Unsupervised Analysis of Days of Week

Tresting crossings each dat as features to learn about the relationships bwteen days of the week



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

import numpy as np
import pandas as pd

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

Get Data



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from jupyterworkflow.data import get_fremont_data
data = get_fremont_data()



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

Principal Component Analysis



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

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









    Out[4]:





(1610, 2)



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

Unsupervised Clustering



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



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



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fig, ax = plt.subplots(1, 2, figsize=(14, 6))

pivoted.T[labels == 0].T.plot(legend=False, alpha=0.01, ax=ax[0]);
pivoted.T[labels == 1].T.plot(legend=False, alpha=0.01, ax=ax[1]);

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

Comparing with Day of the week



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dayofweek = pd.DatetimeIndex(pivoted.columns).dayofweek



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

Analyzing Outliers

The following points are weekdays with a holiday-like pattern



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weekday_label = 0
weekend_label = 1
if pivoted.T[labels == 1].max().max() > pivoted.T[labels == 0].max().max() :
    weekday_label = 1
    weekend_label = 0



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









    Out[12]:





DatetimeIndex(['2012-11-22', '2012-11-23', '2012-12-24', '2012-12-25',
               '2013-01-01', '2013-05-27', '2013-07-04', '2013-07-05',
               '2013-09-02', '2013-11-28', '2013-11-29', '2013-12-20',
               '2013-12-24', '2013-12-25', '2014-01-01', '2014-04-23',
               '2014-05-26', '2014-07-04', '2014-09-01', '2014-11-27',
               '2014-11-28', '2014-12-24', '2014-12-25', '2014-12-26',
               '2015-01-01', '2015-05-25', '2015-07-03', '2015-09-07',
               '2015-11-26', '2015-11-27', '2015-12-24', '2015-12-25',
               '2016-01-01', '2016-05-30', '2016-07-04', '2016-09-05',
               '2016-11-24', '2016-11-25', '2016-12-26', '2017-01-02',
               '2017-02-06'],
              dtype='datetime64[ns]', freq=None)



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