Detailed explanation of FP-Growth algorithm in Python

FP-Growth algorithm is a classic frequent pattern mining algorithm. It is a very efficient algorithm for mining collections of items that often appear together from data sets. This article will introduce you to the principle and implementation method of FP-Growth algorithm in detail.

1. Basic Principle of FP-Growth Algorithm

The basic idea of ​​FP-Growth algorithm is to establish an FP-Tree (frequent itemset tree) to represent the frequent itemsets in the data set, and Mining frequent itemsets from FP-Tree. FP-Tree is an efficient data structure that can mine frequent itemsets without generating candidate frequent itemsets.

FP-Tree contains two parts: root node and tree node. The root node has no value, whereas the tree nodes include the name of an item and the number of times the item occurs. FP-Tree also includes links pointing to the same nodes, these links are called "link pointers".

The process of FP-Growth algorithm includes two parts: building FP-Tree and mining frequent itemsets:

1. Building FP-Tree:

For For each transaction, non-frequent items are deleted and sorted according to the support of frequent items to obtain a frequent itemset.

Traverse each transaction, and insert the frequent itemset of each transaction into the FP-Tree in the order of appearance. If the node already exists, increase its count. If it does not exist, insert a new node. .

2. Mining frequent itemsets:

The methods of mining frequent itemsets from FP-Tree include:

Start from the bottom of FP-Tree , find the conditional pattern library of each item set, and the conditional pattern library contains all transactions that contain the item set. Then, a new FP-Tree is recursively constructed for the conditional pattern library, and frequent itemsets in the tree are searched.

In the new FP-Tree, each frequent item is sorted according to its support, a set of candidates is constructed, and mined recursively. Repeat the above process until all frequent itemsets are found.

2. Implementation of FP-Growth algorithm

The FP-Growth algorithm can be implemented using the Python programming language. The following is a simple example to demonstrate the implementation of the FP-Growth algorithm.

First, define a data set, for example:

dataset = [['v', 'a', 'p', 'e', 's'],
           ['b', 'a', 'k', 'e'],
           ['a', 'p', 'p', 'l', 'e', 's'],
           ['d', 'i', 'n', 'n', 'e', 'r']]

Then, write a function to generate an ordered item set, for example:

def create_ordered_items(dataset):
    # 遍历数据集，统计每个项出现的次数
    item_dict = {}
    for trans in dataset:
        for item in trans:
            if item not in item_dict:
                item_dict[item] = 1
            else:
                item_dict[item] += 1

    # 生成有序项集
    ordered_items = [v[0] for v in sorted(item_dict.items(), key=lambda x: x[1], reverse=True)]
    return ordered_items

Among them, the create_ordered_items function is used to follow Get the ordered itemset by the number of occurrences of the item.

Next, write a function to build FP-Tree:

class TreeNode:
    def __init__(self, name, count, parent):
        self.name = name
        self.count = count
        self.parent = parent
        self.children = {}
        self.node_link = None

    def increase_count(self, count):
        self.count += count

def create_tree(dataset, min_support):
    # 生成有序项集
    ordered_items = create_ordered_items(dataset)

    # 建立根节点
    root_node = TreeNode('Null Set', 0, None)

    # 建立FP-Tree
    head_table = {}
    for trans in dataset:
        # 过滤非频繁项
        filtered_items = [item for item in trans if item in ordered_items]
        # 对每个事务中的项集按频繁项的支持度从大到小排序
        filtered_items.sort(key=lambda x: ordered_items.index(x))
        # 插入到FP-Tree中
        insert_tree(filtered_items, root_node, head_table)

    return root_node, head_table

def insert_tree(items, node, head_table):
    if items[0] in node.children:
        # 如果节点已存在，则增加其计数
        node.children[items[0]].increase_count(1)
    else:
        # 如果节点不存在，则插入新的节点
        new_node = TreeNode(items[0], 1, node)
        node.children[items[0]] = new_node
        # 更新链表中的指针
        if head_table.get(items[0], None) is None:
            head_table[items[0]] = new_node
        else:
            current_node = head_table[items[0]]
            while current_node.node_link is not None:
                current_node = current_node.node_link
            current_node.node_link = new_node

    if len(items) > 1:
        # 对剩余的项进行插入
        insert_tree(items[1:], node.children[items[0]], head_table)

The create_tree function is used to build FP-Tree.

Finally, write a function to mine frequent itemsets:

def find_freq_items(head_table, prefix, freq_items, min_support):
    # 对头指针表中的每个项按照出现的次数从小到大排序
    sorted_items = [v[0] for v in sorted(head_table.items(), key=lambda x: x[1].count)]
    for item in sorted_items:
        # 将前缀加上该项，得到新的频繁项
        freq_set = prefix + [item]
        freq_count = head_table[item].count
        freq_items.append((freq_set, freq_count))
        # 构建该项的条件模式库
        cond_pat_base = get_cond_pat_base(head_table[item])
        # 递归地构建新的FP-Tree，并寻找频繁项集
        sub_head_table, sub_freq_items = create_tree(cond_pat_base, min_support)
        if sub_head_table is not None:
            find_freq_items(sub_head_table, freq_set, freq_items, min_support)

def get_cond_pat_base(tree_node):
    cond_pat_base = []
    while tree_node is not None:
        trans = []
        curr = tree_node.parent
        while curr.parent is not None:
            trans.append(curr.name)
            curr = curr.parent
        cond_pat_base.append(trans)
        tree_node = tree_node.node_link
    return cond_pat_base

def mine_fp_tree(dataset, min_support):
    freq_items = []
    # 构建FP-Tree
    root_node, head_table = create_tree(dataset, min_support)
    # 挖掘频繁项集
    find_freq_items(head_table, [], freq_items, min_support)
    return freq_items

The mine_fp_tree function is used to mine frequent itemsets.

3. Summary

FP-Growth algorithm is an efficient frequent pattern mining algorithm. By constructing FP-Tree, frequent items can be mined without generating candidate frequent item sets. Collection excavation. Python is a programming language that is very suitable for implementing the FP-Growth algorithm. By using Python, we can quickly implement this algorithm and use it in practice to mine frequent itemsets. I hope this article can help you better understand the principles and implementation methods of the FP-Growth algorithm.

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