Unsupervised Analysis of Days of Week

Treating crossings each day as features to learn about the relationships vetween various days.



In [1]:

    
%matplotlib inline
import matplotlib.pyplot as plt
plt.style.use('seaborn')

import pandas as pd
import numpy as np

from sklearn.decomposition import PCA
from sklearn.mixture import GaussianMixture

Get Data



In [2]:

    
from jupyterworkflow.data import get_fremont_data
data = get_fremont_data()
pivoted = data.pivot_table('Total', index=data.index.time, columns=data.index.date)
pivoted.plot(legend=False, alpha=0.01);

Principal Component Analysis



In [3]:

    
X = pivoted.fillna(0).T.values
X.shape









    Out[3]:





(1610, 24)



In [4]:

    
X2 = PCA(2, svd_solver='full').fit_transform(X)

X2.shape









    Out[4]:





(1610, 2)



In [5]:

    
plt.scatter(X2[:, 0], X2[:, 1])









    Out[5]:





<matplotlib.collections.PathCollection at 0x1149db278>

Unsupervised Clustering



In [6]:

    
gmm = GaussianMixture(2)
gmm.fit(X)
labels = gmm.predict(X)



In [7]:

    
plt.scatter(X2[:, 0], X2[:, 1], c=labels, cmap='rainbow')
plt.colorbar();



In [8]:

    
fig, ax = plt.subplots(1, 2, figsize=(14, 6))
pivoted.T[labels == 0].T.plot(legend=False, alpha=0.1, ax=ax[0]);
pivoted.T[labels == 1].T.plot(legend=False, alpha=0.1, ax=ax[1]);

ax[0].set_title('Purple Cluster')
ax[1].set_title('Red Cluster');

Comparing with Day of Week



In [9]:

    
dayofweek = pd.DatetimeIndex(pivoted.columns).dayofweek
plt.scatter(X2[:, 0], X2[:, 1], c=dayofweek, cmap='rainbow')
plt.colorbar();

Analyzing Outliers

The following points are weekdays with a holiday-like pattern



In [10]:

    
dates = pd.DatetimeIndex(pivoted.columns)
dates[(labels==1) & (dayofweek < 5)]









    Out[10]:





DatetimeIndex(['2012-10-03', '2012-10-04', '2012-10-05', '2012-10-08',
               '2012-10-09', '2012-10-10', '2012-10-11', '2012-10-12',
               '2012-10-15', '2012-10-16',
               ...
               '2017-02-15', '2017-02-16', '2017-02-17', '2017-02-20',
               '2017-02-21', '2017-02-22', '2017-02-23', '2017-02-24',
               '2017-02-27', '2017-02-28'],
              dtype='datetime64[ns]', length=1109, freq=None)