Add: FP Growth Algorithm (#10746)

* Add: FP Growth Algorithm

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* Update frequent_pattern_growth.py

---------

Co-authored-by: Jeel Gajera <jeelgajera00@gmail.com>
Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Christian Clauss <cclauss@me.com>
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* [Dimensionality Reduction](machine_learning/dimensionality_reduction.py) * [Dimensionality Reduction](machine_learning/dimensionality_reduction.py)
* Forecasting * Forecasting
* [Run](machine_learning/forecasting/run.py) * [Run](machine_learning/forecasting/run.py)
* [Frequent Pattern Growth Algorithm](machine_learning/frequent_pattern_growth.py)
* [Gradient Descent](machine_learning/gradient_descent.py) * [Gradient Descent](machine_learning/gradient_descent.py)
* [K Means Clust](machine_learning/k_means_clust.py) * [K Means Clust](machine_learning/k_means_clust.py)
* [K Nearest Neighbours](machine_learning/k_nearest_neighbours.py) * [K Nearest Neighbours](machine_learning/k_nearest_neighbours.py)

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"""
The Frequent Pattern Growth algorithm (FP-Growth) is a widely used data mining
technique for discovering frequent itemsets in large transaction databases.
It overcomes some of the limitations of traditional methods such as Apriori by
efficiently constructing the FP-Tree
WIKI: https://athena.ecs.csus.edu/~mei/associationcw/FpGrowth.html
Examples: https://www.javatpoint.com/fp-growth-algorithm-in-data-mining
"""
from __future__ import annotations
from dataclasses import dataclass, field
@dataclass
class TreeNode:
"""
A node in a Frequent Pattern tree.
Args:
name: The name of this node.
num_occur: The number of occurrences of the node.
parent_node: The parent node.
Example:
>>> parent = TreeNode("Parent", 1, None)
>>> child = TreeNode("Child", 2, parent)
>>> child.name
'Child'
>>> child.count
2
"""
name: str
count: int
parent: TreeNode | None = None
children: dict[str, TreeNode] = field(default_factory=dict)
node_link: TreeNode | None = None
def __repr__(self) -> str:
return f"TreeNode({self.name!r}, {self.count!r}, {self.parent!r})"
def inc(self, num_occur: int) -> None:
self.count += num_occur
def disp(self, ind: int = 1) -> None:
print(f"{' ' * ind} {self.name} {self.count}")
for child in self.children.values():
child.disp(ind + 1)
def create_tree(data_set: list, min_sup: int = 1) -> tuple[TreeNode, dict]:
"""
Create Frequent Pattern tree
Args:
data_set: A list of transactions, where each transaction is a list of items.
min_sup: The minimum support threshold.
Items with support less than this will be pruned. Default is 1.
Returns:
The root of the FP-Tree.
header_table: The header table dictionary with item information.
Example:
>>> data_set = [
... ['A', 'B', 'C'],
... ['A', 'C'],
... ['A', 'B', 'E'],
... ['A', 'B', 'C', 'E'],
... ['B', 'E']
... ]
>>> min_sup = 2
>>> fp_tree, header_table = create_tree(data_set, min_sup)
>>> fp_tree
TreeNode('Null Set', 1, None)
>>> len(header_table)
4
>>> header_table["A"]
[[4, None], TreeNode('A', 4, TreeNode('Null Set', 1, None))]
>>> header_table["E"][1] # doctest: +NORMALIZE_WHITESPACE
TreeNode('E', 1, TreeNode('B', 3, TreeNode('A', 4, TreeNode('Null Set', 1, None))))
>>> sorted(header_table)
['A', 'B', 'C', 'E']
>>> fp_tree.name
'Null Set'
>>> sorted(fp_tree.children)
['A', 'B']
>>> fp_tree.children['A'].name
'A'
>>> sorted(fp_tree.children['A'].children)
['B', 'C']
"""
header_table: dict = {}
for trans in data_set:
for item in trans:
header_table[item] = header_table.get(item, [0, None])
header_table[item][0] += 1
for k in list(header_table):
if header_table[k][0] < min_sup:
del header_table[k]
if not (freq_item_set := set(header_table)):
return TreeNode("Null Set", 1, None), {}
for k in header_table:
header_table[k] = [header_table[k], None]
fp_tree = TreeNode("Null Set", 1, None) # Parent is None for the root node
for tran_set in data_set:
local_d = {
item: header_table[item][0] for item in tran_set if item in freq_item_set
}
if local_d:
sorted_items = sorted(
local_d.items(), key=lambda item_info: item_info[1], reverse=True
)
ordered_items = [item[0] for item in sorted_items]
update_tree(ordered_items, fp_tree, header_table, 1)
return fp_tree, header_table
def update_tree(items: list, in_tree: TreeNode, header_table: dict, count: int) -> None:
"""
Update the FP-Tree with a transaction.
Args:
items: List of items in the transaction.
in_tree: The current node in the FP-Tree.
header_table: The header table dictionary with item information.
count: The count of the transaction.
Example:
>>> data_set = [
... ['A', 'B', 'C'],
... ['A', 'C'],
... ['A', 'B', 'E'],
... ['A', 'B', 'C', 'E'],
... ['B', 'E']
... ]
>>> min_sup = 2
>>> fp_tree, header_table = create_tree(data_set, min_sup)
>>> fp_tree
TreeNode('Null Set', 1, None)
>>> transaction = ['A', 'B', 'E']
>>> update_tree(transaction, fp_tree, header_table, 1)
>>> fp_tree
TreeNode('Null Set', 1, None)
>>> fp_tree.children['A'].children['B'].children['E'].children
{}
>>> fp_tree.children['A'].children['B'].children['E'].count
2
>>> header_table['E'][1].name
'E'
"""
if items[0] in in_tree.children:
in_tree.children[items[0]].inc(count)
else:
in_tree.children[items[0]] = TreeNode(items[0], count, in_tree)
if header_table[items[0]][1] is None:
header_table[items[0]][1] = in_tree.children[items[0]]
else:
update_header(header_table[items[0]][1], in_tree.children[items[0]])
if len(items) > 1:
update_tree(items[1:], in_tree.children[items[0]], header_table, count)
def update_header(node_to_test: TreeNode, target_node: TreeNode) -> TreeNode:
"""
Update the header table with a node link.
Args:
node_to_test: The node to be updated in the header table.
target_node: The node to link to.
Example:
>>> data_set = [
... ['A', 'B', 'C'],
... ['A', 'C'],
... ['A', 'B', 'E'],
... ['A', 'B', 'C', 'E'],
... ['B', 'E']
... ]
>>> min_sup = 2
>>> fp_tree, header_table = create_tree(data_set, min_sup)
>>> fp_tree
TreeNode('Null Set', 1, None)
>>> node1 = TreeNode("A", 3, None)
>>> node2 = TreeNode("B", 4, None)
>>> node1
TreeNode('A', 3, None)
>>> node1 = update_header(node1, node2)
>>> node1
TreeNode('A', 3, None)
>>> node1.node_link
TreeNode('B', 4, None)
>>> node2.node_link is None
True
"""
while node_to_test.node_link is not None:
node_to_test = node_to_test.node_link
if node_to_test.node_link is None:
node_to_test.node_link = target_node
# Return the updated node
return node_to_test
def ascend_tree(leaf_node: TreeNode, prefix_path: list[str]) -> None:
"""
Ascend the FP-Tree from a leaf node to its root, adding item names to the prefix
path.
Args:
leaf_node: The leaf node to start ascending from.
prefix_path: A list to store the item as they are ascended.
Example:
>>> data_set = [
... ['A', 'B', 'C'],
... ['A', 'C'],
... ['A', 'B', 'E'],
... ['A', 'B', 'C', 'E'],
... ['B', 'E']
... ]
>>> min_sup = 2
>>> fp_tree, header_table = create_tree(data_set, min_sup)
>>> path = []
>>> ascend_tree(fp_tree.children['A'], path)
>>> path # ascending from a leaf node 'A'
['A']
"""
if leaf_node.parent is not None:
prefix_path.append(leaf_node.name)
ascend_tree(leaf_node.parent, prefix_path)
def find_prefix_path(base_pat: frozenset, tree_node: TreeNode | None) -> dict:
"""
Find the conditional pattern base for a given base pattern.
Args:
base_pat: The base pattern for which to find the conditional pattern base.
tree_node: The node in the FP-Tree.
Example:
>>> data_set = [
... ['A', 'B', 'C'],
... ['A', 'C'],
... ['A', 'B', 'E'],
... ['A', 'B', 'C', 'E'],
... ['B', 'E']
... ]
>>> min_sup = 2
>>> fp_tree, header_table = create_tree(data_set, min_sup)
>>> fp_tree
TreeNode('Null Set', 1, None)
>>> len(header_table)
4
>>> base_pattern = frozenset(['A'])
>>> sorted(find_prefix_path(base_pattern, fp_tree.children['A']))
[]
"""
cond_pats: dict = {}
while tree_node is not None:
prefix_path: list = []
ascend_tree(tree_node, prefix_path)
if len(prefix_path) > 1:
cond_pats[frozenset(prefix_path[1:])] = tree_node.count
tree_node = tree_node.node_link
return cond_pats
def mine_tree(
in_tree: TreeNode,
header_table: dict,
min_sup: int,
pre_fix: set,
freq_item_list: list,
) -> None:
"""
Mine the FP-Tree recursively to discover frequent itemsets.
Args:
in_tree: The FP-Tree to mine.
header_table: The header table dictionary with item information.
min_sup: The minimum support threshold.
pre_fix: A set of items as a prefix for the itemsets being mined.
freq_item_list: A list to store the frequent itemsets.
Example:
>>> data_set = [
... ['A', 'B', 'C'],
... ['A', 'C'],
... ['A', 'B', 'E'],
... ['A', 'B', 'C', 'E'],
... ['B', 'E']
... ]
>>> min_sup = 2
>>> fp_tree, header_table = create_tree(data_set, min_sup)
>>> fp_tree
TreeNode('Null Set', 1, None)
>>> frequent_itemsets = []
>>> mine_tree(fp_tree, header_table, min_sup, set([]), frequent_itemsets)
>>> expe_itm = [{'C'}, {'C', 'A'}, {'E'}, {'A', 'E'}, {'E', 'B'}, {'A'}, {'B'}]
>>> all(expected in frequent_itemsets for expected in expe_itm)
True
"""
sorted_items = sorted(header_table.items(), key=lambda item_info: item_info[1][0])
big_l = [item[0] for item in sorted_items]
for base_pat in big_l:
new_freq_set = pre_fix.copy()
new_freq_set.add(base_pat)
freq_item_list.append(new_freq_set)
cond_patt_bases = find_prefix_path(base_pat, header_table[base_pat][1])
my_cond_tree, my_head = create_tree(list(cond_patt_bases), min_sup)
if my_head is not None:
# Pass header_table[base_pat][1] as node_to_test to update_header
header_table[base_pat][1] = update_header(
header_table[base_pat][1], my_cond_tree
)
mine_tree(my_cond_tree, my_head, min_sup, new_freq_set, freq_item_list)
if __name__ == "__main__":
from doctest import testmod
testmod()
data_set: list[frozenset] = [
frozenset(["bread", "milk", "cheese"]),
frozenset(["bread", "milk"]),
frozenset(["bread", "diapers"]),
frozenset(["bread", "milk", "diapers"]),
frozenset(["milk", "diapers"]),
frozenset(["milk", "cheese"]),
frozenset(["diapers", "cheese"]),
frozenset(["bread", "milk", "cheese", "diapers"]),
]
print(f"{len(data_set) = }")
fp_tree, header_table = create_tree(data_set, min_sup=3)
print(f"{fp_tree = }")
print(f"{len(header_table) = }")
freq_items: list = []
mine_tree(fp_tree, header_table, 3, set(), freq_items)
print(f"{freq_items = }")