目标

尽量使用基础代码实现线性回归.

数据准备

iris 数据集

主线流程

核心公式:
    y=wX+b
读取文件内容,
清洗数据,获取想要的信息:X,y
进行回归
画图看效果

读取文件

    # 读取文件
    data = pd.read_csv("iris.data", names=["x", "y", "c", "d", "itype"])
    # 读取iris的前50行
    first_50 = data.loc[:49]
    # 拿取前两列
    first_50xy = first_50[["x", "y"]]
    # 拿取X,y 并且转换成numpy格式
    X = np.array(first_50xy["x"])
    y = np.array(first_50xy["y"])

回归运算,使用全局梯度下降BGD更新w,b

偏导part

更新θ=θ - α*part

意思是,要更新wb,就是求偏导part,然后不断更新
w = w - α * part1
b = b - α * part2

# 进入argmin  采用全局梯度下降
def BGD(X, y, w, b, alpha, n_iter=1000):
    m = len(X)
    for i in range(n_iter):
        # 注意这里的X.T
        w = w - alpha * np.sum(2 * X.T * (w * X + b - y)) / m
        b = b - alpha * np.sum(2 * (w * X + b - y)) / m
    return w, b

优化方案1

加入loss函数,提前结束算法

def loss(x, y, w, b):
    loss = 0
    length = len(x)
    for ind in range(length):
        loss += (y[ind] - (w * x[ind] + b)) ** 2
    # 除2m 其实对结果没有什么影响
    return loss / (2 * length)

更改BGD,加入判断

def BGD(X, y, w, b, alpha, n_iter=1000):
    m = len(X)
    for i in range(n_iter):
        w = w - alpha * np.sum(2 * X.T * (w * X + b - y)) / m
        b = b - alpha * np.sum(2 * (w * X + b - y)) / m
        # 每1000次,进行一次loss运算,如果已经很小,则直接退出
        if n_iter %1000 ==0 and loss(X, y, w, b) < 0.04:
            print(i)
            return w, b
    return w, b

画图以及主函数整理

if __name__ == "__main__":
    time_start = time.time()
    # 读取文件
    data = pd.read_csv("iris.data", names=["x", "y", "c", "d", "itype"])

    # 读取iris的前50行
    first_50 = data.loc[:49]
    # 拿取前两列
    first_50xy = first_50[["x", "y"]]
    # 拿取X,y 并且转换成numpy格式
    X = np.array(first_50xy["x"])
    y = np.array(first_50xy["y"])

    # 线性回归的输入y=wx+b
    w = 1
    b = 5
    alpha = 0.01

    w, b = BGD(X, y, w, b, alpha, n_iter=100000)

    time_end = time.time()
    print('totally cost', time_end - time_start)
    # 画图
    # 画点
    plt.plot(X, y, "ro")
    # 画线
    x_min = min(X)
    x_max = max(X)
    y_min = x_min * w + b
    y_max = x_max * w + b
    xs = [x_min, x_max]
    ys = [y_min, y_max]
    plt.plot(xs, ys, )
    plt.show()

github地址:
https://github.com/Lin4856/ML-in-Python-485/blob/master/yk_basic/linear/linear_%CE%B1.py

相关友情链接:https://blog.csdn.net/weixin_43944175/article/details/95899457