第0章 本笔记所封装在Pycharm中的函数库

 

各函数包与函数模块之间的所属关系如图：

注意，所有函数包以及Notbook文件都是所属父文件夹的同级别文件，只有这样才能顺利调用所需函数

 

 

 

 

各函数包如下：

kNN

import numpy as np
from math import sqrt
from collections import Counter


class KNNClassifier:

    def __init__(self, k):
        """初始化kNN分类器"""
        assert k >= 1, "k must be valid"
        self.k = k
        self._X_train = None
        self._y_train = None

    def fit(self, X_train, y_train):
        """根据训练数据集X_train和y_train训练kNN分类器"""
        assert X_train.shape[0] == y_train.shape[0],\
            "the size of X_train must be equal to the size of y_train"
        assert self.k <= X_train.shape[0],\
            "the size of X_train must be at least k ."

        self._X_train = X_train
        self._y_train = y_train
        return self

    def predict(self, X_predict):  # predict(self, X_predict)
        """给定待预测数据集X_predict,返回X_predict的结果向量"""
        assert self._X_train is not None and self._y_train is not None,\
            " must fit before predict!"
        assert X_predict.shape[1] == self._X_train.shape[1],\
            " the feature number of X_predict must be equal to X_train"

        y_predict = [self._predict(x) for x in X_predict]
        return np.array(y_predict)

    def _predict(self, x):
        """给定单个待测数据x，返回x的预测结果值"""
        assert x.shape[0] == self._X_train.shape[1],\
            "the feature number of x must be equal to x_train"
        distances = [sqrt(np.sum((x_train - x) ** 2))
                    for x_train in self._X_train]
        nearest = np.argsort(distances)

        topK_y = [self._y_train[i] for i in nearest[:self.k]]
        votes = Counter(topK_y)

        return votes.most_common(1)[0][0]

    def __repr__(self):
        return "KNN(k=%d)" % self.k

 

KNN_function

# KNN_classify()
import numpy as np
from math import sqrt
from collections import Counter


def KNN_classify (k, X_trian, y_trian, x):
    assert 1 <= k <= X_trian.shape[0], ' k must be valid'
    assert X_trian.shape[0] == y_trian.shape[0],\
        'the size of X_trian must equal to the size of y_trian '
    assert X_trian.shape[1] == x.shape[0],\
        "the feature number of must be equal to X_trian "

    distances = [sqrt(np.sum(x_trian - x) ** 2) for x_trian in X_trian]
    nearest = np.argsort(distances)
    topk_y = [y_trian[i] for i in nearest[:k]]
    votes = Counter(topk_y)
    return votes.most_common(1)[0][0]


print(" KNN_classify 已加载.")

 

playML：

kNN.py

import numpy as np
from math import sqrt
from collections import Counter
from .metrics import accuracy_score  # from .metrics 报错


class KNNClassifier:

    def __init__(self, k):
        """初始化kNN分类器"""
        assert k >= 1, "k must be valid"
        self.k = k
        self._X_train = None
        self._y_train = None

    def fit(self, X_train, y_train):
        """根据训练数据集X_train和y_train训练kNN分类器"""
        assert X_train.shape[0] == y_train.shape[0],\
            "the size of X_train must be equal to the size of y_train"
        assert self.k <= X_train.shape[0],\
            "the size of X_train must be at least k ."

        self._X_train = X_train
        self._y_train = y_train
        return self

    def predict(self, X_predict):  # predict(self, X_predict)
        """给定待预测数据集X_predict,返回X_predict的结果向量"""
        assert self._X_train is not None and self._y_train is not None,\
            " must fit before predict!"
        assert X_predict.shape[1] == self._X_train.shape[1],\
            " the feature number of X_predict must be equal to X_train"

        y_predict = [self._predict(x) for x in X_predict]
        return np.array(y_predict)

    def _predict(self, x):
        """给定单个待测数据x，返回x的预测结果值"""
        assert x.shape[0] == self._X_train.shape[1],\
            "the feature number of x must be equal to x_train"
        distances = [sqrt(np.sum((x_train - x) ** 2))
                     for x_train in self._X_train]
        nearest = np.argsort(distances)

        topK_y = [self._y_train[i] for i in nearest[:self.k]]
        votes = Counter(topK_y)

        return votes.most_common(1)[0][0]

    def score(self, X_test, y_test):
        """根据测试数据集 X_test 和 y_test 确定当前模型的准确度"""
        y_predict = self.predict(X_test)  # self._predict(X_test),大意了直接采纳第一个提示
        return accuracy_score(y_test, y_predict)

    def __repr__(self):
        return "KNN(k=%d)" % self.k

 

LinearRegression.py

 

import numpy as np
from .metrics import r2_score
# 源名需加kNN

class LinearRegression:

    def __int__(self):
        """初始化 Linear Regression 模型"""
        self.coef_ = None
        self.interception_ = None
        self._theta = None

    def fit_normal(self, X_train, y_train):
        """根据训练数据集 X_train, y_train 训练 Linear Regression 模型"""
        assert X_train.shape[0] == y_train.shape[0], \
            "the size of X_train must be equal to the size of y_train"

        X_b = np.hstack([np.ones((len(X_train), 1)), X_train])
        self._theta = np.linalg.inv(X_b.T.dot(X_b)).dot(X_b.T).dot(y_train)

        self.interception_ = self._theta[0]
        self.coef_ = self._theta[1:]

        return self

    def fit_gd(self, X_train, y_train, eta=0.001, n_iters=1e4):
        """根据训练数据集 X_trian, y_train,使用梯度下降法训练 Linear Regression模型"""
        assert X_train.shape[0] == y_train.shape[0], \
            "the size of X_train must equal to the size of y_train"

        def J(theta, X_b, y):
            try:
                return np.sum((y - X_b.dot(theta)) ** 2) / len(X_b)
            except:
                return float('inf')

        def dJ(theta, X_b, y):
            # res = np.empty(len(theta))
            # res[0] = np.sum(X_b.dot(theta) - y)
            # for i in range(1, len(theta)):
            #     res[i] = (X_b.dot(theta) - y).dot(X_b[:, i])
            # return res * 2 / len(theta)
            return X_b.T.dot(X_b.dot(theta) - y) * 2 / len(y)

        def gradient_descent(X_b, y, initial_theta, eta, n_iters=1e5, epsilon=1e-8):

            theta = initial_theta
            # theta_history.append(initial_theta)
            i_iters = 0

            while i_iters < n_iters:
                gradient = dJ(theta, X_b, y)
                last_theta = theta
                theta = theta - eta * gradient
                # theta_history.append(theta)

                if (abs(J(theta, X_b, y) - J(last_theta, X_b, y)) < epsilon):
                    break
                i_iters += 1

            return theta

        X_b = np.hstack([np.ones((len(X_trian), 1)), X_trian])
        initial_theta = np.zeros(X_b.shape[1])
        self._theta = gradient_descent(X_b, y_train, initial_theta, eta)

        self.interception_ = self._theta[0]
        self.coef_ = self._theta[1:]

        return self

    def fit_sgd(self, X_train, y_train, n_iters=5, t0=5, t1=50):
        """根据训练数据集 X_trian, y_train,使用梯度下降法训练 Linear Regression模型"""
        assert X_train.shape[0] == y_train.shape[0], \
            "the size of X_train must equal to the size of y_train"
        assert n_iters >= 1,\
            "the size of n_iters must >= 1"
        def dJ_sgd(theta, X_b_i, y_i):

            return X_b_i.T.dot(X_b_i.dot(theta) - y_i) * 2

        def sgd(X_b, y, initial_theta, n_iters, t0=5, t1=50):

            def learning_rate(t):
               return t0 / (t + t1)

            theta = initial_theta
            m = len(X_b)

            for cur_iter in range(n_iters):
               indexes = np.random.permutation(m)
               X_b_new = X_b[indexes]
               y_new = y[indexes]
               for i in range(m):
                   gradient = dJ_sgd(theta, X_b_new[i], y_new[i])
                   theta = theta - learning_rate(cur_iter * m + i) * gradient
            return theta


        X_b = np.hstack([np.ones((len(X_train), 1)), X_train])
        initial_theta = np.zeros(X_b.shape[1])
        self._theta = sgd(X_b, y_train, initial_theta, n_iters, t0, t1)

        self.interception_ = self._theta[0]
        self.coef_ = self._theta[1:]
        return self



    def predict(self, X_predict):
        """给定待测数据集 X_predict,返回表示 X_predict 的结果向量 """
        assert self.interception_ is not None and self.coef_ is not None, \
            "must fit before predict!"
        assert X_predict.shape[1] == len(self.coef_), \
            "the feature number of X_predict must be equal to X_train"

        X_b = np.hstack([np.ones((len(X_predict), 1)), X_predict])
        return X_b.dot(self._theta)

    def score(self, X_test, y_test):
        """根据测试数据集 X_test 和 y_test 确定当前模型的准确度"""

        y_predict = self.predict(X_test)
        return r2_score(y_test, y_predict)

    def __repr__(self):
        return "LinearRegression()"

 

LogistcRegression.py

import numpy as np
from .metrics import accuracy_score
# 源名需加kNN

class LogisticRegression:

    def __int__(self):
        """初始化 LogisticRegression 模型"""
        self.coef_ = None
        self.interception_ = None
        self._theta = None

    def _sigmoid(self, t):
        return 1 / (1 + np.exp(-t))

    def fit(self, X_train, y_train, eta=0.001, n_iters=1e4):
        """根据训练数据集 X_trian, y_train,使用梯度下降法训练 LogisticRegression模型"""
        assert X_train.shape[0] == y_train.shape[0], \
            "the size of X_train must equal to the size of y_train"

        def J(theta, X_b, y):
            y_hat = self._sigmoid(X_b.dot(theta))
            try:
                return - np.sum(y*np.log(y_hat) + (1-y)*np.log(1-y_hat)) / len(y)
            except:
                return float('inf')

        def dJ(theta, X_b, y):
            return X_b.T.dot(self._sigmoid(X_b.dot(theta)) - y) * 2 / len(y)

        def gradient_descent(X_b, y, initial_theta, eta, n_iters=1e5, epsilon=1e-8):

            theta = initial_theta
            # theta_history.append(initial_theta)
            i_iters = 0

            while i_iters < n_iters:
                gradient = dJ(theta, X_b, y)
                last_theta = theta
                theta = theta - eta * gradient
                # theta_history.append(theta)

                if (abs(J(theta, X_b, y) - J(last_theta, X_b, y)) < epsilon):
                    break
                i_iters += 1

            return theta

        X_b = np.hstack([np.ones((len(X_train), 1)), X_train])
        initial_theta = np.zeros(X_b.shape[1])
        self._theta = gradient_descent(X_b, y_train, initial_theta, eta)

        self.interception_ = self._theta[0]
        self.coef_ = self._theta[1:]

        return self

    def predict_proba(self, X_predict):
        """给定待测数据集 X_predict,返回表示 X_predict 的结果概率向量 """
        assert self.interception_ is not None and self.coef_ is not None, \
            "must fit before predict!"
        assert X_predict.shape[1] == len(self.coef_), \
            "the feature number of X_predict must be equal to X_train"

        X_b = np.hstack([np.ones((len(X_predict), 1)), X_predict])
        return self._sigmoid(X_b.dot(self._theta))

    def predict(self, X_predict):
        """给定待测数据集 X_predict,返回表示 X_predict 的结果向量 """
        assert self.interception_ is not None and self.coef_ is not None, \
            "must fit before predict!"
        assert X_predict.shape[1] == len(self.coef_), \
            "the feature number of X_predict must be equal to X_train"

        proba = self.predict_proba(X_predict)
        return np.array(proba >= 0.5, dtype='int')

    def score(self, X_test, y_test):
        """根据测试数据集 X_test 和 y_test 确定当前模型的准确度"""

        y_predict = self.predict(X_test)
        return accuracy_score(y_test, y_predict)

    def __repr__(self):
        return "LogisticRegression()"

metrics.py

import numpy as np
from math import sqrt


def accuracy_score(y_ture, y_predict):
    """计算 y_ture与 y_predict之间的准确度"""
    assert y_ture.shape[0] == y_predict.shape[0]
    "the size of y_ture must be equal to the size of y_predict"

    return sum(y_ture == y_predict)/len(y_ture)


def mean_squared_error(y_ture, y_predict):
    """计算 y_ture,与 y_predict 之间的MSE """
    assert len(y_ture) == len(y_predict), \
        "the size of y_ture must be equal to the size of y_predict "
    return np.sum((y_ture - y_predict) ** 2) / len(y_ture)


def root_mean_squared_error(y_ture, y_predict):
    """计算 y_ture与 y_predict之间的RMSE"""
    assert len(y_ture) == len(y_predict), \
        "the size of y_ture must be equal to the size of y_predict "
    return sqrt(mean_squared_error(y_ture, y_predict))


def mean_absolute_error(y_ture, y_predict):
    """计算 y_ture,与 y_predict 之间的MAE """
    assert len(y_ture) == len(y_predict), \
        "the size of y_ture must be equal to the size of y_predict "
    return np.sum(np.absolute(y_ture - y_predict)) / len(y_predict)


def r2_score(y_ture, y_predict):
    """计算 y_ture,与 y_predict 之间的 R Square """
    return 1 - mean_squared_error(y_ture, y_predict) / np.var(y_ture)

def TN(y_ture, y_predict):
    assert len(y_ture) == len(y_predict)
    return np.sum((y_ture == 0) & (y_predict == 0))

def FP(y_ture, y_predict):
    assert len(y_ture) == len(y_predict)
    return np.sum((y_ture == 0) & (y_predict == 1))

def FN(y_ture, y_predict):
    assert len(y_ture) == len(y_predict)
    return np.sum((y_ture == 1) & (y_predict == 0))

def TP(y_ture, y_predict):
    assert len(y_ture) == len(y_predict)
    return np.sum((y_ture == 1) & (y_predict == 1))

def confusion_matrix(y_true, y_predict):
    return np.array([
        [TN(y_true,y_predict), FP(y_true,y_predict)],
        [FN(y_true,y_predict), TP(y_true,y_predict)]
    ])

def precision_score(y_true, y_predict):
    tp = TP(y_true, y_predict)
    fp = FP(y_true, y_predict)
    try:
        return tp / (tp + fp)
    except:
        return 0.0

def recall_score(y_true, y_predict):
    tp = TP(y_true, y_predict)
    fn = FN(y_true, y_predict)
    try:
        return tp / (tp + fn)
    except:
        return 0.0

def f1_score(precision, recall):
    try:
        return 2 * precision * recall / ( precision + recall)
    except:
        return 0.0

def TPR(y_true, y_predict):
    tp = TP(y_true, y_predict)
    fn = FN(y_true, y_predict)
    try:
        return tp / (tp + fn)
    except:
        return 0.0

def FPR(y_true, y_predict):
    tp = TP(y_true, y_predict)
    tn = TN(y_true, y_predict)
    try:
        return tp / (tp + tn)
    except:
        return 0.0

model_selection.py

import numpy as np


def train_test_split(X, y, test_radio=0.2, seed=None):
    """将数据X和y按照test_radio分割成X_train、y_train、X_test、y_test"""
    assert X.shape[0] == y.shape[0],\
        "the size of X must be equal to the size of y"
    assert 0.0 <= test_radio <= 1.0,\
        "test_ration must be valid"

    if seed:
        np.random.seed(seed)

    shuffled_indexes = np.random.permutation(len(X))

    test_size = int(test_radio * len(X))
    test_indexes = shuffled_indexes[:test_size]
    train_indexes = shuffled_indexes[test_size:]

    X_train = X[train_indexes]
    y_train = y[train_indexes]

    X_test = X[test_indexes]
    y_test = y[test_indexes]

    return X_train, X_test, y_train, y_test

PCA.py

import numpy as np


class PCA:

    def __init__(self, n_components):
        """ 初始化"""
        assert n_components >= 1, "n_components must be valid"
        self.n_components = n_components
        self.components = None

    def fit(self, X, eta=0.01, n_iters=1e4):
        """获得数据集 X 的前 n 个主成分"""
        assert self.n_components <= X.shape[1], \
            "n_components must not be greater than feature number of X"

        def demean(X):
            return X - np.mean(X, axis=0)

        def f(w, X):
            return np.sum((X.dot(w) ** 2)) / len(X)

        def df(w, X):
            return X.T.dot(X.dot(w)) * 2.0 / len(X)

        def direction(w):
            return w / np.linalg.norm(w)

        def first_componet(X, initial_w, eta, n_iters=1e4, epsilon=1e-8):
            w = direction(initial_w)
            i_iters = 0

            while i_iters < n_iters:
                gradient = df(w, X)
                last_w = w
                w = w + eta * gradient
                w = direction(w)  # 注意1：每次求一个单位方向
                if (abs(f(w, X) - f(last_w, X)) < epsilon):
                    break

                i_iters += 1

            return w

        X_pca = demean(X)
        self.components_ = np.empty(shape=(self.n_components, X.shape[1]))
        res = []
        for i in range(self.n_components):
            initial_w = np.random.random(X_pca.shape[1])
            w = first_componet(X_pca, initial_w, eta, n_iters)
            self.components_[i, :] = w

            X_pca = X_pca - X_pca.dot(w).reshape(-1, 1) * w

        return self

    def transform(self, X):
        """将X给定的，映射到各个主成分分量中"""
        assert X.shape[1] == self.components_.shape[1]

        return X.dot(self.components_.T)

    def inverse_transform(self, X):
        """将给定的X，反向映射回原来的特征空间"""
        assert X.shape[1] == self.components_.shape[0]

        return X.dot(self.components_)

    def __repr__(self):
        return "PCA(n_components=%d)" % self.n_components

preprocessing.py

import numpy as np


class StandardScaler:

    def __int__(self):
        self.mean_ = None
        self.scale_ = None

    def fit(self, X):
        """根据训练数据集X获得数据的均值和方差"""
        assert X.ndim == 2, "The dimension of X must be 2"

        self.mean_ = np.array(np.mean(X[:, i]) for i in range(X.shape[1]))
        self.scale_ = np.array(np.std(X[:, i]) for i in range(X.shape[1]))

        return self

    def transform(self, X):
        """ 将 X 根据这个StandardScaler进行均值方差归一化处理"""
        assert X.ndim == 2, "The dimension of X must be 2"
        assert self.mean_ is not None and self.scale_ is not None,\
            "must fit before transform!"
        assert X.shape[1] == len(self.mean_), \
            "The feature number of X must be equal to mean_ and std_"

        resX = np.empty(shape=X.shape, dtype=float)
        for col in range(X.shape[1]):
            resX[:, col] = (X[:, col] - self.mean_[col]) / self.scale_[col]
        return resX

 

SimpleLinearRegression.py

import numpy as np
from .metrics import r2_score  # 加点下标运行报错，不加点下标jupyter 能运行


class SimpleLinearRegression1:

    def __int__(self):
        """初始化 Simple Linear Regression 模型"""
        self.a_ = None
        self.b_ = None

    def fit(self, x_train, y_train):
        """根据训练数据集x_train，y_train 训练 Simple Linear Regression 模型"""
        assert x_train.ndim == 1, \
            " Simple Linear Regression can only solve single feature training data"
        assert len(x_train) == len(y_train), \
            "the size of x_train must be equal to the size of y_train"

        x_mean = np.mean(x_train)
        y_mean = np.mean(y_train)

        num = 0.0
        d = 0.0
        for x, y in zip(x_train, y_train):
            num += (x - x_mean) * (y - y_mean)
            d += (x - x_mean) ** 2

        self.a_ = num / d
        self.b_ = y_mean - self.a_ * x_mean

        return self

    def predict(self, x_predict):
        """给定待测数据集x_predict，返回表示x_predict的结果向量"""
        # print(x_predict.ndim)
        assert x_predict.ndim == 1, \
            "Simple Linear Regression can only solve single feature training data"
        assert self.a_ is not None and self.b_ is not None, \
            "must fit before predict!"

        return np.array([self._predict(x) for x in x_predict])  # predict(x)无下划线问题严重

    def _predict(self, x_single):
        """给定单个待测数据 x_single,返回x_single的预测结果值"""
        return self.a_ * x_single + self.b_

    def __repr__(self):
        return "Simple Linear Regression1()"


class SimpleLinearRegression2:

    def __int__(self):
        """初始化 Simple Linear Regression 模型"""
        self.a_ = None
        self.b_ = None

    def fit(self, x_train, y_train):
        """根据训练数据集x_train，y_train 训练 Simple Linear Regression 模型"""
        assert x_train.ndim == 1, \
            " Simple Linear Regression can only solve single feature training data"
        assert len(x_train) == len(y_train), \
            "the size of x_train must be equal to the size of y_train"

        x_mean = np.mean(x_train)
        y_mean = np.mean(y_train)

        num = 0.0
        d = 0.0
        num = (x_train - x_mean).dot(y_train - y_mean)
        d = (x_train - x_mean).dot(x_train - x_mean)
        self.a_ = num / d
        self.b_ = y_mean - self.a_ * x_mean

        return self

    def predict(self, x_predict):
        """给定待测数据集x_predict，返回表示x_predict的结果向量"""
        # print(x_predict.ndim)
        assert x_predict.ndim == 1, \
            "Simple Linear Regression can only solve single feature training data"
        assert self.a_ is not None and self.b_ is not None, \
            "must fit before predict!"

        return np.array([self._predict(x) for x in x_predict])  # predict(x)无下划线问题严重

    def _predict(self, x_single):
        """给定单个待测数据 x_single,返回x_single的预测结果值"""
        return self.a_ * x_single + self.b_

    def score(self, x_test, y_test):
        """根据测试数据集 x_test 和 y_test 确定当前模型的准确度"""
        y_predict = self.predict(x_test)
        return r2_score(y_test, y_predict)

    def __repr__(self):
        return "Simple Linear Regression2()"