Correlation visualization of features and objective variables

Introduction

Before modeling in business or analysis competitions, we made it possible to quickly see the correlation between the created features and the objective variables. Here, in particular, modeling is targeted when the objective variable such as sales forecast is a continuous value.

The code below uses Signate's bento demand forecast data. (Data: https://signate.jp/competitions/24/data)

This data is the task of creating a model that predicts the number of bento boxes sold in column y.

Library to use

import numpy as np
import pandas as pd

import matplotlib.pyplot as plt
%matplotlib inline

Data confirmation

df = pd.read_csv('./signate/train.csv')
# df.shape >> (207, 12)

df.head(2)

Data preprocessing

df['precipitation'] = df.precipitation.replace({'--' : '0'}).astype(float)
df = pd.get_dummies(df[['y', 'week', 'soldout', 'kcal', 'payday', 'weather', 'precipitation', 'temperature']])
df['payday'] = df.payday.fillna(0).astype(str)
df.head()

Statistic confirmation

df.describe()

Function that visualizes features and objective variables

argument

--df: Data frame to be visualized --target: Column name of objective variable

def make_plot(df, target):
    plt_col = sorted([c for c in df.columns if  c != target and len(df[c].unique()) > 1])
    
    col_num = len(plt_col)
    row_num = col_num // 2 + col_num % 2
    col_num = 2

    fig, ax = plt.subplots(row_num, col_num, figsize=(18, 3*row_num), sharex=False, sharey=False)
    fig.subplots_adjust(left=0.1, right=0.95, hspace=0.7, wspace=0.4)

    for i,col in enumerate(plt_col):
        tmp = df[[target, col]]
        tmp = tmp[~pd.isna(tmp[col])].reset_index(drop=True)
        if len(tmp[col].unique()) == 1:
            continue

        p = ((i+1) // 2) + ((i+1) % 2) -1
        q = abs(((i+1) % 2) - 1)
        if len(tmp[col].unique()) > 2:
            percentile095 = tmp[col].quantile(0.95)
            over_tmp = tmp[tmp[col] >= percentile095].reset_index(drop=True)
            over_tmp[col] = percentile095

            if tmp[col].min() < 0:
                percentile005 = tmp[col].quantile(0.05)
                under_tmp = tmp[tmp[col] <= percentile005].reset_index(drop=True)
                under_tmp[col] = percentile005

                outof_percentile = tmp[(percentile005 < tmp[col]) & ( tmp[col] < percentile095)].reset_index(drop=True)
                new_tmp = pd.concat([outof_percentile, under_tmp, over_tmp], axis=0)
                if percentile095 == percentile005:
                    new_tmp = tmp.copy()
            else:
                percentile095 = tmp[col].quantile(0.95)
                over_tmp = tmp[tmp[col] >= percentile095].reset_index(drop=True)
                over_tmp[col] = percentile095

                outof_percentile = tmp[tmp[col] < percentile095].reset_index(drop=True)
                new_tmp = pd.concat([outof_percentile, over_tmp], axis=0)
                if percentile095 == 0:
                    new_tmp = tmp.copy()
            ax1 = ax[p,q]
            ax2 = ax1.twinx()
            n, bins, pathces = ax1.hist(new_tmp[col], bins='auto', label='Feature value: {}'.format(col), ec='black')

            new_tmp['bins'] = pd.cut(new_tmp[col], bins.tolist(), right=False).values.astype(str)
            if len([f for f in new_tmp[col].unique() if bins[-2] <= f and f < bins[-1]]) > 0:
                new_tmp['bins_start'] = [float(b.split(',')[0].replace('[', '')) for b in new_tmp['bins']]
                bins_max = new_tmp['bins_start'].max()
                nan_value = new_tmp.query('bins_start == @bins_max').bins.unique()[0]
                new_tmp['bins'] = new_tmp['bins'].replace({'nan' : nan_value})
            else:
                new_tmp['bins'] = new_tmp['bins'].replace({'nan' : '[{}, {}]'.format(bins[-2], bins[-1])})

            num_bin = new_tmp.groupby('bins').size().reset_index(name='cnt')
            mean_target_bin = new_tmp.groupby('bins')[target].mean().reset_index().rename(columns={target : '{}_mean'.format(target)})
            center_feature_bin = new_tmp.groupby('bins').agg({col : {np.max, np.min}}).reset_index()
            center_feature_bin.columns = ['bins', 'feature_max', 'feature_min']
            center_feature_bin['feature_center'] = center_feature_bin.apply(lambda x : (x['feature_max'] + x['feature_min']) / 2, axis=1)
            plt_data = mean_target_bin.merge(center_feature_bin, on='bins', how='inner').merge(num_bin, on='bins', how='inner').sort_values('feature_center', ascending=True).reset_index(drop=True)
            ax2.plot(plt_data['feature_center'], plt_data['{}_mean'.format(target)], label='Mean value of objective variable (for each bin)', marker='.', color='orange')

        else:
            new_tmp = tmp.copy()
            ax1 = ax[p,q]
            ax2 = ax1.twinx()
            bins_list = sorted(new_tmp[col].unique().tolist())
            a = new_tmp.groupby([col]).agg({col : len, target : np.mean}).rename(columns={col : 'count', target : '{}_mean'.format(target)}).reset_index().astype({col : str})
            ax1.bar(a[col], a['count'], label='Feature value: {}'.format(col), ec='black')
            ax2.plot(a[col], a['{}_mean'.format(target)], label='Mean value of objective variable (for each bin)', marker='.', color='orange')

        ax2.hlines([new_tmp[target].mean()], new_tmp[col].min(), new_tmp[col].max(), color="darkred", linestyles='dashed', label='Mean of objective variables (whole data)')

        handler1, label1 = ax1.get_legend_handles_labels()
        handler2, label2 = ax2.get_legend_handles_labels()
        ax1.legend(handler1 + handler2, label1 + label2, borderaxespad=0., bbox_to_anchor=(0, 1.45), loc='upper left', fontsize=9)
        ax1.set_ylabel('count', fontsize=12)
        ax2.set_ylabel('Objective variable', fontsize=12)
        ax1.set_title('{}'.format(col), loc='right', fontsize=12)

    plt.show()

target = 'y'  #Specifying the objective variable
make_plot(df, target)  #plot

Visualization result

Items to visualize ** 1. Histogram or bar graph (blue) **

--Histogram when features are continuous values --Bar graph when features are binary

** 2. Mean value of objective variable for each bin (yellow) **

--Line graph of the mean value of the objective variable for each bin (for each value in the case of two values)

** 3. Mean of objective variables for the entire data (red) **