Building Machine Learning Systems with Python - Richert, Coelho

Chapter 8
Formally, Apriori takes a collection of sets (that is, your shopping baskets) and
returns sets that are very frequent as subsets (that is, items that together are part of
many shopping baskets).
The algorithm works according to the bottom-up approach: starting with the smallest
candidates (those composed of one single element), it builds up, adding one element
at a time. We need to define the minimum support we are looking for:
minsupport = 80
Support is the number of times that a set of products was purchased together. The
goal of Apriori is to find itemsets with high support. Logically, any itemset with
more than minimal support can only be composed of items that themselves have at
least minimal support:
valid = set(k for k,v in counts.items()
if (v >= minsupport))
Our initial itemsets are singletons (sets with a single element). In particular,
all singletons that have at least minimal support are frequent itemsets.
itemsets = [frozenset([v]) for v in valid]
Now our iteration is very simple and is given as follows:
new_itemsets = []
for iset in itemsets:
for v in valid:
if v not in iset:
# we create a new possible set
# which is the same as the previous,
#with the addition of v
newset = (ell|set([v_]))
# loop over the dataset to count the number
# of times newset appears. This step is slow
# and not used proper implementation
c_newset = 0
for d in dataset:
if d.issuperset(c):
c_newset += 1
if c_newset > minsupport:
newsets.append(newset)
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