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Predicting Hotel Cancellations with Support Vector Machines and ARIMA: Part 1
Hotel cancellations can cause issues for many businesses in the industry. Not only is there the lost revenue as a result of the customer cancelling, but this can also cause difficulty in coordinating bookings and adjusting revenue management practices.
Data analytics can help to overcome this issue, in terms of identifying the customers who are most likely to cancel – allowing a hotel chain to adjust its marketing strategy accordingly.
To investigate how machine learning can aid in this task, the ExtraTreesClassifer, logistic regression, and support vector machine models were employed in Python to determine whether cancellations can be accurately predicted with this model. For this example, both hotels are based in Portugal. The Algarve Hotel dataset available from Science Direct was used to train and validate the model, and then the logistic regression was used to generate predictions on a second dataset for a hotel in Lisbon.
Data Processing
At the outset, there is the consideration of overfitting when building the model with the data.
For example, in the original H1 file, there were 11,122 cancellations while 28,938 bookings did not cancel. Therefore, noncancellations could likely end up being overrepresented in the model. For this reason, the H1 dataset was filtered to include 10,000 cancellations and 10,000 noncancellations.
For the test dataset (H2.csv), 12,000 observations were selected at random, irrespective of whether the booking was cancelled or not.
The relevant libraries were imported and the relevant data type for each variable was classified:
import os
import csv
import random
import statsmodels.api as sm
import statsmodels.formula.api as smf
import numpy as np
import pandas as pd
from sklearn.model_selection import train_test_split
from sklearn.linear_model import LogisticRegression
from sklearn.ensemble import ExtraTreesClassifier
from sklearn.preprocessing import MinMaxScaler
As we can see, there are many variables that can potentially influence whether a customer is going to cancel or not, and not all of these variables will necessarily be relevant in determining this.
The data is imported:
train_df = pd.read_csv('H1.csv', dtype=dtypes)
a=train_df.head()
b=train_df
b.sort_values(['ArrivalDateYear','ArrivalDateWeekNumber'], ascending=True)
b
The variables are then stacked together under the numpy format:
# Dependent variable
IsCanceled = train_df['IsCanceled']
y = IsCanceled
# Numerical variables
leadtime = train_df['LeadTime'] #1
staysweekendnights = train_df['StaysInWeekendNights'] #2
staysweeknights = train_df['StaysInWeekNights'] #3
adults = train_df['Adults'] #4
children = train_df['Children'] #5
babies = train_df['Babies'] #6
isrepeatedguest = train_df['IsRepeatedGuest'] #11
previouscancellations = train_df['PreviousCancellations'] #12
previousbookingsnotcanceled = train_df['PreviousBookingsNotCanceled'] #13
bookingchanges = train_df['BookingChanges'] #16
agent = train_df['Agent'] #18
company = train_df['Company'] #19
dayswaitinglist = train_df['DaysInWaitingList'] #20
adr = train_df['ADR'] #22
rcps = train_df['RequiredCarParkingSpaces'] #23
totalsqr = train_df['TotalOfSpecialRequests'] #24
# Categorical variables
mealcat=train_df.Meal.astype("category").cat.codes
mealcat=pd.Series(mealcat)
countrycat=train_df.Country.astype("category").cat.codes
countrycat=pd.Series(countrycat)
marketsegmentcat=train_df.MarketSegment.astype("category").cat.codes
marketsegmentcat=pd.Series(marketsegmentcat)
distributionchannelcat=train_df.DistributionChannel.astype("category").cat.codes
distributionchannelcat=pd.Series(distributionchannelcat)
reservedroomtypecat=train_df.ReservedRoomType.astype("category").cat.codes
reservedroomtypecat=pd.Series(reservedroomtypecat)
assignedroomtypecat=train_df.AssignedRoomType.astype("category").cat.codes
assignedroomtypecat=pd.Series(assignedroomtypecat)
deposittypecat=train_df.DepositType.astype("category").cat.codes
deposittypecat=pd.Series(deposittypecat)
customertypecat=train_df.CustomerType.astype("category").cat.codes
customertypecat=pd.Series(customertypecat)
reservationstatuscat=train_df.ReservationStatus.astype("category").cat.codes
reservationstatuscat=pd.Series(reservationstatuscat)
# Numpy column stack
x = np.column_stack((leadtime,staysweekendnights,staysweeknights,adults,children,babies,mealcat,countrycat,marketsegmentcat,distributionchannelcat,isrepeatedguest,previouscancellations,previousbookingsnotcanceled,reservedroomtypecat,assignedroomtypecat,bookingchanges,deposittypecat,dayswaitinglist,customertypecat,adr,rcps,totalsqr,reservationstatuscat))
x = sm.add_constant(x, prepend=True)
Extra Trees Classifier
As mentioned, there are many variables included in the analysis – not all of them will be relevant in determining whether a customer is likely to cancel or not.
To solve this issue, the Extra Trees Classifier is used to print the importance of each variable in numerical format, and the variables with the highest ranked importance are then chosen accordingly.
from sklearn.ensemble import ExtraTreesClassifier
model = ExtraTreesClassifier()
model.fit(x, y)
print(model.feature_importances_)
Here are the generated readings:
[0. 0.04070268 0.0052648 0.00701335 0.00396219 0.00806383
0.00075091 0.00614394 0.05941394 0.03322725 0.01097485 0.01110851
0.00733542 0.00147088 0.0076557 0.01338097 0.00640656 0.03391769
0.0010779 0.018724 0.01788529 0.06105368 0.0082012 0.63626446]
Here is a breakdown of the feature ranking by order with the top features:
From the above, the top six identified features of importance are reservation status, country, required car parking spaces, deposit type, customer type, and lead time.
However, a couple of caveats worth mentioning:

Reservation status cannot be used to predict hotel cancellations as the two are highly correlated, i.e. if the reservation status is cancelled, then this variable will already reflect this.

When an initial logistic regression was run, customer type and required car parking spaces were shown as insignificant. Therefore, the regression was run again as below with these variables having been dropped from the model.
Logistic Regression
The data was split into training and test data, and the logistic regression was generated:
x1_train, x1_test, y1_train, y1_test = train_test_split(x1, y1, random_state=0)
logreg = LogisticRegression().fit(x1_train,y1_train)
logreg
print("Training set score: {:.3f}".format(logreg.score(x1_train,y1_train)))
print("Test set score: {:.3f}".format(logreg.score(x1_test,y1_test)))
The following training and test set scores were generated:
Training set score: 0.699
Test set score: 0.699
Then, the coefficients for the logistic regression itself were generated:
import statsmodels.api as sm
logit_model=sm.Logit(y1,x1)
result=logit_model.fit()
print(result.summary())
Here are the updated results:
Optimization terminated successfully.
Current function value: 0.596755
Iterations 7
Logit Regression Results
==============================================================================
Dep. Variable: IsCanceled No. Observations: 20000
Model: Logit Df Residuals: 19996
Method: MLE Df Model: 3
Date: Sat, 17 Aug 2019 Pseudo Rsqu.: 0.1391
Time: 23:58:55 LogLikelihood: 11935.
converged: True LLNull: 13863.
LLR pvalue: 0.000
==============================================================================
coef std err z P>z [0.025 0.975]

const 2.1417 0.050 43.216 0.000 2.239 2.045
x1 0.0055 0.000 32.013 0.000 0.005 0.006
x2 0.0236 0.001 36.465 0.000 0.022 0.025
x3 2.1137 0.104 20.400 0.000 1.911 2.317
==============================================================================
Now, the logistic regression is used to predict cancellations for the test data, and a confusion matrix is generated to determine the incidence of true/false positives and negatives:
pr = logreg.predict(x1_test)
from sklearn.metrics import classification_report,confusion_matrix
print(confusion_matrix(y1_test,pr))
print(classification_report(y1_test,pr))
The confusion matrix is generated:
[[1898 633]
[ 874 1595]]
precision recall f1score support
0 0.68 0.75 0.72 2531
1 0.72 0.65 0.68 2469
accuracy 0.70 5000
macro avg 0.70 0.70 0.70 5000
weighted avg 0.70 0.70 0.70 5000
Here is an ROC curve illustrating the true vs false positive rate.
import matplotlib.pyplot as plt
from sklearn.metrics import roc_curve
falsepos,truepos,thresholds=roc_curve(y1_test,logreg.decision_function(x1_test))
plt.plot(falsepos,truepos,label="ROC")
plt.xlabel("False Positive Rate")
plt.ylabel("True Positive Rate")
cutoff=np.argmin(np.abs(thresholds))
plt.plot(falsepos[cutoff],truepos[cutoff],'o',markersize=10,label="cutoff",fillstyle="none")
plt.show()
Support Vector Machine (SVM) generation
The above model has shown a 70% classification accuracy in determining whether a customer will cancel. The prediction for noncancellations was 68% based on precision while it was 72% for cancellations (also based on precision).
Therefore, an SVM was generated using the training and validation data to determine whether this model would yield higher classification accuracy.
from sklearn import svm
clf = svm.SVC(gamma='scale')
clf.fit(x1, y1)
prclf = clf.predict(x1_test)
prclf
A new prediction array is generated:
array([1, 0, 0, ..., 1, 1, 0])
Here is the new ROC curve generated:
This is the updated confusion matrix:
[[2085 446]
[ 963 1506]]
precision recall f1score support
0 0.68 0.82 0.75 2531
1 0.77 0.61 0.68 2469
accuracy 0.72 5000
macro avg 0.73 0.72 0.71 5000
weighted avg 0.73 0.72 0.71 5000
The overall accuracy has increased to 73%, but note that the predictive accuracy for cancellations specifically has improved quite significantly to 77%, while it remains at 68% for noncancellations.
Testing against unseen data
Now that the SVM has shown improved accuracy against the validation dataset, another dataset H2.csv (also available from Science direct) is used for comparison purposes, i.e. the SVM generated using the last dataset is now used to predict classifications across this dataset (for a different hotel located in Lisbon, Portugal).
The second dataset is loaded using pandas:
h2data = pd.read_csv('H2.csv', dtype=dtypes)
a=h2data.head()
b=h2data
b
The new variables are sorted into a numpy column stack, and an SVM is run:
# Numerical variables
t_leadtime = h2data['LeadTime'] #1
t_staysweekendnights = h2data['StaysInWeekendNights'] #2
t_staysweeknights = h2data['StaysInWeekNights'] #3
t_adults = h2data['Adults'] #4
t_children = h2data['Children'] #5
t_babies = h2data['Babies'] #6
t_isrepeatedguest = h2data['IsRepeatedGuest'] #11
t_previouscancellations = h2data['PreviousCancellations'] #12
t_previousbookingsnotcanceled = h2data['PreviousBookingsNotCanceled'] #13
t_bookingchanges = h2data['BookingChanges'] #16
t_agent = h2data['Agent'] #18
t_company = h2data['Company'] #19
t_dayswaitinglist = h2data['DaysInWaitingList'] #20
t_adr = h2data['ADR'] #22
t_rcps = h2data['RequiredCarParkingSpaces'] #23
t_totalsqr = h2data['TotalOfSpecialRequests'] #24
# Categorical variables
t_mealcat=h2data.Meal.astype("category").cat.codes
t_mealcat=pd.Series(t_mealcat)
t_countrycat=h2data.Country.astype("category").cat.codes
t_countrycat=pd.Series(t_countrycat)
t_marketsegmentcat=h2data.MarketSegment.astype("category").cat.codes
t_marketsegmentcat=pd.Series(t_marketsegmentcat)
t_distributionchannelcat=h2data.DistributionChannel.astype("category").cat.codes
t_distributionchannelcat=pd.Series(t_distributionchannelcat)
t_reservedroomtypecat=h2data.ReservedRoomType.astype("category").cat.codes
t_reservedroomtypecat=pd.Series(t_reservedroomtypecat)
t_assignedroomtypecat=h2data.AssignedRoomType.astype("category").cat.codes
t_assignedroomtypecat=pd.Series(t_assignedroomtypecat)
t_deposittypecat=h2data.DepositType.astype("category").cat.codes
t_deposittypecat=pd.Series(t_deposittypecat)
t_customertypecat=h2data.CustomerType.astype("category").cat.codes
t_customertypecat=pd.Series(t_customertypecat)
t_reservationstatuscat=h2data.ReservationStatus.astype("category").cat.codes
t_reservationstatuscat=pd.Series(t_reservationstatuscat)
a = np.column_stack((t_leadtime,t_countrycat,t_deposittypecat))
a = sm.add_constant(a, prepend=True)
IsCanceled = h2data['IsCanceled']
b = IsCanceled
b=b.values
prh2 = clf.predict(a)
prh2
The array of predictions is generated once again:
array([0, 0, 1, ..., 0, 1, 0])
A classification matrix is generated:
from sklearn.metrics import classification_report,confusion_matrix
print(confusion_matrix(b,prh2))
print(classification_report(b,prh2))
Classification Output
[[5654 1350]
[2038 2958]]
precision recall f1score support
0 0.74 0.81 0.77 7004
1 0.69 0.59 0.64 4996
accuracy 0.72 12000
macro avg 0.71 0.70 0.70 12000
weighted avg 0.71 0.72 0.71 12000
The ROC curve is generated:
Across the test set, the overall prediction accuracy increased to 72%, while the accuracy for cancellation incidences fell slightly to 69%.
metrics.auc(falsepos, truepos)
The computed AUC (area under the curve) is 0.74.
0.7437825188763232
ARIMA Modelling of Hotel Cancellations
Having investigated the main drivers of hotel cancellations, it would also be useful to determine whether hotel cancellations can also be predicted in advance. This will be done for the Algarve Hotel (H1.csv).
To do this, cancellations are analysed on a weekly basis (i.e. the number of cancellations summed up per week).
Firstly, data manipulation procedures were carried out to sum up the number of cancellations per week and order them correctly.
Here is a snippet of the output:
The time series is visualised, and the autocorrelation and partial autocorrelation plots are generated:
Time Series
Autocorrelation
Partial Autocorrelation
#DickeyFuller Test
result = ts.adfuller(train)
result
print('ADF Statistic: %f' % result[0])
print('pvalue: %f' % result[1])
print('Critical Values:')
for key, value in result[4].items():
print('\t%s: %.3f' % (key, value))
When a DickeyFuller test is run, a pvalue of less than 0.05 is generated, indicating that the null hypothesis of nonstationarity is rejected (i.e. the data is stationary).
ADF Statistic: 2.998923
pvalue: 0.034995
Critical Values:
1%: 3.498
5%: 2.891
10%: 2.582
An ARIMA model is then run using auto_arima from the pyramid library. This is used to select the optimal (p,d,q) coordinates for the ARIMA model.
from pyramid.arima import auto_arima
Arima_model=auto_arima(train, start_p=0, start_q=0, max_p=10, max_q=10, start_P=0, start_Q=0, max_P=10, max_Q=10, m=52, seasonal=True, trace=True, d=1, D=1, error_action='warn', suppress_warnings=True, random_state = 20, n_fits=30)
The following output is generated:
Fit ARIMA: order=(0, 1, 0) seasonal_order=(0, 1, 0, 52); AIC=574.094, BIC=577.918, Fit time=0.232 seconds
Fit ARIMA: order=(1, 1, 0) seasonal_order=(1, 1, 0, 52); AIC=nan, BIC=nan, Fit time=nan seconds
Fit ARIMA: order=(0, 1, 1) seasonal_order=(0, 1, 1, 52); AIC=nan, BIC=nan, Fit time=nan seconds
Fit ARIMA: order=(0, 1, 0) seasonal_order=(1, 1, 0, 52); AIC=nan, BIC=nan, Fit time=nan seconds
Fit ARIMA: order=(0, 1, 0) seasonal_order=(0, 1, 1, 52); AIC=nan, BIC=nan, Fit time=nan seconds
Fit ARIMA: order=(0, 1, 0) seasonal_order=(1, 1, 1, 52); AIC=nan, BIC=nan, Fit time=nan seconds
Fit ARIMA: order=(1, 1, 0) seasonal_order=(0, 1, 0, 52); AIC=559.620, BIC=565.356, Fit time=1.638 seconds
Fit ARIMA: order=(1, 1, 1) seasonal_order=(0, 1, 0, 52); AIC=543.988, BIC=551.637, Fit time=4.383 seconds
Fit ARIMA: order=(2, 1, 2) seasonal_order=(0, 1, 0, 52); AIC=547.819, BIC=559.291, Fit time=8.437 seconds
Fit ARIMA: order=(1, 1, 1) seasonal_order=(1, 1, 0, 52); AIC=nan, BIC=nan, Fit time=nan seconds
Fit ARIMA: order=(1, 1, 1) seasonal_order=(0, 1, 1, 52); AIC=nan, BIC=nan, Fit time=nan seconds
Fit ARIMA: order=(1, 1, 1) seasonal_order=(1, 1, 1, 52); AIC=nan, BIC=nan, Fit time=nan seconds
Fit ARIMA: order=(0, 1, 1) seasonal_order=(0, 1, 0, 52); AIC=542.114, BIC=547.850, Fit time=2.471 seconds
Fit ARIMA: order=(0, 1, 2) seasonal_order=(0, 1, 0, 52); AIC=543.993, BIC=551.641, Fit time=3.739 seconds
Fit ARIMA: order=(1, 1, 2) seasonal_order=(0, 1, 0, 52); AIC=546.114, BIC=555.674, Fit time=2.240 seconds
Fit ARIMA: order=(0, 1, 1) seasonal_order=(1, 1, 0, 52); AIC=nan, BIC=nan, Fit time=nan seconds
Fit ARIMA: order=(0, 1, 1) seasonal_order=(1, 1, 1, 52); AIC=nan, BIC=nan, Fit time=nan seconds
Total fit time: 23.187 seconds
Based on the lowest AIC, the SARIMAX(0, 1, 1)x(0, 1, 0, 52) configuration is identified as the most optimal for modelling the time series.
Here is the output of the model:
With 90% of the series used as the training data to build the ARIMA model, the remaining 10% is now used to test the predictions of the model. Here are the predictions vs the actual data:
We can see that while the prediction values were lower than the actual test values, the direction of the two series seem to be following each other.
From a business standpoint, a hotel is likely more interested in predicting whether the degree of cancellations will increase/decrease in a particular week  as opposed to the precise number of cancellations  which will no doubt be more subject to error and influenced by extraneous factors.
In this regard, the mean directional accuracy is used to determine the degree to which the model accurately forecasts the directional changes in cancellation frequency from week to week.
def mda(actual: np.ndarray, predicted: np.ndarray):
""" Mean Directional Accuracy """
return np.mean((np.sign(actual[1:]  actual[:1]) == np.sign(predicted[1:]  predicted[:1])).astype(int))
An MDA of above 80% is yielded:
mda(test, predictions)
0.8181818181818182
In this regard, the ARIMA model has shown a reasonably high degree of accuracy in predicting directional changes for hotel cancellations across the test set.
Monte Carlo Simulation with pyplot
Often times, a business may wish to conduct a scenario analysis rather than an outright prediction as above.
One useful visualisation that can be used in this instance is an overlaid histogram, or a histogram that displays two separate periods.
Let’s consider two time periods:
 Period 1: Weeks 120 (July 2015 to November 2015)
 Period 2: Weeks 2140 (November 2015 to March 2016)
A Monte Carlo simulation is generated, i.e. the mean and standard deviation for each period is calculated, and 1000 random numbers are generated using the same.
import plotly.plotly as py
import plotly.graph_objs as go
import numpy as np
m1 = np.mean(tseriesr[1:20]) # mean of distribution (July to November)
s1 = np.std(tseriesr[1:20]) # standard deviation of distribution
m2 = np.mean(tseriesr[21:40]) # mean of distribution (November to March)
s2 = np.std(tseriesr[21:40]) # standard deviation of distribution
x0 = m1 + s1 * np.random.randn(1000)
x1 = m2 + s2 * np.random.randn(1000)
period1 = go.Histogram(
x=x0,
opacity=0.75
)
period2 = go.Histogram(
x=x1,
opacity=0.75
)
data = [period1, period2]
layout = go.Layout(barmode='overlay')
fig = go.Figure(data=data, layout=layout)
py.iplot(fig, filename='overlaid histogram')
Here is the overlaid histogram:
We can see that for the first period (trace 0), the incidence of cancellations is skewed more to the right. This implies that the hotel has a higher chance of seeing more cancellations during the period of July to November  part of this is during the holiday season which implies that cancellation incidences are more volatile.
Conclusion
This has been an illustration of how logistic regression and SVM models can be used to predict hotel cancellations. We have also seen how the Extra Trees Classifier can be used as a feature selection tool to identify the most reliable predictors of customer cancellations. Moreover, the ARIMA model has also been used to predict the degree of hotel cancellations on a weekbyweek basis, and the MDA demonstrated 81% accuracy in doing so across the test set.
Of course, a limitation of these findings is that both hotels under study are based in Portugal. Testing the model across hotels in other countries would help to validate the accuracy of this model further.