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486 lines (406 loc) · 15 KB
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from collections import defaultdict, deque, OrderedDict
def _sort_transactions_by_freq(
transactions, key_func, reverse_int=False,
reverse_ext=False, sort_ext=True):
key_seqs = [{key_func(i) for i in sequence} for sequence in transactions]
frequencies = get_frequencies(key_seqs)
asorted_seqs = []
for key_seq in key_seqs:
if not key_seq:
continue
# Sort each transaction (infrequent key first)
l = [(frequencies[i], i) for i in key_seq]
l.sort(reverse=reverse_int)
asorted_seqs.append(tuple(l))
# Sort all transactions. Those with infrequent key first, first
if sort_ext:
asorted_seqs.sort(reverse=reverse_ext)
return (asorted_seqs, frequencies)
def get_frequencies(transactions):
'''Computes a dictionary, {key:frequencies} containing the frequency of
each key in all transactions. Duplicate keys in a transaction are
counted twice.
:param transactions: a sequence of sequences. [ [transaction items...]]
'''
frequencies = defaultdict(int)
for transaction in transactions:
for item in transaction:
frequencies[item] += 1
return frequencies
def get_sam_input(transactions, key_func=None):
'''Given a list of transactions and a key function, returns a data
structure used as the input of the sam algorithm.
:param transactions: a sequence of sequences. [ [transaction items...]]
:param key_func: a function that returns a comparable key for a
transaction item.
'''
if key_func is None:
def key_func(e):
return e
(asorted_seqs, _) = _sort_transactions_by_freq(transactions, key_func)
# Group same transactions together
sam_input = deque()
visited = {}
current = 0
for seq in asorted_seqs:
if seq not in visited:
sam_input.append((1, seq))
visited[seq] = current
current += 1
else:
i = visited[seq]
(count, oldseq) = sam_input[i]
sam_input[i] = (count + 1, oldseq)
return sam_input
def sam(sam_input, min_support=2):
'''Finds frequent item sets of items appearing in a list of transactions
based on the Split and Merge algorithm by Christian Borgelt.
:param sam_input: The input of the algorithm. Must come from
`get_sam_input`.
:param min_support: The minimal support of a set to be included.
:rtype: A set containing the frequent item sets and their support.
'''
fis = set()
report = {}
_sam(sam_input, fis, report, min_support)
return report
def _sam(sam_input, fis, report, min_support):
n = 0
a = deque(sam_input)
while len(a) > 0 and len(a[0][1]) > 0:
b = deque()
s = 0
i = a[0][1][0]
while len(a) > 0 and len(a[0][1]) > 0 and a[0][1][0] == i:
s = s + a[0][0]
a[0] = (a[0][0], a[0][1][1:])
if len(a[0][1]) > 0:
b.append(a.popleft())
else:
a.popleft()
c = deque(b)
d = deque()
while len(a) > 0 and len(b) > 0:
if a[0][1] > b[0][1]:
d.append(b.popleft())
elif a[0][1] < b[0][1]:
d.append(a.popleft())
else:
b[0] = (b[0][0] + a[0][0], b[0][1])
d.append(b.popleft())
a.popleft()
while len(a) > 0:
d.append(a.popleft())
while len(b) > 0:
d.append(b.popleft())
a = d
if s >= min_support:
fis.add(i[1])
report[frozenset(fis)] = s
n = n + 1 + _sam(c, fis, report, min_support)
fis.remove(i[1])
return n
def _new_relim_input(size, key_map):
i = 0
l = []
for key in key_map:
if i >= size:
break
l.append(((0, key), []))
i = i + 1
return l
def _get_key_map(frequencies):
l = [(frequencies[k], k) for k in frequencies]
l.sort(reverse=True)
key_map = OrderedDict()
for i, v in enumerate(l):
key_map[v] = i
return key_map
def get_relim_input(transactions, key_func=None):
'''Given a list of transactions and a key function, returns a data
structure used as the input of the relim algorithm.
:param transactions: a sequence of sequences. [ [transaction items...]]
:param key_func: a function that returns a comparable key for a
transaction item.
'''
# Data Structure
# relim_input[x][0] = (count, key_freq)
# relim_input[x][1] = [(count, (key_freq, )]
#
# in other words:
# relim_input[x][0][0] = count of trans with prefix key_freq
# relim_input[x][0][1] = prefix key_freq
# relim_input[x][1] = lists of transaction rests
# relim_input[x][1][x][0] = number of times a rest of transaction appears
# relim_input[x][1][x][1] = rest of transaction prefixed by key_freq
if key_func is None:
def key_func(e):
return e
(asorted_seqs, frequencies) = _sort_transactions_by_freq(
transactions, key_func)
key_map = _get_key_map(frequencies)
relim_input = _new_relim_input(len(key_map), key_map)
for seq in asorted_seqs:
if not seq:
continue
index = key_map[seq[0]]
((count, char), lists) = relim_input[index]
rest = seq[1:]
found = False
for i, (rest_count, rest_seq) in enumerate(lists):
if rest_seq == rest:
lists[i] = (rest_count + 1, rest_seq)
found = True
break
if not found:
lists.append((1, rest))
relim_input[index] = ((count + 1, char), lists)
return (relim_input, key_map)
def relim(rinput, min_support=2):
'''Finds frequent item sets of items appearing in a list of transactions
based on Recursive Elimination algorithm by Christian Borgelt.
In my synthetic tests, Relim outperforms other algorithms by a large
margin. This is unexpected as FP-Growth is supposed to be superior, but
this may be due to my implementation of these algorithms.
:param rinput: The input of the algorithm. Must come from
`get_relim_input`.
:param min_support: The minimal support of a set to be included.
:rtype: A set containing the frequent item sets and their support.
'''
fis = set()
report = {}
_relim(rinput, fis, report, min_support)
return report
def _relim(rinput, fis, report, min_support):
(relim_input, key_map) = rinput
n = 0
a = relim_input
while len(a) > 0:
item = a[-1][0][1]
s = a[-1][0][0]
if s >= min_support:
fis.add(item[1])
report[frozenset(fis)] = s
b = _new_relim_input(len(a) - 1, key_map)
rest_lists = a[-1][1]
for (count, rest) in rest_lists:
if not rest:
continue
k = rest[0]
index = key_map[k]
new_rest = rest[1:]
# Only add this rest if it's not empty!
((k_count, k), lists) = b[index]
if len(new_rest) > 0:
lists.append((count, new_rest))
b[index] = ((k_count + count, k), lists)
n = n + 1 + _relim((b, key_map), fis, report, min_support)
fis.remove(item[1])
rest_lists = a[-1][1]
for (count, rest) in rest_lists:
if not rest:
continue
k = rest[0]
index = key_map[k]
new_rest = rest[1:]
((k_count, k), lists) = a[index]
if len(new_rest) > 0:
lists.append((count, new_rest))
a[index] = ((k_count + count, k), lists)
a.pop()
return n
class FPNode(object):
root_key = object()
def __init__(self, key, parent):
self.children = {}
self.parent = parent
self.key = key
self.count = 0
self.next_node = None
def add_path(self, path, index, length, heads, last_insert):
if index >= length:
return
child_key = path[index]
index += 1
try:
child = self.children[child_key]
except Exception:
child = self._create_child(child_key, heads, last_insert)
child.count += 1
heads[child_key][1] += 1
child.add_path(path, index, length, heads, last_insert)
def _create_child(self, child_key, heads, last_insert):
child = FPNode(child_key, self)
self.children[child_key] = child
try:
last_child = last_insert[child_key]
last_child.next_node = child
except Exception:
heads[child_key] = [child, 0]
last_insert[child_key] = child
return child
def get_cond_tree(
self, child, count, visited, heads, last_insert,
dont_create=False):
key = self.key
if dont_create:
# This is a head, we don't want to copy it.
cond_node = None
else:
try:
cond_node = visited[self]
except Exception:
cond_node = self._create_cond_child(
visited, heads, last_insert)
if self.parent is not None:
# Recursion
parent_node = self.parent.get_cond_tree(
cond_node, count, visited, heads, last_insert, False)
if cond_node is not None:
cond_node.count += count
heads[key][1] += count
cond_node.parent = parent_node
return cond_node
def _create_cond_child(self, visited, heads, last_insert):
key = self.key
cond_node = FPNode(key, None)
visited[self] = cond_node
try:
last_cond_node = last_insert[key]
last_cond_node.next_node = cond_node
except Exception:
# Don't add root!
if self.parent is not None:
heads[key] = [cond_node, 0]
last_insert[key] = cond_node
return cond_node
def _find_ancestor(self, heads, min_support):
ancestor = self.parent
while ancestor.key != FPNode.root_key:
support = heads[ancestor.key][1]
if support >= min_support:
break
else:
ancestor = ancestor.parent
return ancestor
def prune_me(
self, from_head_list, visited_parents, merged_before,
merged_now, heads, min_support):
try:
# Parent was merged
new_parent = merged_before[self.parent]
self.parent = new_parent
except KeyError:
# Ok, no need to change parent
pass
ancestor = self._find_ancestor(heads, min_support)
self.parent = ancestor
try:
# Oh, we visited another child of this parent!
other_node = visited_parents[ancestor]
merged_now[self] = other_node
other_node.count += self.count
# Remove yourself from the list
if from_head_list is not None:
from_head_list.next_node = self.next_node
self.next_node = None
except KeyError:
# We are a new child!
visited_parents[ancestor] = self
def __str__(self):
child_str = ','.join([str(key) for key in self.children])
return '{0} ({1}) [{2}] {3}'.format(
self.key, self.count, child_str,
self.next_node is not None)
def __repr__(self):
return self.__str__()
def get_fptree(transactions, key_func=None, min_support=2):
'''Given a list of transactions and a key function, returns a data
structure used as the input of the relim algorithm.
:param transactions: a sequence of sequences. [ [transaction items...]]
:param key_func: a function that returns a comparable key for a
transaction item.
:param min_support: minimum support.
'''
if key_func is None:
def key_func(e):
return e
asorted_seqs, frequencies = _sort_transactions_by_freq(
transactions, key_func, True, False, False)
transactions = [
[item[1] for item in aseq if item[0] >= min_support] for
aseq in asorted_seqs]
root = FPNode(FPNode.root_key, None)
heads = {}
last_insert = {}
for transaction in transactions:
root.add_path(transaction, 0, len(transaction), heads, last_insert)
# Here, v[1] is = to the frequency
sorted_heads = sorted(heads.values(), key=lambda v: (v[1], v[0].key))
new_heads = OrderedDict()
for (head, head_support) in sorted_heads:
new_heads[head.key] = (head, head_support)
return (root, new_heads)
def _init_heads(orig_heads):
new_heads = OrderedDict()
for key in orig_heads:
new_heads[key] = (None, 0)
return new_heads
def _create_cond_tree(head_node, new_heads, pruning):
visited = {}
last_insert = {}
while head_node is not None:
head_node.get_cond_tree(
None, head_node.count, visited, new_heads,
last_insert, True)
head_node = head_node.next_node
return new_heads
def _prune_cond_tree(heads, min_support):
merged_before = {}
merged_now = {}
for key in reversed(heads):
(node, head_support) = heads[key]
if head_support > 0:
visited_parents = {}
previous_node = None
while node is not None:
# If the node is merged, we lose the next_node
next_node = node.next_node
node.prune_me(
previous_node, visited_parents, merged_before,
merged_now, heads, min_support)
if node.next_node is not None:
# Only change the previous node if it wasn't merged.
previous_node = node
node = next_node
merged_before = merged_now
merged_now = {}
def fpgrowth(fptree, min_support=2, pruning=False):
'''Finds frequent item sets of items appearing in a list of transactions
based on FP-Growth by Han et al.
:param fptree: The input of the algorithm. Must come from
`get_fptree`.
:param min_support: The minimal support of a set.
:param pruning: Perform a pruning operation. Default to False.
:rtype: A set containing the frequent item sets and their support.
'''
fis = set()
report = {}
_fpgrowth(fptree, fis, report, min_support, pruning)
return report
def _fpgrowth(fptree, fis, report, min_support=2, pruning=True):
(_, heads) = fptree
n = 0
for (head_node, head_support) in heads.values():
if head_support < min_support:
continue
fis.add(head_node.key)
report[frozenset(fis)] = head_support
new_heads = _init_heads(heads)
_create_cond_tree(head_node, new_heads, pruning)
if pruning:
_prune_cond_tree(new_heads, min_support)
n = n + 1 + _fpgrowth(
(None, new_heads), fis, report, min_support, pruning)
fis.remove(head_node.key)
return n