Unsupervised Analysis of Days of Week

Treating crossings each day as features to learn about relationships between 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()



In [3]:

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









    Out[3]:





<matplotlib.axes._subplots.AxesSubplot at 0x7fa8fc29cb70>

Principal Component Analysis



In [4]:

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









    Out[4]:





(1610, 24)



In [5]:

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









    Out[5]:





(1610, 2)



In [6]:

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









    Out[6]:





<matplotlib.collections.PathCollection at 0x7fa8f5265320>

Unsupervised Clustering



In [7]:

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









    Out[7]:





array([1, 1, 1, ..., 0, 1, 1])



In [8]:

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









    Out[8]:





<matplotlib.colorbar.Colorbar at 0x7fa8f50721d0>



In [9]:

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

pivoted.T[labels == 1].T.plot(legend=False, alpha=0.1, ax=ax[1])
pivoted.T[labels == 0].T.plot(legend=False, alpha=0.1, ax=ax[0])

ax[0].set_title("Purple Cluster")
ax[0].set_title("Red Cluster")









    Out[9]:





<matplotlib.text.Text at 0x7fa8f5167e80>

Comparing with Day of Week



In [10]:

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









    Out[10]:





<matplotlib.colorbar.Colorbar at 0x7fa8eca140f0>

Analysing Outliers

The following points are weekdays with a holiday-like pattern



In [11]:

    
dates = pd.DatetimeIndex(pivoted.columns)
dates[(labels == 0) & (day_of_week < 5)]









    Out[11]:





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)

What's up with Feb 6, 2017? Snow Storm



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