，类型为ndarray
:param label:数据集中的标签，类型为ndarray
:return:信息熵，类型float
'''
label_set = set(label)
result = 0
for l in label_set:
count = 0
for j in range(len(label)):
if label[j] == l:
count += 1
# 计算标签在数据集中出现的概率
p = count / len(label)
# 计算熵
result -= p * np.log2(p)
return result
# 计算条件熵
def calcHDA(feature, label, index, value):
'''
计算信息熵
:param feature:数据集中的特征，类型为ndarray
:param label:数据集中的标签，类型为ndarray
:param index:需要使用的特征列索引，类型为int
:param value:index所表示的特征列中需要考察的特征值，类型为int
:return:信息熵，类型float
'''
count = 0
# sub_feature和sub_label表示根据特征列和特征值分割出的子数据集中的特征和标签
sub_feature = []
sub_label = []
for i in range(len(feature)):
if feature[i][index] == value:
count += 1
sub_feature.append(feature[i])
sub_label.append(label[i])
pHA = count / len(feature)
e = calcInfoEntropy(sub_feature, sub_label)
return pHA * e
base_e = calcInfoEntropy(feature, label)
f = np.array(feature)
# 得到指定特征列的值的集合
f_set = set(f[:, index])
sum_HDA = 0
# 计算条件熵
for value in f_set:
sum_HDA += calcHDA(feature, label, index, value)
# 计算信息增益
return base_e - sum_HDA
# 获得信息增益最高的特征
def getBestFeature(self, feature, label):
max_infogain = 0
best_feature = 0
for i in range(len(feature[0])):
infogain = self.calcInfoGain(feature, label, i)
if infogain > max_infogain:
max_infogain = infogain
best_feature = i
return best_feature
# 计算验证集准确率
def calc_acc_val(self, the_tree, val_feature, val_label):
result = []
def classify(tree, feature):
if not isinstance(tree, dict):
return tree
t_index, t_value = list(tree.items())[0]
f_value = feature[t_index]
if isinstance(t_value, dict):
classLabel = classify(tree[t_index][f_value], feature)
return classLabel
else:
return t_value
for f in val_feature:
result.append(classify(the_tree, f))
result = np.array(result)
return np.mean(result == val_label)
def createTree(self, train_feature, train_label):
# 样本里都是同一个label没必要继续分叉了
if len(set(train_label)) == 1:
return train_label[0]
# 样本中只有一个特征或者所有样本的特征都一样的话就看哪个label的票数高
if len(train_feature[0]) == 1 or len(np.unique(train_feature, axis=0)) == 1:
vote = {}
for l in train_label:
if l in vote.keys():
vote[l] += 1
else:
vote[l] = 1
max_count = 0
vote_label = None
for k, v in vote.items():
if v > max_count:
max_count = v
vote_label = k
return vote_label
# 根据信息增益拿到特征的索引
best_feature = self.getBestFeature(train_feature, train_label)
tree = {best_feature: {}}
f = np.array(train_feature)
# 拿到bestfeature的所有特征值
f_set = set(f[:, best_feature])
# 构建对应特征值的子样本集sub_feature, sub_label
for v in f_set:
sub_feature = []
sub_label = []
for i in range(len(train_feature)):
if train_feature[i][best_feature] == v:
sub_feature.append(train_feature[i])
sub_label.append(train_label[i])
# 递归构建决策树
tree[best_feature][v] = self.createTree(sub_feature, sub_label)
return tree
# 后剪枝
def post_cut(self, val_feature, val_label):
# 拿到非叶子节点的数量
def get_non_leaf_node_count(tree):
non_leaf_node_path = []
def dfs(tree, path, all_path):
for k in tree.keys():
if isinstance(tree[k], dict):
path.append(k)
dfs(tree[k], path, all_path)
if len(path) > 0:
path.pop()
else:
all_path.append(path[:])
dfs(tree, [], non_leaf_node_path)
unique_non_leaf_node = []
for path in non_leaf_node_path:
isFind = False
for p in unique_non_leaf_node:
if path == p:
isFind = True
break
if not isFind:
unique_non_leaf_node.append(path)
return len(unique_non_leaf_node)
# 拿到树中深度最深的从根节点到非叶子节点的路径
def get_the_most_deep_path(tree):
non_leaf_node_path = []
def dfs(tree, path, all_path):
for k in tree.keys():
if isinstance(tree[k], dict):
path.append(k)
dfs(tree[k], path, all_path)
if len(path) > 0:
path.pop()
else:
all_path.append(path[:])
dfs(tree, [], non_leaf_node_path)
max_depth = 0
result = None
for path in non_leaf_node_path:
if len(path) > max_depth:
max_depth = len(path)
result = path
return result
# 剪枝
def set_vote_label(tree, path, label):
for i in range(len(path)-1):
tree = tree[path[i]]
tree[path[len(path)-1]] = vote_label
acc_before_cut = self.calc_acc_val(self.tree, val_feature, val_label)
# 遍历所有非叶子节点
for _ in range(get_non_leaf_node_count(self.tree)):
path = get_the_most_deep_path(self.tree)
# 备份树
tree = deepcopy(self.tree)
step = deepcopy(tree)
# 跟着路径走
for k in path:
step = step[k]
# 叶子节点中票数最多的标签
vote_label = sorted(step.items(), key=lambda item: item[1], reverse=True)[0][0]
# 在备份的树上剪枝
set_vote_label(tree, path, vote_label)
acc_after_cut = self.calc_acc_val(tree, val_feature, val_label)
# 验证集准确率高于0.9才剪枝
if acc_after_cut > acc_before_cut:
set_vote_label(self.tree, path, vote_label)
acc_before_cut = acc_after_cut
def fit(self, train_feature, train_label, val_feature, val_label):
'''
:param train_feature:训练集数据，类型为ndarray
:param train_label:训练集标签，类型为ndarray
:param val_feature:验证集数据，类型为ndarray
:param val_label:验证集标签，类型为ndarray
:return: None
'''
#************* Begin ************#
self.tree = self.createTree(train_feature, train_label)
# 后剪枝
self.post_cut(val_feature, val_label)
# 后剪枝
#************* End **************#
def predict(self, feature):
'''
:param feature:测试集数据，类型为ndarray
:return:预测结果，如np.array([0, 1, 2, 2, 1, 0])
'''
#************* Begin ************#
result = []
# 单个样本分类
def classify(tree, feature):
if not isinstance(tree, dict):
return tree
t_index, t_value = list(tree.items())[0]
f_value = feature[t_index]
if isinstance(t_value, dict):
classLabel = classify(tree[t_index][f_value], feature)
return classLabel
else:
return t_value
for f in feature:
result.append(classify(self.tree, f))
return np.array(result)
# 单个样本分类
#************* End **************#7、鸢尾花识别
#********* Begin *********#
import pandas as pd
from sklearn.tree import DecisionTreeClassifier
train_df = pd.read_csv('./step7/train_data.csv').as_matrix()
train_label = pd.read_csv('./step7/train_label.csv').as_matrix()
test_df = pd.read_csv('./step7/test_data.csv').as_matrix()
dt = DecisionTreeClassifier()
dt.fit(train_df, train_label)
result = dt.predict(test_df)
result = pd.DataFrame({'target':result})
result.to_csv('./step7/predict.csv', index=False)
#********* End *********#3、朴素贝叶斯分类器
1、条件概率
2、贝叶斯公式
3、朴素贝叶斯分类算法流程
import numpy as np
class NaiveBayesClassifier(object):
def __init__(self):
self.label_prob = {}
self.condition_prob = {}
def fit(self, feature, label):
# 计算标签的概率
unique_labels, counts = np.unique(label, return_counts=True)
total_samples = len(label)
for label, count in zip(unique_labels, counts):
self.label_prob[label] = (count + 1) / (total_samples + len(unique_labels)) # Laplace smoothing
# 计算条件概率
for label in unique_labels:
self.condition_prob[label] = {}
# 只考虑当前标签的数据
subset = feature[label == label]
for i in range(feature.shape[1]):
unique_features, counts = np.unique(subset[:, i], return_counts=True)
total_feature_count = len(subset)
self.condition_prob[label][i] = {feat: (cnt + 1) / (total_feature_count + len(unique_features))
for feat, cnt in zip(unique_features, counts)}
def predict(self, feature):
predictions = []
for sample in feature:
max_posterior = -np.inf
predicted_label = None
for label in self.label_prob.keys():
posterior = np.log(self.label_prob[label])
for i, value in enumerate(sample):
if value in self.condition_prob[label][i]:
posterior += np.log(self.condition_prob[label][i][value])
if posterior > max_posterior:
max_posterior = posterior
predicted_label = label
predictions.append(predicted_label)
return np.array(predictions)
# 使用示例
X = np.array([[2, 1, 1],
[1, 2, 2],
[2, 2, 2],
[2, 1, 2],
[1, 2, 3],
[2, 1, 1]])
y = np.array([1, 0, 1, 0, 1, 0])
nb_classifier = NaiveBayesClassifier()
nb_classifier.fit(X, y)
# 假设我们有一个新的样本需要预测
new_sample = np.array([[1, 2, 2]])
prediction = nb_classifier.predict(new_sample)
#print("预测结果：", prediction)4、拉普拉斯平滑
import numpy as np
class NaiveBayesClassifier(object):
def __init__(self):
self.label_prob = {}
self.condition_prob = {}
def fit(self, feature, label):
# 计算标签的先验概率
unique_labels, counts = np.unique(label, return_counts=True)
total_samples = len(label)
for label, count in zip(unique_labels, counts):
self.label_prob[label] = (count + 1) / (total_samples + len(unique_labels)) # 拉普拉斯平滑
# 初始化条件概率字典
self.condition_prob = {label: {} for label in unique_labels}
# 对于每个特征列
for i in range(feature.shape[1]):
# 获取当前特征的所有可能取值
unique_features = np.unique(feature[:, i])
# 对于每个类别
for label in unique_labels:
# 只考虑当前类别的数据
subset = feature[label == label]
# 初始化当前特征的条件概率
self.condition_prob[label][i] = {feat: 1 / (len(subset) + len(unique_features)) for feat in unique_features}
# 更新条件概率
for feat in unique_features:
self.condition_prob[label][i][feat] = (np.sum(subset[:, i] == feat) + 1) / (len(subset) + len(unique_features))
def predict(self, feature):
result = []
# 对每条测试数据都进行预测
for f in feature:
# 可能的类别的概率
prob = np.zeros(len(self.label_prob.keys()))
ii = 0
for label, label_prob in self.label_prob.items():
# 计算概率
prob[ii] = label_prob
for j in range(len(f)):
if f[j] in self.condition_prob[label][j]:
prob[ii] *= self.condition_prob[label][j][f[j]]
else:
prob[ii] *= 1e-10 # 如果特征值未出现在训练集中，则赋予一个很小的概率
ii += 1
# 取概率最大的类别作为结果
result.append(list(self.label_prob.keys())[np.argmax(prob)])
return np.array(result)
# 使用示例
X = np.array([[2, 1, 1],
[1, 2, 2],
[2, 2, 2],
[2, 1, 2],
[1, 2, 3],
[2, 1, 2]])
y = np.array([1, 0, 1, 1, 1, 0])
nb_classifier = NaiveBayesClassifier()
nb_classifier.fit(X, y)
# 假设我们有一个新的样本需要预测
new_sample = np.array([[1, 2, 2]])
prediction = nb_classifier.predict(new_sample)
#print("预测结果：", prediction)5、新闻文本主题分类
from sklearn.feature_extraction.text import CountVectorizer # 从sklearn.feature_extraction.text里导入文本特征向量化模块
from sklearn.naive_bayes import MultinomialNB
from sklearn.feature_extraction.text import TfidfTransformer
def news_predict(train_sample, train_label, test_sample):
'''
训练模型并进行预测，返回预测结果
:param train_sample:原始训练集中的新闻文本，类型为ndarray
:param train_label:训练集中新闻文本对应的主题标签，类型为ndarray
:test_sample:原始测试集中的新闻文本，类型为ndarray
'''
# ********* Begin *********#
vec = CountVectorizer()
train_sample = vec.fit_transform(train_sample)
test_sample = vec.transform(test_sample)
tfidf = TfidfTransformer()
train_sample = tfidf.fit_transform(train_sample)
test_sample = tfidf.transform(test_sample)
mnb = MultinomialNB(alpha=0.01) # 使用默认配置初始化朴素贝叶斯
mnb.fit(train_sample, train_label) # 利用训练数据对模型参数进行估计
predict = mnb.predict(test_sample) # 对参数进行预测
return predict
# ********* End *********#4、感知机
1、感知机 - 西瓜好坏自动识别
#encoding=utf8
import numpy as np
#构建感知机算法
class Perceptron(object):
def __init__(self, learning_rate = 0.01, max_iter = 200):
self.lr = learning_rate
self.max_iter = max_iter
def fit(self, data, label):
'''
input:data(ndarray):训练数据特征
label(ndarray):训练数据标签
output:w(ndarray):训练好的权重
b(ndarry):训练好的偏置
'''
#编写感知机训练方法，w为权重，b为偏置
self.w = np.array([1.]*data.shape[1])
self.b = np.array([1.])
#********* Begin *********#
i = 0
while i < self.max_iter:
flag = True
for j in range(len(label)):
if label[j] * (np.inner(self.w, data[j]) + self.b) <= 0:
flag = False
self.w += self.lr * (label[j] * data[j])
self.b += self.lr * label[j]
if flag:
break
i+=1
#********* End *********#
def predict(self, data):
'''
input:data(ndarray):测试数据特征
output:predict(ndarray):预测标签
'''
#********* Begin *********#
y = np.inner(data, self.w) + self.b
for i in range(len(y)): # range(0,6)
if y[i] >= 0:
y[i] = 1
else:
y[i] = -1
predict = y
#********* End *********#
return predict2、scikit-learn感知机实践 - 癌细胞精准识别
#encoding=utf8
import os
if os.path.exists('./step2/result.csv'):
os.remove('./step2/result.csv')
#********* Begin *********#
import pandas as pd
train_data = pd.read_csv('./step2/train_data.csv')
train_label = pd.read_csv('./step2/train_label.csv')
train_label = train_label['target']
test_data = pd.read_csv('./step2/test_data.csv')
from sklearn.linear_model.perceptron import Perceptron
clf = Perceptron(eta0 = 0.01,max_iter = 200)
clf.fit(train_data, train_label)
result = clf.predict(test_data)
frameResult = pd.DataFrame({'result':result})
frameResult.to_csv('./step2/result.csv', index = False)
#********* End *********#5、EM算法
1、极大似然估计
2、实现EM算法的单次迭代过程
import numpy as np
from scipy import stats
def em_single(init_values, observations):
"""
模拟抛掷硬币实验并估计在一次迭代中，硬币A与硬币B正面朝上的概率
:param init_values:硬币A与硬币B正面朝上的概率的初始值，类型为list，如[0.2, 0.7]代表硬币A正面朝上的概率为0.2，硬币B正面朝上的概率为0.7。
:param observations:抛掷硬币的实验结果记录，类型为list。
:return:将估计出来的硬币A和硬币B正面朝上的概率组成list返回。如[0.4, 0.6]表示你认为硬币A正面朝上的概率为0.4，硬币B正面朝上的概率为0.6。
"""
#********* Begin *********#
observations = np.array(observations)
counts = {'A': {'H': 0, 'T': 0}, 'B': {'H': 0, 'T': 0}}
theta_A = init_values[0]
theta_B = init_values[1]
# E step
for observation in observations:
len_observation = len(observation)
num_heads = observation.sum()
num_tails = len_observation - num_heads
# 两个二项分布
contribution_A = stats.binom.pmf(num_heads, len_observation, theta_A)
contribution_B = stats.binom.pmf(num_heads, len_observation, theta_B)
weight_A = contribution_A / (contribution_A + contribution_B)
weight_B = contribution_B / (contribution_A + contribution_B)
# 更新在当前参数下A、B硬币产生的正反面次数
counts['A']['H'] += weight_A * num_heads
counts['A']['T'] += weight_A * num_tails
counts['B']['H'] += weight_B * num_heads
counts['B']['T'] += weight_B * num_tails
# M step
new_theta_A = counts['A']['H'] / (counts['A']['H'] + counts['A']['T'])
new_theta_B = counts['B']['H'] / (counts['B']['H'] + counts['B']['T'])
return [new_theta_A, new_theta_B]
#********* End *********#
3、实现EM算法的主循环
import numpy as np
from scipy import stats
def em_single(init_values, observations):
"""
模拟抛掷硬币实验并估计在一次迭代中，硬币A与硬币B正面朝上的概率。请不要修改！！
:param init_values:硬币A与硬币B正面朝上的概率的初始值，类型为list，如[0.2, 0.7]代表硬币A正面朝上的概率为0.2，硬币B正面朝上的概率为0.7。
:param observations:抛掷硬币的实验结果记录，类型为list。
:return:将估计出来的硬币A和硬币B正面朝上的概率组成list返回。如[0.4, 0.6]表示你认为硬币A正面朝上的概率为0.4，硬币B正面朝上的概率为0.6。
"""
observations = np.array(observations)
counts = {'A': {'H': 0, 'T': 0}, 'B': {'H': 0, 'T': 0}}
theta_A = init_values[0]
theta_B = init_values[1]
# E step
for observation in observations:
len_observation = len(observation)
num_heads = observation.sum()
num_tails = len_observation - num_heads
# 两个二项分布
contribution_A = stats.binom.pmf(num_heads, len_observation, theta_A)
contribution_B = stats.binom.pmf(num_heads, len_observation, theta_B)
weight_A = contribution_A / (contribution_A + contribution_B)
weight_B = contribution_B / (contribution_A + contribution_B)
# 更新在当前参数下A、B硬币产生的正反面次数
counts['A']['H'] += weight_A * num_heads
counts['A']['T'] += weight_A * num_tails
counts['B']['H'] += weight_B * num_heads
counts['B']['T'] += weight_B * num_tails
# M step
new_theta_A = counts['A']['H'] / (counts['A']['H'] + counts['A']['T'])
new_theta_B = counts['B']['H'] / (counts['B']['H'] + counts['B']['T'])
return [new_theta_A, new_theta_B]
def em(observations, thetas, tol=1e-4, iterations=100):
"""
模拟抛掷硬币实验并使用EM算法估计硬币A与硬币B正面朝上的概率。
:param observations: 抛掷硬币的实验结果记录，类型为list。
:param thetas: 硬币A与硬币B正面朝上的概率的初始值，类型为list，如[0.2, 0.7]代表硬币A正面朝上的概率为0.2，硬币B正面朝上的概率为0.7。
:param tol: 差异容忍度，即当EM算法估计出来的参数theta不怎么变化时，可以提前挑出循环。例如容忍度为1e-4，则表示若这次迭代的估计结果与上一次迭代的估计结果之间的L1距离小于1e-4则跳出循环。为了正确的评测，请不要修改该值。
:param iterations: EM算法的最大迭代次数。为了正确的评测，请不要修改该值。
:return: 将估计出来的硬币A和硬币B正面朝上的概率组成list或者ndarray返回。如[0.4, 0.6]表示你认为硬币A正面朝上的概率为0.4，硬币B正面朝上的概率为0.6。
"""
#********* Begin *********#
theta = np.array(thetas)#初始值
# 循环iterations次
for i in range(iterations):
new_theta = np.array(em_single(theta, observations))
# 当差异小于iterations跳出循环
if np.sum(np.abs(new_theta-theta))<tol:
break;
theta = new_theta
return theta
#********* End *********#
6、神经网络
1、神经网络基本概念
2、激活函数
#encoding=utf8
def relu(x):
'''
x:负无穷到正无穷的实数
'''
#********* Begin *********#
if x<=0:
return 0
else:
return x
#********* End *********#3、反向传播算法
#encoding=utf8
import os
import pandas as pd
from sklearn.neural_network import MLPClassifier
if os.path.exists('./step2/result.csv'):
os.remove('./step2/result.csv')
#********* Begin *********#
train_data = pd.read_csv('./step2/train_data.csv')
train_label = pd.read_csv('./step2/train_label.csv')
train_label = train_label['target']
test_data = pd.read_csv('./step2/test_data.csv')
mlp = MLPClassifier(solver='lbfgs',max_iter=30, alpha=1e-4,hidden_layer_sizes=(20, ))
mlp.fit(train_data, train_label)
predict = mlp.predict(test_data)
df = pd.DataFrame({'result':predict})
df.to_csv('./step2/result.csv', index=False)
#********* End *********#4、使用pytorch搭建卷积神经网络识别手写数字
#encoding=utf8
import torch
import torch.nn as nn
from torch.autograd import Variable
import torch.utils.data as Data
import torchvision
import os
if os.path.exists('./step3/cnn.pkl'):
os.remove('./step3/cnn.pkl')
#加载数据
train_data = torchvision.datasets.MNIST(
root='./step3/mnist/',
train=True, # this is training data
transform=torchvision.transforms.ToTensor(), # Converts a PIL.Image or numpy.ndarray to
download=False,
)
#取6000个样本为训练集
train_data_tiny = []
for i in range(6000):
train_data_tiny.append(train_data[i])
train_data = train_data_tiny
#********* Begin *********#
train_loader = Data.DataLoader(
dataset=train_data,
batch_size=64,
num_workers=2,
shuffle=True
)
# 构建卷积神经网络模型
class CNN(nn.Module):
def __init__(self):
super(CNN, self).__init__()
self.conv1 = nn.Sequential( # input shape (1, 28, 28)
nn.Conv2d(
in_channels=1, # input height
out_channels=16, # n_filters
kernel_size=5, # filter size
stride=1, # filter movement/step
padding=2,
# if want same width and length of this image after con2d, padding=(kernel_size-1)/2 if stride=1
), # output shape (16, 28, 28)
nn.ReLU(), # activation
nn.MaxPool2d(kernel_size=2), # choose max value in 2x2 area, output shape (16, 14, 14)
)
self.conv2 = nn.Sequential( # input shape (16, 14, 14)
nn.Conv2d(16, 32, 5, 1, 2), # output shape (32, 14, 14)
nn.ReLU(), # activation
nn.MaxPool2d(2), # output shape (32, 7, 7)
)
self.out = nn.Linear(32 * 7 * 7, 10) # fully connected layer, output 10 classes
def forward(self, x):
x = self.conv1(x)
x = self.conv2(x)
x = x.view(x.size(0), -1) # flatten the output of conv2 to (batch_size, 32 * 7 * 7)
output = self.out(x)
return output
cnn = CNN()
# SGD表示使用随机梯度下降方法，lr为学习率，momentum为动量项系数
optimizer = torch.optim.SGD(cnn.parameters(), lr=0.01, momentum=0.9)
# 交叉熵损失函数
loss_func = nn.CrossEntropyLoss()
EPOCH = 3
for e in range(EPOCH):
for x, y in train_loader:
batch_x = Variable(x)
batch_y = Variable(y)
outputs = cnn(batch_x)
loss = loss_func(outputs, batch_y)
optimizer.zero_grad()
loss.backward()
optimizer.step()
#********* End *********#
#保存模型
torch.save(cnn.state_dict(), './step3/cnn.pkl')7、支持向量回归
1、线性可分支持向量机
2、线性支持向量机
#encoding=utf8
from sklearn.svm import LinearSVC
def linearsvc_predict(train_data,train_label,test_data):
'''
input:train_data(ndarray):训练数据
train_label(ndarray):训练标签
output:predict(ndarray):测试集预测标签
'''
#********* Begin *********#
clf = LinearSVC(dual=False)
clf.fit(train_data,train_label)
predict = clf.predict(test_data)
#********* End *********#
return predict
3、非线性支持向量机
#encoding=utf8
from sklearn.svm import SVC
def svc_predict(train_data,train_label,test_data,kernel):
'''
input:train_data(ndarray):训练数据
train_label(ndarray):训练标签
kernel(str):使用核函数类型:
'linear':线性核函数
'poly':多项式核函数
'rbf':径像核函数/高斯核
output:predict(ndarray):测试集预测标签
'''
#********* Begin *********#
clf =SVC(kernel=kernel)
clf.fit(train_data,train_label)
predict = clf.predict(test_data)
#********* End *********#
return predict
4、序列最小优化算法
#encoding=utf8
import numpy as np
class smo:
def __init__(self, max_iter=100, kernel='linear'):
'''
input:max_iter(int):最大训练轮数
kernel(str):核函数，等于'linear'表示线性，等于'poly'表示多项式
'''
self.max_iter = max_iter
self._kernel = kernel
#初始化模型
def init_args(self, features, labels):
self.m, self.n = features.shape
self.X = features
self.Y = labels
self.b = 0.0
# 将Ei保存在一个列表里
self.alpha = np.ones(self.m)
self.E = [self._E(i) for i in range(self.m)]
# 错误惩罚参数
self.C = 1.0
#********* Begin *********#
#kkt条件
def _KKT(self, i):
y_g = self._g(i)*self.Y[i]
if self.alpha[i] == 0:
return y_g >= 1
elif 0 < self.alpha[i] < self.C:
return y_g == 1
else:
return y_g <= 1
# g(x)预测值，输入xi（X[i]）
def _g(self, i):
r = self.b
for j in range(self.m):
r += self.alpha[j]*self.Y[j]*self.kernel(self.X[i], self.X[j])
return r
# 核函数,多项式添加二次项即可
def kernel(self, x1, x2):
if self._kernel == 'linear':
return sum([x1[k]*x2[k] for k in range(self.n)])
elif self._kernel == 'poly':
return (sum([x1[k]*x2[k] for k in range(self.n)]) + 1)**2
return 0
# E（x）为g(x)对输入x的预测值和y的差
def _E(self, i):
return self._g(i) - self.Y[i]
#初始alpha
def _init_alpha(self):
# 外层循环首先遍历所有满足0<a<C的样本点，检验是否满足KKT
index_list = [i for i in range(self.m) if 0 < self.alpha[i] < self.C]
# 否则遍历整个训练集
non_satisfy_list = [i for i in range(self.m) if i not in index_list]
index_list.extend(non_satisfy_list)
for i in index_list:
if self._KKT(i):
continue
E1 = self.E[i]
# 如果E2是+，选择最小的；如果E2是负的，选择最大的
if E1 >= 0:
j = min(range(self.m), key=lambda x: self.E[x])
else:
j = max(range(self.m), key=lambda x: self.E[x])
return i, j
#选择alpha参数
def _compare(self, _alpha, L, H):
if _alpha > H:
return H
elif _alpha < L:
return L
else:
return _alpha
#训练
def fit(self, features, labels):
'''
input:features(ndarray):特征
label(ndarray):标签
'''
self.init_args(features, labels)
for t in range(self.max_iter):
i1, i2 = self._init_alpha()
# 边界
if self.Y[i1] == self.Y[i2]:
L = max(0, self.alpha[i1]+self.alpha[i2]-self.C)
H = min(self.C, self.alpha[i1]+self.alpha[i2])
else:
L = max(0, self.alpha[i2]-self.alpha[i1])
H = min(self.C, self.C+self.alpha[i2]-self.alpha[i1])
E1 = self.E[i1]
E2 = self.E[i2]
# eta=K11+K22-2K12
eta = self.kernel(self.X[i1], self.X[i1]) + self.kernel(self.X[i2], self.X[i2]) - 2*self.kernel(self.X[i1], self.X[i2])
if eta <= 0:
continue
alpha2_new_unc = self.alpha[i2] + self.Y[i2] * (E2 - E1) / eta
alpha2_new = self._compare(alpha2_new_unc, L, H)
alpha1_new = self.alpha[i1] + self.Y[i1] * self.Y[i2] * (self.alpha[i2] - alpha2_new)
b1_new = -E1 - self.Y[i1] * self.kernel(self.X[i1], self.X[i1]) * (alpha1_new-self.alpha[i1]) - self.Y[i2] * self.kernel(self.X[i2], self.X[i1]) * (alpha2_new-self.alpha[i2])+ self.b
b2_new = -E2 - self.Y[i1] * self.kernel(self.X[i1], self.X[i2]) * (alpha1_new-self.alpha[i1]) - self.Y[i2] * self.kernel(self.X[i2], self.X[i2]) * (alpha2_new-self.alpha[i2])+ self.b
if 0 < alpha1_new < self.C:
b_new = b1_new
elif 0 < alpha2_new < self.C:
b_new = b2_new
else:
# 选择中点
b_new = (b1_new + b2_new) / 2
# 更新参数
self.alpha[i1] = alpha1_new
self.alpha[i2] = alpha2_new
self.b = b_new
self.E[i1] = self._E(i1)
self.E[i2] = self._E(i2)
def predict(self, data):
'''
input:data(ndarray):单个样本
output:预测为正样本返回+1，负样本返回-1
'''
r = self.b
for i in range(self.m):
r += self.alpha[i] * self.Y[i] * self.kernel(data, self.X[i])
return 1 if r > 0 else -1
#********* End *********#
5、支持向量回归
#encoding=utf8
from sklearn.svm import SVR
def svr_predict(train_data,train_label,test_data):
'''
input:train_data(ndarray):训练数据
train_label(ndarray):训练标签
output:predict(ndarray):测试集预测标签
'''
#********* Begin *********#
svr = SVR(kernel='rbf',C=100,gamma= 0.001,epsilon=0.1)
svr.fit(train_data,train_label)
predict = svr.predict(test_data)
#********* End *********#
return predict
8、模型评估、选择与验证
1、为什么要有训练集与测试集
2、欠拟合与过拟合
3、偏差与方差
4、验证集与交叉验证
5、衡量回归的性能指标
6、准确度的陷阱与混淆矩阵
import numpy as np
def confusion_matrix(y_true, y_predict):
'''
构建二分类的混淆矩阵，并将其返回
:param y_true: 真实类别，类型为ndarray
:param y_predict: 预测类别，类型为ndarray
:return: shape为(2, 2)的ndarray
'''
#********* Begin *********#
def TN(y_true,y_predict):
return np.sum((y_true==0) & (y_predict==0))
def FP(y_true,y_predict):
return np.sum((y_true==0) & (y_predict==1))
def FN (y_true,y_predict):
return np.sum((y_true==1)& (y_predict==0))
def TP(y_true,y_predict):
return np.sum((y_true==1)& (y_predict==1))
return np.array([
[TN(y_true,y_predict),FP(y_true,y_predict)],
[FN(y_true,y_predict),TP(y_true,y_predict)]
])
#********* End *********#
7、精准率与召回率
import numpy as np
def precision_score(y_true, y_predict):
'''
计算精准率并返回
:param y_true: 真实类别，类型为ndarray
:param y_predict: 预测类别，类型为ndarray
:return: 精准率，类型为float
'''
#********* Begin *********#
def TN(y_true,y_predict):
return np.sum((y_true==0) & (y_predict==0))
def FP(y_true,y_predict):
return np.sum((y_true==0)& (y_predict==1))
def FN(y_true,y_predict):
return np.sum((y_true==1) & (y_predict==0))
def TP(y_true,y_predict):
return np.sum((y_true==1)& (y_predict==1))
return TP(y_true,y_predict)/(TP(y_true,y_predict)+FP(y_true,y_predict))
#********* End *********#
def recall_score(y_true, y_predict):
'''
计算召回率并召回
:param y_true: 真实类别，类型为ndarray
:param y_predict: 预测类别，类型为ndarray
:return: 召回率，类型为float
'''
#********* Begin *********#
def TP(y_true,y_predict):
return np.sum((y_true==1) & (y_predict==1))
def FN(y_true,y_predict):
return np.sum((y_true==1)& (y_predict==0))
tp=TP(y_true,y_predict)
fn=FN(y_true,y_predict)
try:
return tp/(tp+fn)
except:
return 0.0
#********* End *********#
8、F1 Score
import numpy as np
def f1_score(precision, recall):
'''
计算f1 score并返回
:param precision: 模型的精准率，类型为float
:param recall: 模型的召回率，类型为float
:return: 模型的f1 score，类型为float
'''
#********* Begin *********#
score=(2*precision*recall)/(precision+recall)
return score
#********* End ***********#
9、ROC曲线与AUC
import numpy as np
def calAUC(prob, labels):
'''
计算AUC并返回
:param prob: 模型预测样本为Positive的概率列表，类型为ndarray
:param labels: 样本的真实类别列表，其中1表示Positive，0表示Negtive，类型为ndarray
:return: AUC，类型为float
'''
#********* Begin *********#
f=list(zip(prob,labels))
rank=[values2 for values1,values2 in sorted(f,key=lambda x:x[0])]
rankList=[i+1 for i in range(len(rank)) if rank[i]==1]
posNum=0
negNum=0
for i in range(len(labels)):
if(labels[i]==1):
posNum+=1
else:
negNum+=1
auc=(sum(rankList)-(posNum*(posNum+1))/2)/(posNum*negNum)
return auc
#********* End *********#
10、sklearn中的分类性能指标
from sklearn.metrics import accuracy_score, precision_score, recall_score, f1_score, roc_auc_score
def classification_performance(y_true, y_pred, y_prob):
'''
返回准确度、精准率、召回率、f1 Score和AUC
:param y_true:样本的真实类别，类型为`ndarray`
:param y_pred:模型预测出的类别，类型为`ndarray`
:param y_prob:模型预测样本为`Positive`的概率，类型为`ndarray`
:return:
'''
#********* Begin *********#
a=accuracy_score(y_true,y_pred)
b=precision_score(y_true,y_pred)
c=recall_score(y_true,y_pred)
d=f1_score(y_true,y_pred)
e=roc_auc_score(y_true,y_prob)
return (a,b,c,d,e)
#********* End *********#
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