We grouped the regions of the US into 9 bins, trying to keep states with similar climates together. This bin allows for region-level analysis which is important when working with a widespread dataset. Review counts by region are below, as well as the definition in Table 3.1. We dropped 8 reviews that did not fall into the US, which is discussed further in Section 5.

Next, we binned the seasons, based on the 2017 calendar, up until the most recent review in the dataset, which is from 10/4/17. Again, we passed explicit bins to the data. The majority are from Summer. Results are below in Table 3.2.

Finally, we created TCAT by binning the numerical variable TAVG into 5 bins by passing the range of temperatures explicitly. As shown in Table 3.3, the majority of reviews fall into the Mild category at 16-30°C, as expected since the majority of the reviews are from Summer. This bin makes working with the temperature data easier, and in particular, makes excluding extreme temperatures easier.

In clustering, the goal is to detect high similarity and low similarity within a group. We created a group with the restaurant's latitude (rest_lat) and longitude (rest_long), average temperature (TAVG) of the day on which the review was posted and the sentiment polarity (sentiment_polarity) of the review. Our goal was to determine if these variables are interrelated and form a pattern. We used the KMeans clustering method with k=3. This results in a Silhouette score of 0.316. As shown in the PCA projection in Figure 9.1, there are some outliers. The clusters are not well separated, indicating the KMeans clustering analysis is not appropriate for this data.

We used the same group of attributes for DBSCAN - rest_lat, rest_long, TAVG, and sentiment_polarity. Since DBSCAN is a density-based spatial clustering algorithm, it formed better clusters than KMeans. The PCA projection, in Figure 9.2, indicates that all the data points in the group were similar and thus form one big cluster. The outliers were properly detected (in purple and pale yellow). The cluster and the outliers are well-separated justifying the high Silhouette score of 0.626.

Different regions of the US may use different vocabulary when writing Yelp reviews. This could be related to regional cuisine, for example, grits in the South or lobster in New England. It could also be related to the language that reviewers use, for example, describing something as "wicked" in New England. We used hierarchical clustering on the text of the reviews by region to determine their relationship. Using cosine similarity, the clustering resulted in three clusters from the nine regions. The Silhouette score is 0.58.

The dendrogram, in Figure 9.3, shows that the most similar reviews are from the Mid-Atlantic and the Southeast, which makes sense since the states from those regions are adjacent. The Midwest, Mountain and New England regions stand apart as being the most different.

To test this hypothesis, we used an ANOVA 1-way test. Looking at the ratings by region, there is a seemingly small difference between them. Reviews from the Southeast are the highest on average, while those from New England are the lowest.



After running the test, the resulting p-value is extremely small, at 5.95e-5. Therefore, we reject the null hypothesis and determine that there is a significant difference in the means of the ratings by region. This result supports the decision to group the data by region, since there is a significant difference.

First, we select the subset of data that contains rainy days' information only. Then we select data from several different states to conduct multivariate linear regression. The X attributes are PRCP and TAVG. The Y attribute is sentiment_polarity. We split the data into train and test datasets. Then we build a multivariate linear regression model based on the train dataset. Next, we use the test dataset to examine the performance of the model. The performance of this model is poor. The R² is -0.0061766461038, which shows there is no relationship between X (weather attributes) and Y (sentiment_polarity). The 3D plot below in Figure 11.1 also illustrates the same point.



Then we select five states, which are CA, VA, NE, NY and AL, to build state-level multivariate linear regression models. The performance of these models is also poor. For example, the R² for VA is only 0.0585879846678. Therefore, even when analyzing a single state, we cannot determine a relationship between sentiment and weather.

To test whether we could predict the rating based on location and weather alone, we used five different machine learning techniques: k-Nearest Neighbor (kNN), Decision Tree (CART), Naive Bayes (NB), Support Vector Machines (SVM), and Random Forest.

First, we grouped the rating into two classes: High (4-5 stars) and Low (0-3 stars). Next, we applied each machine learning algorithm. The results for cross-validation are below in Table 11.4. Naive Bayes and SVC performed the best in cross-validation, with ~80% accuracy.



Next, we compare the confusion matrix results for each method.

kNN
The kNN algorithm works by setting a value for k, we the default k=5, and then classifying data through a Nearest Neighbor algorithm. The algorithm finds the distance of the point to the nearest five clusters, and then classifies based on the classification of the closest cluster. The confusion matrix results are below in Table 11.5. The kNN correctly classified (the true positives) 2338 points from the test data.



CART
CART is a decision tree classifying method. It works by splitting the features until it reaches a pure node, and then uses the resulting tree to classify. The confusion matrix results are below in Table 11.6. This method performed slightly worse than kNN for identifying true positives, but better at identifying true negatives (low ratings).



Naive Bayes
Naive Bayes is a probability-based classifying method. It assumes independence among the features, which does not fit with our data since weather features are interdependent. However, we used the method and results are below in Table 11.7. The NB classified all points as having a High rating.



SVC
SVC works by maximizing the margin of a support vector through the data. This method can handle high dimensional data, in our case we are using just 4-dimensions. SVC also classified all points as positive, or as High rating as seen in Table 11.8.



RF
Random Forest (RF) is a method that uses an ensemble of decision trees. This method, similar to CART, performed relatively well. It correctly classified 2316 points as true positive, and 57 points as true negative.



Finally, we generated the ROC curve for each method. The dotted line indicates the results if the classification was left to random chance. Our machine learning algorithms just barely outperform the dotted line. This indicates that we cannot predict the rating by weather and location alone better than random chance.