一、机器学习概述
第1关机器学习概述
B AD B BC
第2关常见分类算法
#编码方式encoding=utf8
from sklearn.neighbors import KNeighborsClassifier
def knn(train_data,train_label,test_data):
'''
input:train_data用来训练的数据
train_label用来训练的标签
test_data用来测试的数据
'''
#********* Begin *********#开始填补空缺处代码
knn = KNeighborsClassifier()
#利用训练数据与标签对模型进行训练
knn.fit(train_data, train_label)
#对测试数据类别进行预测
predict = knn.predict(test_data)
#********* End *********#结束填补位置
return predict
第3关常见回归算法
#编码方式encoding=utf8
from sklearn.linear_model import LinearRegression
def lr(train_data,train_label,test_data):
'''
input:train_data用来训练的数据
train_label用来训练的标签
test_data用来测试的数据
'''
#********* Begin *********#开始填补空缺处代码
lr = LinearRegression()
#利用已知数据与标签对模型进行训练
lr.fit(train_data, train_label)
#对未知数据进行预测
predict = lr.predict(test_data)
#********* End *********#
return predict
第4关常见聚类算法
from sklearn.cluster import KMeans
def kmeans(data):
'''
input:data需要进行聚类的数据
'''
# 假设我们想要将数据聚成3类，这个数字可以根据实际情况调整
kmeans = KMeans(n_clusters=3, random_state=888)
# 使用fit_predict一步完成模型训练和预测
predict = kmeans.fit_predict(data)
return predict # 返回聚类结果
第五关实现KNN算法
import numpy as np
class kNNClassifier(object):
def __init__(self, k):
'''
初始化函数
:param k:kNN算法中的k
'''
self.k = k
# 用来存放训练数据，类型为ndarray
self.train_feature = None
# 用来存放训练标签，类型为ndarray
self.train_label = None
def fit(self, feature, label):
'''
kNN算法的训练过程
:param feature: 训练集数据，类型为ndarray
:param label: 训练集标签，类型为ndarray
:return: 无返回
'''
# 将传入的训练数据和标签保存在对象内部，以便后续的预测使用
self.train_feature = np.array(feature)
self.train_label = np.array(label)
def predict(self, feature):
'''
kNN算法的预测过程
:param feature: 测试集数据，类型为ndarray
:return: 预测结果，类型为ndarray或list
'''
def _predict(test_data):
# 计算测试数据与所有训练数据之间的欧氏距离
distances = [np.sqrt(np.sum((test_data - vec) ** 2)) for vec in self.train_feature]
# 获取距离最近的训练数据的索引
nearest = np.argsort(distances)
# 选取最近的 k 个邻居
topK = [self.train_label[i] for i in nearest[:self.k]]
votes = {} # 用字典来记录每个类别的投票数
result = None
max_count = 0 # 用来记录最高票数
for label in topK:
if label in votes:
votes[label] += 1
else:
votes[label] = 1
# 更新最高票数和对应的类别
if votes[label] > max_count:
max_count = votes[label]
result = label
return result
# 对测试集中的每个数据进行预测
predict_result = [_predict(test_data) for test_data in feature]
return predict_result
二、机器学习—线性回归
第1关简单线性回归与多元线性回归
第2关线性回归的正规方程解
import numpy as np
def mse_score(y_predict, y_test):
'''
input:y_predict(ndarray):预测值
y_test(ndarray):真实值
output:mse(float):mse损失函数值
'''
# 计算均方误差
mse = np.mean((y_predict - y_test) ** 2)
return mse
class LinearRegression:
def __init__(self):
'''初始化线性回归模型'''
self.theta = None
def fit_normal(self, train_data, train_label):
'''
input:train_data(ndarray):训练样本
train_label(ndarray):训练标签
'''
# 在训练数据前添加一列1，对应theta0
X_b = np.hstack([np.ones((len(train_data), 1)), train_data])
# 使用正规方程求解theta
self.theta = np.linalg.inv(X_b.T.dot(X_b)).dot(X_b.T).dot(train_label)
def predict(self, test_data):
'''
input:test_data(ndarray):测试样本
'''
# 在测试数据前添加一列1，对应theta0
X_b = np.hstack([np.ones((len(test_data), 1)), test_data])
# 使用模型进行预测
y_predict = X_b.dot(self.theta)
return y_predict
第3关衡量线性回归的性能指标
import numpy as np
#mse
def mse_score(y_predict, y_test):
mse = np.mean((y_predict - y_test) ** 2)
return mse
#r2
def r2_score(y_predict, y_test):
'''
input:y_predict(ndarray):预测值
y_test(ndarray):真实值
output:r2(float):r2值
'''
# 计算R2分数
ss_total = np.sum((y_test - np.mean(y_test)) ** 2)
ss_residual = np.sum((y_test - y_predict) ** 2)
r2 = 1 - (ss_residual / ss_total)
return r2
class LinearRegression:
def __init__(self):
'''初始化线性回归模型'''
self.theta = None
def fit_normal(self, train_data, train_label):
'''
input:train_data(ndarray):训练样本
train_label(ndarray):训练标签
'''
# 在训练数据前添加一列1，对应theta0
X_b = np.hstack([np.ones((len(train_data), 1)), train_data])
# 使用正规方程求解theta
self.theta = np.linalg.inv(X_b.T.dot(X_b)).dot(X_b.T).dot(train_label)
return self
def predict(self, test_data):
'''
input:test_data(ndarray):测试样本
'''
# 在测试数据前添加一列1，对应theta0
X_b = np.hstack([np.ones((len(test_data), 1)), test_data])
# 使用模型进行预测
y_predict = X_b.dot(self.theta)
return y_predict
第4关scikit-learn线性回归实践 - 波斯顿房价预测
#encoding=utf8
#encoding=utf8
#********* Begin *********#
import pandas as pd
from sklearn.linear_model import LinearRegression
# 获取训练数据
train_data = pd.read_csv('./step3/train_data.csv')
# 获取训练标签
train_label = pd.read_csv('./step3/train_label.csv')
train_label = train_label['target']
# 获取测试数据
test_data = pd.read_csv('./step3/test_data.csv')
lr = LinearRegression()
# 训练模型
lr.fit(train_data, train_label)
# 获取预测标签
predict = lr.predict(test_data)
# 将预测标签写入csv
df = pd.DataFrame({'result': predict})
df.to_csv('./step3/result.csv', index=False)
#********* End *********#
三、机器学习 --- 模型评估、选择与验证
第1关：为什么要有训练集与测试集
第2关欠拟合与过拟合
第3关偏差与方差
第4关验证集与交叉验证
第5关衡量回归性能指标
第6关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
'''
# 定义计算混淆矩阵各元素的函数
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))
# 构建并返回混淆矩阵
return np.array([
[TN(y_true, y_predict), FP(y_true, y_predict)],
[FN(y_true, y_predict), TP(y_true, y_predict)]
])
第7关精准率与召回率
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
'''
# 定义计算真正例（TP）和假正例（FP）的函数
def TP(y_true, y_predict):
return np.sum((y_true == 1) & (y_predict == 1))
def FP(y_true, y_predict):
return np.sum((y_true == 0) & (y_predict == 1))
# 计算TP和FP
tp = TP(y_true, y_predict)
fp = FP(y_true, y_predict)
# 计算精准率并返回
try:
return tp / (tp + fp)
except:
return 0.0
def recall_score(y_true, y_predict):
'''
计算召回率并返回
:param y_true: 真实类别，类型为ndarray
:param y_predict: 预测类别，类型为ndarray
:return: 召回率，类型为float
'''
# 定义计算真正例（TP）和假负例（FN）的函数
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))
# 计算TP和FN
tp = TP(y_true, y_predict)
fn = FN(y_true, y_predict)
# 计算召回率并返回
try:
return tp / (tp + fn)
except:
return 0.0
第8关F1 Score
import numpy as np
def f1_score(precision, recall):
'''
计算模型的F1分数并返回
: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
'''
# 计算F1分数
try:
return 2 * precision * recall / (precision + recall)
except:
return 0.0
第9关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
'''
# 将概率和标签组合并按概率排序
f = list(zip(prob, labels))
rank = [values2 for values1, values2 in sorted(f, key=lambda x: x[0])]
# 获取正样本的排名列表
rankList = [i + 1 for i in range(len(rank)) if rank[i] == 1]
# 计算正负样本的数量
posNum = sum(labels)
negNum = len(labels) - posNum
# 根据公式计算AUC
auc = (sum(rankList) - (posNum * (posNum + 1)) / 2) / (posNum * negNum)
return auc
第10关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: 准确度、精准率、召回率、f1 Score和AUC，类型为tuple
'''
# 计算并返回各种性能指标
return accuracy_score(y_true, y_pred), precision_score(y_true, y_pred), recall_score(y_true, y_pred), f1_score(y_true, y_pred), roc_auc_score(y_true, y_prob)
四、聚类性能评估指标
第1关外部指标
import numpy as np
def calc_JC(y_true, y_pred):
'''
计算并返回JC系数
:param y_true: 参考模型给出的簇，类型为ndarray
:param y_pred: 聚类模型给出的簇，类型为ndarray
:return: JC系数
'''
def a(y_true, y_pred):
result = 0
for i in range(len(y_true)):
for j in range(len(y_pred)):
if i < j:
if y_true[i] == y_true[j] and y_pred[i] == y_pred[j]:
result += 1
return result
def b(y_true, y_pred):
result = 0
for i in range(len(y_true)):
for j in range(len(y_pred)):
if i < j:
if y_true[i] != y_true[j] and y_pred[i] == y_pred[j]:
result += 1
return result
def c(y_true, y_pred):
result = 0
for i in range(len(y_true)):
for j in range(len(y_pred)):
if i < j:
if y_true[i] == y_true[j] and y_pred[i] != y_pred[j]:
result += 1
return result
return a(y_true, y_pred) / (a(y_true, y_pred) + b(y_true, y_pred) + c(y_true, y_pred))
def calc_FM(y_true, y_pred):
'''
计算并返回FM指数
:param y_true: 参考模型给出的簇，类型为ndarray
:param y_pred: 聚类模型给出的簇，类型为ndarray
:return: FM指数
'''
def a(y_true, y_pred):
result = 0
for i in range(len(y_true)):
for j in range(len(y_pred)):
if i < j:
if y_true[i] == y_true[j] and y_pred[i] == y_pred[j]:
result += 1
return result
def b(y_true, y_pred):
result = 0
for i in range(len(y_true)):
for j in range(len(y_pred)):
if i < j:
if y_true[i] != y_true[j] and y_pred[i] == y_pred[j]:
result += 1
return result
def c(y_true, y_pred):
result = 0
for i in range(len(y_true)):
for j in range(len(y_pred)):
if i < j:
if y_true[i] == y_true[j] and y_pred[i] != y_pred[j]:
result += 1
return result
return a(y_true, y_pred) / np.sqrt((a(y_true, y_pred) + b(y_true, y_pred)) * (a(y_true, y_pred) + c(y_true, y_pred)))
def calc_Rand(y_true, y_pred):
'''
计算并返回Rand指数
:param y_true: 参考模型给出的簇，类型为ndarray
:param y_pred: 聚类模型给出的簇，类型为ndarray
:return: Rand指数
'''
def a(y_true, y_pred):
result = 0
for i in range(len(y_true)):
for j in range(len(y_pred)):
if i < j:
if y_true[i] == y_true[j] and y_pred[i] == y_pred[j]:
result += 1
return result
def d(y_true, y_pred):
result = 0
for i in range(len(y_true)):
for j in range(len(y_pred)):
if i < j:
if y_true[i] != y_true[j] and y_pred[i] != y_pred[j]:
result += 1
return result
m = len(y_true)
return (2 * (a(y_true, y_pred) + d(y_true, y_pred))) / (m * (m - 1))
第2关内部指标
import numpy as np
def calc_DBI(feature, pred):
'''
计算并返回DB指数
:param feature: 待聚类数据的特征，类型为`ndarray`
:param pred: 聚类后数据所对应的簇，类型为`ndarray`
:return: DB指数
'''
#********* Begin *********#
label_set = np.unique(pred)
mu = {}
label_count = {}
#计算簇的中点
for label in label_set:
mu[label] = np.zeros([len(feature[0])])
label_count[label] = 0
for i in range(len(pred)):
mu[pred[i]] += feature[i]
label_count[pred[i]] += 1
for key in mu.keys():
mu[key] /= label_count[key]
#算数据到中心点的平均距离
avg_d = {}
for label in label_set:
avg_d[label] = 0
for i in range(len(pred)):
avg_d[pred[i]] += np.sqrt(np.sum(np.square(feature[i] - mu[pred[i]])))
for key in mu.keys():
avg_d[key] /= label_count[key]
#算两个簇的中点之间的距离
cen_d = []
for i in range(len(label_set)-1):
t = {'c1':label_set[i], 'c2':label_set[i+1], 'dist':np.sqrt(np.sum(np.square(mu[label_set[i]] - mu[label_set[i+1]])))}
cen_d.append(t)
dbi = 0
for k in range(len(label_set)):
max_item = 0
for i in range(len(label_set)):
for j in range(i, len(label_set)):
for p in range(len(cen_d)):
if cen_d[p]['c1'] == label_set[i] and cen_d[p]['c2'] == label_set[j]:
d = (avg_d[label_set[i]] + avg_d[label_set[j]])/cen_d[p]['dist']
if d > max_item:
max_item = d
dbi += max_item
dbi /= len(label_set)
return dbi
#********* End *********#
def calc_DI(feature, pred):
'''
计算并返回Dunn指数
:param feature: 待聚类数据的特征，类型为`ndarray`
:param pred: 聚类后数据所对应的簇，类型为`ndarray`
:return: Dunn指数
'''
#********* Begin *********#
label_set = np.unique(pred)
min_d = []
for i in range(len(label_set)-1):
t = {'c1': label_set[i], 'c2': label_set[i+1], 'dist': np.inf}
min_d.append(t)
#计算两个簇之间的最短距离
for i in range(len(feature)):
for j in range(i, len(feature)):
for p in range(len(min_d)):
if min_d[p]['c1'] == pred[i] and min_d[p]['c2'] == pred[j]:
d = np.sqrt(np.sum(np.square(feature[i] - feature[j])))
if d < min_d[p]['dist']:
min_d[p]['dist'] = d
#计算同一个簇中距离最远的样本对的距离
max_diam = 0
for i in range(len(feature)):
for j in range(i, len(feature)):
if pred[i] == pred[j]:
d = np.sqrt(np.sum(np.square(feature[i] - feature[j])))
if d > max_diam:
max_diam = d
di = np.inf
for i in range(len(label_set)):
for j in range(i, len(label_set)):
for p in range(len(min_d)):
d = min_d[p]['dist']/max_diam
if d < di:
di = d
return d
第3关sklearn中的聚类性能评估指标
from sklearn.metrics.cluster import fowlkes_mallows_score, adjusted_rand_score
def cluster_performance(y_true, y_pred):
'''
返回Rand指数和FM指数
:param y_true:参考模型的簇划分，类型为`ndarray`
:param y_pred:聚类模型给出的簇划分，类型为`ndarray`
:return: Rand指数，FM指数
'''
#********* Begin *********#
return fowlkes_mallows_score(y_true, y_pred), adjusted_rand_score(y_true, y_pred)
#********* End *********#
七、机器学习—逻辑回归
第1关逻辑回归核心思想
#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
'''
# 使用np.exp()函数计算e的t次方，然后除以1加上e的t次方
return 1 / (1 + np.exp(-t))
第2关逻辑回归的损失函数
A ACD AB D
第3关梯度下降
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
'''
theta = initial_theta
i = 0
while i < n_iters:
i += 1
gradient = 2 * (theta - 3)
if abs(gradient) < epslion:
break
theta = theta - eta * gradient
return theta
# 调用梯度下降函数
theta = gradient_descent(initial_theta=0)
后面的暂时不写
前面四个时必须写的其他等我闲了再写
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