本文采编自寒小阳老师上课讲义

案例：自行车租赁数据分析与可视化 {#案例：自行车租赁数据分析与可视化}

导入数据，做简单的数据处理 {#步骤1：导入数据，做简单的数据处理}

import pandas as pd # 读取数据到DataFrame
import urllib # 获取网络数据
import tempfile # 创建临时文件系统
import shutil # 文件操作
import zipfile # 压缩解压

temp_dir = tempfile.mkdtemp() # 建立临时目录
data_source = 'http://archive.ics.uci.edu/ml/machine-learning-databases/00275/Bike-Sharing-Dataset.zip' # 网络数据地址
zipname = temp_dir + '/Bike-Sharing-Dataset.zip' # 拼接文件和路径
urllib.urlretrieve(data_source, zipname) # 获得数据

zip_ref = zipfile.ZipFile(zipname, 'r') # 创建一个ZipFile对象处理压缩文件
zip_ref.extractall(temp_dir) # 解压
zip_ref.close()

daily_path = 'data/day.csv'
daily_data = pd.read_csv(daily_path) # 读取csv文件
daily_data['dteday'] = pd.to_datetime(daily_data['dteday']) # 把字符串数据传换成日期数据
drop_list = ['instant', 'season', 'yr', 'mnth', 'holiday', 'workingday', 'weathersit', 'atemp', 'hum'] # 不关注的列
daily_data.drop(drop_list, inplace = True, axis = 1) # inplace=true在对象上直接操作

shutil.rmtree(temp_dir) # 删除临时文件目录

daily_data.head() # 预览数据

配置全局参数 {#步骤2：配置参数}

from matplotlib import pyplot as plt
import pandas as pd
import numpy as np
# 在notebook中显示绘图结果
%matplotlib inline

# 设置一些全局的资源参数，可以进行个性化修改
import matplotlib
# 设置图片尺寸 14" x 7"
# rc: resource configuration
matplotlib.rc('figure', figsize = (14, 7))
# 设置字体 14
matplotlib.rc('font', size = 14)
# 不显示顶部和右侧的坐标线
matplotlib.rc('axes.spines', top = False, right = False)
# 不显示网格
matplotlib.rc('axes', grid = False)
# 设置背景颜色是白色
matplotlib.rc('axes', facecolor = 'white')

关联分析 {#步骤3：关联分析}

# 包装一个散点图的函数便于复用
def scatterplot(x_data, y_data, x_label, y_label, title):

    # 创建一个绘图对象
    fig, ax = plt.subplots()

    # 设置数据、点的大小、点的颜色和透明度
    ax.scatter(x_data, y_data, s = 10, color = '#539caf', alpha = 0.75) 

    # 添加标题和坐标说明
    ax.set_title(title)
    ax.set_xlabel(x_label)
    ax.set_ylabel(y_label)

# 绘制散点图
scatterplot(x_data = daily_data['temp']
            , y_data = daily_data['cnt']
            , x_label = 'Normalized temperature (C)'
            , y_label = 'Check outs'
            , title = 'Number of Check Outs vs Temperature')

# 线性回归
import statsmodels.api as sm # 最小二乘
from statsmodels.stats.outliers_influence import summary_table # 获得汇总信息
x = sm.add_constant(daily_data['temp']) # 其实可以看成这个series 前面加了一列 变成datadrame 这一列全为1 作为线性回归的常数项
y = daily_data['cnt']
regr = sm.OLS(y, x) # 普通最小二乘模型，ordinary least square model
res = regr.fit()
# 从模型获得拟合数据
st, data, ss2 = summary_table(res, alpha=0.05) # 置信水平alpha=5%，st数据汇总，data数据详情，ss2数据列名
fitted_values = data[:,2]#第三列是拟合值 如果有兴趣可以自己去这个库的包 返回的data是一个很大的dataframe 每一列都是它的含义

# 包装曲线绘制函数
def lineplot(x_data, y_data, x_label, y_label, title):
    # 创建绘图对象
    _, ax = plt.subplots()

    # 绘制拟合曲线，lw=linewidth，alpha=transparancy
    ax.plot(x_data, y_data, lw = 2, color = '#539caf', alpha = 1)

    # 添加标题和坐标说明
    ax.set_title(title)
    ax.set_xlabel(x_label)
    ax.set_ylabel(y_label)

# 调用绘图函数
lineplot(x_data = daily_data['temp']
         , y_data = fitted_values
         , x_label = 'Normalized temperature (C)'
         , y_label = 'Check outs'
         , title = 'Line of Best Fit for Number of Check Outs vs Temperature')

带置信区间的曲线图 {#带置信区间的曲线图}

• 评估曲线拟合结果

# 获得5%置信区间的上下界
predict_mean_ci_low, predict_mean_ci_upp = data[:,4:6].T# 4.5列为5%置信区间的上下界

# 创建置信区间DataFrame，上下界
CI_df = pd.DataFrame(columns = ['x_data', 'low_CI', 'upper_CI'])
CI_df['x_data'] = daily_data['temp']
CI_df['low_CI'] = predict_mean_ci_low
CI_df['upper_CI'] = predict_mean_ci_upp
CI_df.sort_values('x_data', inplace = True) # 根据x_data进行排序

# 绘制置信区间
def lineplotCI(x_data, y_data, sorted_x, low_CI, upper_CI, x_label, y_label, title):
    # 创建绘图对象
    _, ax = plt.subplots()

    # 绘制预测曲线
    ax.plot(x_data, y_data, lw = 1, color = '#539caf', alpha = 1, label = 'Fit')
    # 绘制置信区间，顺序填充
    ax.fill_between(sorted_x, low_CI, upper_CI, color = '#539caf', alpha = 0.4, label = '95% CI')
    # 添加标题和坐标说明
    ax.set_title(title)
    ax.set_xlabel(x_label)
    ax.set_ylabel(y_label)

    # 显示图例，配合label参数，loc=“best”自适应方式
    ax.legend(loc = 'best')

# Call the function to create plot
lineplotCI(x_data = daily_data['temp']
           , y_data = fitted_values
           , sorted_x = CI_df['x_data']
           , low_CI = CI_df['low_CI']
           , upper_CI = CI_df['upper_CI']
           , x_label = 'Normalized temperature (C)'
           , y_label = 'Check outs'
           , title = 'Line of Best Fit for Number of Check Outs vs Temperature')

双坐标曲线图 {#双坐标曲线图}

• 曲线拟合不满足置信阈值时，考虑增加独立变量
• 分析不同尺度多变量的关系

# 双纵坐标绘图函数
def lineplot2y(x_data, x_label, y1_data, y1_color, y1_label, y2_data, y2_color, y2_label, title):
    _, ax1 = plt.subplots()
    ax1.plot(x_data, y1_data, color = y1_color)
    # 添加标题和坐标说明
    ax1.set_ylabel(y1_label, color = y1_color)
    ax1.set_xlabel(x_label)
    ax1.set_title(title)

    ax2 = ax1.twinx() # 两个绘图对象共享横坐标轴
    ax2.plot(x_data, y2_data, color = y2_color)
    ax2.set_ylabel(y2_label, color = y2_color)
    # 右侧坐标轴可见
    ax2.spines['right'].set_visible(True)

# 调用绘图函数
lineplot2y(x_data = daily_data['dteday']
           , x_label = 'Day'
           , y1_data = daily_data['cnt']
           , y1_color = '#539caf'
           , y1_label = 'Check outs'
           , y2_data = daily_data['windspeed']
           , y2_color = '#7663b0'
           , y2_label = 'Normalized windspeed'
           , title = 'Check Outs and Windspeed Over Time')

分布分析¶ {#步骤4：分布分析}

直方图（灰度图） {#灰度图}

• 粗略区间计数

# 绘制灰度图的函数
def histogram(data, x_label, y_label, title):
    _, ax = plt.subplots()
    res = ax.hist(data, color = '#539caf', bins=10) # 设置bin的数量
    ax.set_ylabel(y_label)
    ax.set_xlabel(x_label)
    ax.set_title(title)
    return res

# 绘图函数调用
res = histogram(data = daily_data['registered']
           , x_label = 'Check outs'
           , y_label = 'Frequency'
           , title = 'Distribution of Registered Check Outs')
res[0] # value of bins
res[1] # boundary of bins

堆叠直方图

• 比较两个分布

# 绘制堆叠的直方图
def overlaid_histogram(data1, data1_name, data1_color, data2, data2_name, data2_color, x_label, y_label, title):
    # 归一化数据区间，对齐两个直方图的bins
    max_nbins = 10
    data_range = [min(min(data1), min(data2)), max(max(data1), max(data2))]
    binwidth = (data_range[1] - data_range[0]) / max_nbins
    bins = np.arange(data_range[0], data_range[1] + binwidth, binwidth) # 生成直方图bins区间

    # Create the plot
    _, ax = plt.subplots()
    ax.hist(data1, bins = bins, color = data1_color, alpha = 1, label = data1_name)
    ax.hist(data2, bins = bins, color = data2_color, alpha = 0.75, label = data2_name)
    ax.set_ylabel(y_label)
    ax.set_xlabel(x_label)
    ax.set_title(title)
    ax.legend(loc = 'best')

# Call the function to create plot
overlaid_histogram(data1 = daily_data['registered']
                   , data1_name = 'Registered'
                   , data1_color = '#539caf'
                   , data2 = daily_data['casual']
                   , data2_name = 'Casual'
                   , data2_color = '#7663b0'
                   , x_label = 'Check outs'
                   , y_label = 'Frequency'
                   , title = 'Distribution of Check Outs By Type')

registered：注册的分布，正态分布，why

casual：偶然的分布，疑似指数分布，why

以上两个问题均可以查询这两个概念得出结论

密度图 {#密度图}

• 精细刻画概率分布

KDE: kernal density estimate

$$\hat{f}h(x) = \frac{1}{n}\sum\limits{i=1}^n K_h(x-x_i) = \frac{1}{nh}\sum\limits_{i=1}^n K(\frac{x-x_i}{h})$$

# 计算概率密度
from scipy.stats import gaussian_kde
data = daily_data['registered']
density_est = gaussian_kde(data) # kernal density estimate: https://en.wikipedia.org/wiki/Kernel_density_estimation
# 控制平滑程度，数值越大，越平滑
density_est.covariance_factor = lambda : .3
density_est._compute_covariance()
x_data = np.arange(min(data), max(data), 200)

# 绘制密度估计曲线
def densityplot(x_data, density_est, x_label, y_label, title):
    _, ax = plt.subplots()
    ax.plot(x_data, density_est(x_data), color = '#539caf', lw = 2)
    ax.set_ylabel(y_label)
    ax.set_xlabel(x_label)
    ax.set_title(title)

# 调用绘图函数
densityplot(x_data = x_data
            , density_est = density_est
            , x_label = 'Check outs'
            , y_label = 'Frequency'
            , title = 'Distribution of Registered Check Outs')

组间分析 {#步骤5：组间分析}

• 组间定量比较
• 分组粒度
• 组间聚类

柱状图 {#柱状图}

• 一级类间均值方差比较

# 分天分析统计特征
mean_total_co_day = daily_data[['weekday', 'cnt']].groupby('weekday').agg([np.mean, np.std])
mean_total_co_day.columns = mean_total_co_day.columns.droplevel()

# 定义绘制柱状图的函数
def barplot(x_data, y_data, error_data, x_label, y_label, title):
    _, ax = plt.subplots()
    # 柱状图
    ax.bar(x_data, y_data, color = '#539caf', align = 'center')
    # 绘制方差
    # ls='none'去掉bar之间的连线
    ax.errorbar(x_data, y_data, yerr = error_data, color = '#297083', ls = 'none', lw = 5)
    ax.set_ylabel(y_label)
    ax.set_xlabel(x_label)
    ax.set_title(title)

# 绘图函数调用
barplot(x_data = mean_total_co_day.index.values
        , y_data = mean_total_co_day['mean']
        , error_data = mean_total_co_day['std']
        , x_label = 'Day of week'
        , y_label = 'Check outs'
        , title = 'Total Check Outs By Day of Week (0 = Sunday)')

mean_total_co_day.columns
daily_data[['weekday', 'cnt']].groupby('weekday').agg([np.mean, np.std])

        registered    casual
weekday     
0   4228.828571 1872.496462
1   4338.123810 1793.073897
2   4510.663462 1826.911602
3   4548.538462 2038.095680
4   4667.259615 1939.433165
5   4690.288462 1874.624762
6   4550.542857 2196.692969

# 分天统计注册和偶然使用的情况
mean_by_reg_co_day = daily_data[['weekday', 'registered', 'casual']].groupby('weekday').mean()
# 分天统计注册和偶然使用的占比
mean_by_reg_co_day['total'] = mean_by_reg_co_day['registered'] + mean_by_reg_co_day['casual']
mean_by_reg_co_day['reg_prop'] = mean_by_reg_co_day['registered'] / mean_by_reg_co_day['total']
mean_by_reg_co_day['casual_prop'] = mean_by_reg_co_day['casual'] / mean_by_reg_co_day['total']


# 绘制堆积柱状图
def stackedbarplot(x_data, y_data_list, y_data_names, colors, x_label, y_label, title):
    _, ax = plt.subplots()
    # 循环绘制堆积柱状图
    for i in range(0, len(y_data_list)):
        if i == 0:
            ax.bar(x_data, y_data_list[i], color = colors[i], align = 'center', label = y_data_names[i])
        else:
            # 采用堆积的方式，除了第一个分类，后面的分类都从前一个分类的柱状图接着画
            # 用归一化保证最终累积结果为1
            ax.bar(x_data, y_data_list[i], color = colors[i], bottom = y_data_list[i - 1], align = 'center', label = y_data_names[i])
    ax.set_ylabel(y_label)
    ax.set_xlabel(x_label)
    ax.set_title(title)
    ax.legend(loc = 'upper right') # 设定图例位置

# 调用绘图函数
stackedbarplot(x_data = mean_by_reg_co_day.index.values
               , y_data_list = [mean_by_reg_co_day['reg_prop'], mean_by_reg_co_day['casual_prop']]
               , y_data_names = ['Registered', 'Casual']
               , colors = ['#539caf', '#7663b0']
               , x_label = 'Day of week'
               , y_label = 'Proportion of check outs'
               , title = 'Check Outs By Registration Status and Day of Week (0 = Sunday)')

• 从这幅图你看出了什么？工作日 VS 节假日

• 为什么会有这样的差别？

分组柱状图 {#分组柱状图}

• 多级类间绝对数值比较

# 绘制分组柱状图的函数
def groupedbarplot(x_data, y_data_list, y_data_names, colors, x_label, y_label, title):
    _, ax = plt.subplots()
    # 设置每一组柱状图的宽度
    total_width = 0.8
    # 设置每一个柱状图的宽度
    ind_width = total_width / len(y_data_list)
    # 计算每一个柱状图的中心偏移
    alteration = np.arange(-total_width/2+ind_width/2, total_width/2+ind_width/2, ind_width)

    # 分别绘制每一个柱状图
    for i in range(0, len(y_data_list)):
        # 横向散开绘制
        ax.bar(x_data + alteration[i], y_data_list[i], color = colors[i], label = y_data_names[i], width = ind_width)
    ax.set_ylabel(y_label)
    ax.set_xlabel(x_label)
    ax.set_title(title)
    ax.legend(loc = 'upper right')

# 调用绘图函数
groupedbarplot(x_data = mean_by_reg_co_day.index.values
               , y_data_list = [mean_by_reg_co_day['registered'], mean_by_reg_co_day['casual']]
               , y_data_names = ['Registered', 'Casual']
               , colors = ['#539caf', '#7663b0']
               , x_label = 'Day of week'
               , y_label = 'Check outs'
               , title = 'Check Outs By Registration Status and Day of Week (0 = Sunday)')

• 偏移前：ind_width/2

• 偏移后：total_width/2

• 偏移量：total_width/2-ind_width/2

箱式图 {#箱式图}

• 多级类间数据分布比较
• 柱状图 + 堆叠灰度图

# 只需要指定分类的依据，就能自动绘制箱式图
days = np.unique(daily_data['weekday'])
bp_data = []
for day in days:
    bp_data.append(daily_data[daily_data['weekday'] == day]['cnt'].values)

# 定义绘图函数
def boxplot(x_data, y_data, base_color, median_color, x_label, y_label, title):
    _, ax = plt.subplots()

    # 设置样式
    ax.boxplot(y_data
               # 箱子是否颜色填充
               , patch_artist = True
               # 中位数线颜色
               , medianprops = {'color': base_color}
               # 箱子颜色设置，color：边框颜色，facecolor：填充颜色
               , boxprops = {'color': base_color, 'facecolor': median_color}
               # 猫须颜色whisker
               , whiskerprops = {'color': median_color}
               # 猫须界限颜色whisker cap
               , capprops = {'color': base_color})

    # 箱图与x_data保持一致
    ax.set_xticklabels(x_data)
    ax.set_ylabel(y_label)
    ax.set_xlabel(x_label)
    ax.set_title(title)

# 调用绘图函数
boxplot(x_data = days
        , y_data = bp_data
        , base_color = 'b'
        , median_color = 'r'
        , x_label = 'Day of week'
        , y_label = 'Check outs'
        , title = 'Total Check Outs By Day of Week (0 = Sunday)')

简单总结 {#简单总结}

• 关联分析、数值比较：散点图、曲线图
• 分布分析：灰度图、密度图
• 涉及分类的分析：柱状图、箱式图