Extracting association rules
After the Apriori algorithm has completed, we have a list of frequent itemsets. These aren't exactly association rules, but they can easily be converted into these rules. A frequent itemset is a set of items with a minimum support, while an association rule has a premise and a conclusion. The data is the same for the two.
We can make an association rule from a frequent itemset by taking one of the movies in the itemset and denoting it as the conclusion. The other movies in the itemset will be the premise. This will form rules of the following form: if a reviewer recommends all of the movies in the premise, they will also recommend the conclusion movie.
For each itemset, we can generate a number of association rules by setting each movie to be the conclusion and the remaining movies as the premise.
In code, we first generate a list of all of the rules from each of the frequent itemsets, by iterating over each of the discovered frequent itemsets of each length. We then iterate over every movie in the itemset, as the conclusion.
candidate_rules = []
for itemset_length, itemset_counts in frequent_itemsets.items():
for itemset in itemset_counts.keys():
for conclusion in itemset:
premise = itemset - set((conclusion,))
candidate_rules.append((premise, conclusion))
This returns a very large number of candidate rules. We can see some by printing out the first few rules in the list:
print(candidate_rules[:5])
The resulting output shows the rules that were obtained:
[(frozenset({79}), 258), (frozenset({258}), 79), (frozenset({50}), 64), (frozenset({64}), 50), (frozenset({127}), 181)]
In these rules, the first part (the frozenset) is the list of movies in the premise, while the number after it is the conclusion. In the first case, if a reviewer recommends movie 79, they are also likely to recommend movie 258.
Next, we compute the confidence of each of these rules. This is performed much like in Chapter 1, Getting Started with Data Mining, with the only changes being those necessary for computing using the new data format.
The process of computing confidence starts by creating dictionaries to store how many times we see the premise leading to the conclusion (a correct example of the rule) and how many times it doesn't (an incorrect example). We then iterate over all reviews and rules, working out whether the premise of the rule applies and, if it does, whether the conclusion is accurate.
correct_counts = defaultdict(int)
incorrect_counts = defaultdict(int)
for user, reviews in favorable_reviews_by_users.items():
for candidate_rule in candidate_rules:
premise, conclusion = candidate_rule
if premise.issubset(reviews):
if conclusion in reviews:
correct_counts[candidate_rule] += 1
else:
incorrect_counts[candidate_rule] += 1
We then compute the confidence for each rule by piding the correct count by the total number of times the rule was seen:
rule_confidence = {candidate_rule:
(correct_counts[candidate_rule] / float(correct_counts[candidate_rule] +
incorrect_counts[candidate_rule]))
for candidate_rule in candidate_rules}
Now we can print the top five rules by sorting this confidence dictionary and printing the results:
from operator import itemgetter
sorted_confidence = sorted(rule_confidence.items(), key=itemgetter(1), reverse=True)
for index in range(5):
print("Rule #{0}".format(index + 1))
premise, conclusion = sorted_confidence[index][0]
print("Rule: If a person recommends {0} they will also recommend {1}".format(premise, conclusion))
print(" - Confidence: {0:.3f}".format(rule_confidence[(premise, conclusion)]))
print("")
The resulting printout shows only the movie IDs, which isn't very helpful without the names of the movies also. The dataset came with a file called u.items, which stores the movie names and their corresponding MovieID (as well as other information, such as the genre).
We can load the titles from this file using pandas. Additional information about the file and categories is available in the README file that came with the dataset. The data in the files is in CSV format, but with data separated by the | symbol; it has no header
and the encoding is important to set. The column names were found in the README file.
movie_name_filename = os.path.join(data_folder, "u.item")
movie_name_data = pd.read_csv(movie_name_filename, delimiter="|", header=None,
encoding = "mac-roman")
movie_name_data.columns = ["MovieID", "Title", "Release Date", "Video Release", "IMDB", "<UNK>",
"Action", "Adventure", "Animation", "Children's", "Comedy", "Crime",
"Documentary", "Drama", "Fantasy", "Film-Noir", "Horror", "Musical",
"Mystery", "Romance", "Sci-Fi", "Thriller", "War", "Western"]
Getting the movie title is an important and frequently used step, therefore it makes sense to turn it into a function. We will create a function that will return a movie's title from its MovieID, saving us the trouble of looking it up each time. Let's look at the code:
def get_movie_name(movie_id):
title_object = movie_name_data[movie_name_data["MovieID"] == movie_id]["Title"]
title = title_object.values[0]
return title
In a new Jupyter Notebook cell, we adjust our previous code for printing out the top rules to also include the titles:
for index in range(5):
print("Rule #{0}".format(index + 1))
premise, conclusion = sorted_confidence[index][0]
premise_names = ", ".join(get_movie_name(idx) for idx in premise)
conclusion_name = get_movie_name(conclusion)
print("Rule: If a person recommends {0} they will also recommend {1}".format(premise_names, conclusion_name))
print(" - Confidence: {0:.3f}".format(rule_confidence[(premise, conclusion)]))
print("")
The result is much more readable (there are still some issues, but we can ignore them for now):
Rule #1
Rule: If a person recommends Shawshank Redemption, The (1994), Silence of the Lambs, The (1991), Pulp Fiction (1994), Star Wars (1977), Twelve Monkeys (1995) they will also recommend Raiders of the Lost Ark (1981)
- Confidence: 1.000
Rule #2
Rule: If a person recommends Silence of the Lambs, The (1991), Fargo (1996), Empire Strikes Back, The (1980), Fugitive, The (1993), Star Wars (1977), Pulp Fiction (1994) they will also recommend Twelve Monkeys (1995)
- Confidence: 1.000
Rule #3
Rule: If a person recommends Silence of the Lambs, The (1991), Empire Strikes Back, The (1980), Return of the Jedi (1983), Raiders of the Lost Ark (1981), Twelve Monkeys (1995) they will also recommend Star Wars (1977)
- Confidence: 1.000
Rule #4
Rule: If a person recommends Shawshank Redemption, The (1994), Silence of the Lambs, The (1991), Fargo (1996), Twelve Monkeys (1995), Empire Strikes Back, The (1980), Star Wars (1977) they will also recommend Raiders of the Lost Ark (1981)
- Confidence: 1.000
Rule #5
Rule: If a person recommends Shawshank Redemption, The (1994), Toy Story (1995), Twelve Monkeys (1995), Empire Strikes Back, The (1980), Fugitive, The (1993), Star Wars (1977) they will also recommend Return of the Jedi (1983)
- Confidence: 1.000