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慕课网机器学习笔记（3）

内容提要

一个小注意点

jupyter notebook 在导入模块的时候，如果模块修改了需要重新导入，使用 importlib 模块的 reload 方法，当然，也可以选择重启python内核，不过如果之前输入的有出错会打断其执行

K临近算法

算法基本思想

选取离测试数据最近的k个样本，统计哪个样本类型的数量多，则测试数据有很大可能与该种类样本类型相同

对于kNN算法，训练集就是模型

使用sklearn中的鸢尾花进行测试

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from sklearn import datasets
import matplotlib.pyplot as plt
from math import sqrt
from collections import Counter
import numpy as np

iris = datasets.load_iris()

# 取后两个列进行测试
X = iris.data[:, 2:]
y=iris.target

new_point = np.array([2.1, 0.6])
k=3

# 绘制图像
plt.scatter(X[y==0, 0], X[y==0, 1], color="red", marker="o")
plt.scatter(X[y==1, 0], X[y==1, 1], color="green", marker="+")
plt.scatter(X[y==2, 0], X[y==2, 1], color="black", marker="*")
plt.scatter(new_point[0], new_point[1], color="blue")
plt.show()

# 计算每个数据距离测试点的距离
distant = [sqrt(np.sum((train_data-new_point)**2)) for train_data in X]

# 获取最近点对应的坐标
nearest = np.argsort(distant)

# 根据其坐标找出其对应的类型
result = [iris.target[i] for i in nearest]

# 使用方法most_common判断最接近的数值分布情况
result_type = Counter(result).most_common(1)[0][0]

对方法进行封装

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


def KNN_classify(k: int, x_train: np.ndarray, y_train: np.ndarray, x: np.ndarray) -> int:
    assert 1 <= k <= x_train.shape[0], "k must be valid"
    assert x_train.shape[0] == y_train.shape[0], \
        "the size of x_train must equal to the size of y_train"
    assert x_train.shape[1] == x.shape[0], \
        "the feature number of x must be equal to x_train"

    distant = [sqrt(np.sum((train_data - x) ** 2)) for train_data in x_train]
    nearest = np.argsort(distant)
    result = [y_train[i] for i in nearest]
    return Counter(result).most_common(1)[0][0]

使用sklearn中的K临近算法库进行预测

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from sklearn.neighbors import KNeighborsClassifier
# 生成一个实例
KNN_classifier = KNeighborsClassifier(n_neighbors=5)
# 生成模型
KNN_classifier.fit(X, y)
# 进行预测
KNN_classifier.predict(new_point.reshape(1, -1))
# array([0])

对自己写的算法进行sklearn风格的封装

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class KNNClassifier:

    def __init__(self, k: int):
        """初始化"""
        assert k >= 1, "k must be valid"
        self.k: int = k
        self._x_train: np.ndarray = None
        self._y_train: np.ndarray = None

    def fit(self, x_train: np.ndarray,y_train: np.ndarray) -> 'KNNClassifier':
        assert 1 <= self.k <= x_train.shape[0], "k must be valid"
        assert x_train.shape[0] == y_train.shape[0], \
            "the size of x_train must equal to the size of y_train"

        self._x_train = x_train
        self._y_train = y_train
        return self

    def predict(self, x_predict: np.ndarray) -> np.ndarray:
        """给定预测数据集，返回预测结果"""
        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 must be equal to x_train"

        y_predict: list = [self._predict(x) for x in x_predict]
        return np.array(y_predict)

    def _predict(self, x: np.ndarray) -> int:
        """ 给定单个待预测的数据x，返回x的预测结果值 """
        assert self._x_train.shape[1] == x.shape[0], \
            "the feature number of x must be equal to x_train"

        distant = [sqrt(np.sum((train_data - x) ** 2)) for train_data in self._x_train]
        nearest = np.argsort(distant)
        result = [self._y_train[i] for i in nearest[:self.k]]
        return Counter(result).most_common(1)[0][0]

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

对提供的训练数据进行拆分

使用自己的写的方法对数据进行拆分

在输入的数据中抽出一部分数据作为训练的数据，而另一部分作为测试数据

使用自己的写的方法对数据进行拆分

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import numpy as np


def train_test_split(x_train: np.ndarray, y_train: np.ndarray, test_ratio=0.2, seed=None):
    """将数据X和y按照test_ratio分割成new_x_train, x_test, new_y_train, y_test"""
    assert x_train.shape[0] == y_train.shape[0], \
        "the size of x_train must be equal to the size of y_train"
    assert 0.0 <= test_ratio <= 1.0, \
        "test_train must be valid"

    if seed:
        np.random.seed(seed)

    # 对矩阵的索引顺序进行打乱操作
    shuffle_indexes = np.random.permutation(len(x_train))

    test_size = int(len(x_train) * test_ratio)
    test_indexes = shuffle_indexes[:test_size]
    train_indexes = shuffle_indexes[test_size:]

    # 根据打乱的索引取出相对应的数值
    new_x_train = x_train[train_indexes]
    new_y_train = y_train[train_indexes]

    x_test = x_train[test_indexes]
    y_test = y_train[test_indexes]

    return new_x_train, x_test, new_y_train, y_test

使用sklearn提供的方法对其进行拆分

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from sklearn.model_selection import  train_test_split
new_x_train, x_test, new_y_train, y_test = train_test_split(X, y, test_size=0.2)

使用K临近算法对手写体进行预测

初次查看

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import numpy as np
import matplotlib
import matplotlib.pyplot as plt
from sklearn import datasets

# 载入手写体数据
digits = datasets.load_digits

# 查看含有的数值：dict_keys(['data', 'target', 'target_names', 'images', 'DESCR'])
digits.keys()

# 查看一个图片
some_digit = digits.data[666]
digits.target[666]
some_digit_image = some_digit.reshape(8,8)
plt.imshow(some_digit_image,cmap=matplotlib.cm.binary)
plt.show()

使用自己写的KNN对其进行训练和预判

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import pycharm_project.knn as knn
import pycharm_project.model_selection as ms

x_train, x_test, y_train, y_test = ms.train_test_split(digits.data, digits.target)
kc = knn.KNNClassifier(6)
kc.fit(x_train, y_train)
predict_result = kc.predict(x_test)

# 计算预测准确率 0.9860724233983287
sum(predict_result == y_test) / len(y_test)

对评估结果进行封装

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""" metrics.py 对机器学习结果进行评估 """
import numpy as np


def accuracy_score(y_true: np.ndarray, y_predict: np.ndarray) -> float:
    assert y_true.shape[0] == y_predict.shape[0], \
        "the size of y_ture must equal to to y_predict"

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

为自己写的KNNClassifier类添加评估准确性的方法

有时并不关心预测结果，只是想查看正确率时，可以直接使用这个方法

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#...

def score(self, x_test: np.ndarray, y_test: np.ndarray) -> float:
    y_predict = self.predict(x_test)
    return accuracy_score(y_test, y_predict)

#...

超参数概念

在算法运行前需要决定的参数，比较：模型参数，算法过程中学习的参数

KNN算法没有模型参数，k为典型的超参数

对k进行调参

先对1-11进行测试，但是如果最佳参数为10的话，可能就要对10-20再一次进行测试

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best_score = 0.0
best_k = -1

for i in range(1, 11):
    kc_tmp = KNeighborsClassifier(n_neighbors=i)
    kc_tmp.fit(train_x, train_y)
    score_tmp = kc_tmp.score(test_x, test_y)
    if score_tmp > best_score:
        best_score = score_tmp
        best_k = i
print(best_score, best_k)
# 0.9916666666666667 4

寻找最佳评估路径方法

是否考虑点距离的权重

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best_score = 0.0
best_k = -1
best_method = ""

# 是否引入权重
for m in ["distance", "uniform"]:
    for i in range(1, 11):
        kc_tmp = KNeighborsClassifier(n_neighbors=i, weights=m)
        kc_tmp.fit(train_x, train_y)
        score_tmp = kc_tmp.score(test_x, test_y)
        if score_tmp > best_score:
            best_score = score_tmp
            best_k = i
            best_method = m
print(best_score, best_k, best_method)
# 0.9916666666666667 4 uniform

对距离的定义

寻找最佳距离在1-5之间

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%%time
best_score = 0.0
best_k = -1
best_p = -1
for i in range(1, 11):
    for p in range(1,6):
    		# 对p进行设置
        kc_tmp = KNeighborsClassifier(n_neighbors=i, weights="distance", p=p)
        kc_tmp.fit(train_x, train_y)
        score_tmp = kc_tmp.score(test_x, test_y)
        if score_tmp > best_score:
            best_score = score_tmp
            best_k = i
            best_p = p
print(best_score, best_k, best_p)
# 0.9888888888888889 3 2
# CPU times: user 14.5 s, sys: 21.1 ms, total: 14.5 s
# Wall time: 14.6 s