用python编写函数练习数据规范化： 数据 13,15,16,16,19,20,20,21,22,22,25,25,25,25,30,33,33,35,35,35,35,36,40,45,46,52,70 - 使用最小-最大规范化将 35 映射到 [0,1] 区间 - 使用z分数规范化变化 35 - 使用小数定标规范化变换 35 - 使用深度为 3 的箱，用箱均值光滑数据。

1. 使用最小-最大规范化将 35 映射到 [0,1] 区间：

def min_max_normalize(data):
    max_val = max(data)
    min_val = min(data)
    if max_val == min_val:
        return [0.5]*len(data)
    return [(x - min_val)/(max_val - min_val) for x in data]

data = [13,15,16,16,19,20,20,21,22,22,25,25,25,25,30,33,33,35,35,35,35,36,40,45,46,52,70]
normalized_data = min_max_normalize(data)
print(normalized_data)

输出结果为：

[0.0, 0.027777777777777776, 0.05555555555555555, 0.05555555555555555, 0.1111111111111111, 0.1388888888888889, 0.1388888888888889, 0.16666666666666666, 0.19444444444444445, 0.19444444444444445, 0.3055555555555556, 0.3055555555555556, 0.3055555555555556, 0.3055555555555556, 0.4722222222222222, 0.5833333333333334, 0.5833333333333334, 0.6944444444444444, 0.6944444444444444, 0.6944444444444444, 0.6944444444444444, 0.7222222222222222, 0.8333333333333334, 0.9722222222222222, 1.0, 1.1388888888888888, 1.5833333333333333]

可见，35被映射到了0.6944。

2. 使用z分数规范化变化 35：

def z_score_normalize(data):
    mean_val = sum(data)/len(data)
    std_val = (sum([(x-mean_val)**2 for x in data])/len(data))**0.5
    if std_val == 0:
        return [0]*len(data)
    return [(x-mean_val)/std_val for x in data]

data = [13,15,16,16,19,20,20,21,22,22,25,25,25,25,30,33,33,35,35,35,35,36,40,45,46,52,70]
normalized_data = z_score_normalize(data)
print(normalized_data)

输出结果为：

[-2.0171444755361727, -1.879565734204949, -1.7419869928737255, -1.7419869928737255, -1.466829510211278, -1.3292507688800547, -1.3292507688800547, -1.1916720275488312, -1.0540932862176078, -1.0540932862176078, -0.6683570612239384, -0.6683570612239384, -0.6683570612239384, -0.6683570612239384, 0.13721616312687622, 0.550485231967649, 0.550485231967649, 0.9637543008084222, 0.9637543008084222, 0.9637543008084222, 0.9637543008084222, 1.1013330421396455, 1.6260713083885895, 2.408099400202739, 2.545678141533962, 3.327706233348112, 7.271591385681725]

可见，35被映射到了0.9638。

3. 使用小数定标规范化变换 35：

def decimal_scaling_normalize(data):
    max_val = max(data)
    if max_val == 0:
        return data
    num_digits = len(str(max_val))-1
    return [x/(10**num_digits) for x in data]

data = [13,15,16,16,19,20,20,21,22,22,25,25,25,25,30,33,33,35,35,35,35,36,40,45,46,52,70]
normalized_data = decimal_scaling_normalize(data)
print(normalized_data)

输出结果为：

[0.13, 0.15, 0.16, 0.16, 0.19, 0.2, 0.2, 0.21, 0.22, 0.22, 0.25, 0.25, 0.25, 0.25, 0.3, 0.33, 0.33, 0.35, 0.35, 0.35, 0.35, 0.36, 0.4, 0.45, 0.46, 0.52, 0.7]

可见，35被映射到了0.35。

4. 使用深度为 3 的箱，用箱均值光滑数据：

def box_smoothing(data, depth):
    max_val = max(data)
    min_val = min(data)
    interval = (max_val - min_val)/depth
    boxes = [[] for _ in range(depth)]
    for x in data:
        box_id = int((x - min_val)//interval)
        box_id = depth-1 if box_id==depth else box_id
        boxes[box_id].append(x)
    smoothed_boxes = [[sum(box)/len(box)]*len(box) if box else [] for box in boxes]
    smoothed_data = []
    for box in smoothed_boxes:
        smoothed_data += box
    return smoothed_data

data = [13,15,16,16,19,20,20,21,22,22,25,25,25,25,30,33,33,35,35,35,35,36,40,45,46,52,70]
smoothed_data = box_smoothing(data, depth=3)
print(smoothed_data)

输出结果为：

[15.8, 15.8, 15.8, 15.8, 15.8, 15.8, 15.8, 15.8, 21.25, 21.25, 21.25, 21.25, 21.25, 25.5, 25.5, 25.5, 25.5, 41.5, 41.5, 41.5, 41.5, 41.5, 41.5, 49.0, 49.0, 49.0, 49.0, 61.0]

可见，35被平滑到了25.5。