浅谈Python实现Apriori算法介绍

"""
# Python 2.7
# Filename: apriori.py
# Author: llhthinker
# Email: hangliu56[AT]gmail[DOT]com
# Blog: http://www.cnblogs.com/llhthinker/p/6719779.html
# Date: 2017-04-16
"""


def load_data_set():
  """
  Load a sample data set (From Data Mining: Concepts and Techniques, 3th Edition)
  Returns: 
    A data set: A list of transactions. Each transaction contains several items.
  """
  data_set = [['l1', 'l2', 'l5'], ['l2', 'l4'], ['l2', 'l3'],
      ['l1', 'l2', 'l4'], ['l1', 'l3'], ['l2', 'l3'],
      ['l1', 'l3'], ['l1', 'l2', 'l3', 'l5'], ['l1', 'l2', 'l3']]
  return data_set


def create_C1(data_set):
  """
  Create frequent candidate 1-itemset C1 by scaning data set.
  Args:
    data_set: A list of transactions. Each transaction contains several items.
  Returns:
    C1: A set which contains all frequent candidate 1-itemsets
  """
  C1 = set()
  for t in data_set:
    for item in t:
      item_set = frozenset([item])
      C1.add(item_set)
  return C1


def is_apriori(Ck_item, Lksub1):
  """
  Judge whether a frequent candidate k-itemset satisfy Apriori property.
  Args:
    Ck_item: a frequent candidate k-itemset in Ck which contains all frequent
         candidate k-itemsets.
    Lksub1: Lk-1, a set which contains all frequent candidate (k-1)-itemsets.
  Returns:
    True: satisfying Apriori property.
    False: Not satisfying Apriori property.
  """
  for item in Ck_item:
    sub_Ck = Ck_item - frozenset([item])
    if sub_Ck not in Lksub1:
      return False
  return True


def create_Ck(Lksub1, k):
  """
  Create Ck, a set which contains all all frequent candidate k-itemsets
  by Lk-1's own connection operation.
  Args:
    Lksub1: Lk-1, a set which contains all frequent candidate (k-1)-itemsets.
    k: the item number of a frequent itemset.
  Return:
    Ck: a set which contains all all frequent candidate k-itemsets.
  """
  Ck = set()
  len_Lksub1 = len(Lksub1)
  list_Lksub1 = list(Lksub1)
  for i in range(len_Lksub1):
    for j in range(1, len_Lksub1):
      l1 = list(list_Lksub1[i])
      l2 = list(list_Lksub1[j])
      l1.sort()
      l2.sort()
      if l1[0:k-2] == l2[0:k-2]:
        Ck_item = list_Lksub1[i] | list_Lksub1[j]
        # pruning
        if is_apriori(Ck_item, Lksub1):
          Ck.add(Ck_item)
  return Ck


def generate_Lk_by_Ck(data_set, Ck, min_support, support_data):
  """
  Generate Lk by executing a delete policy from Ck.
  Args:
    data_set: A list of transactions. Each transaction contains several items.
    Ck: A set which contains all all frequent candidate k-itemsets.
    min_support: The minimum support.
    support_data: A dictionary. The key is frequent itemset and the value is support.
  Returns:
    Lk: A set which contains all all frequent k-itemsets.
  """
  Lk = set()
  item_count = {}
  for t in data_set:
    for item in Ck:
      if item.issubset(t):
        if item not in item_count:
          item_count[item] = 1
        else:
          item_count[item] += 1
  t_num = float(len(data_set))
  for item in item_count:
    if (item_count[item] / t_num) >= min_support:
      Lk.add(item)
      support_data[item] = item_count[item] / t_num
  return Lk


def generate_L(data_set, k, min_support):
  """
  Generate all frequent itemsets.
  Args:
    data_set: A list of transactions. Each transaction contains several items.
    k: Maximum number of items for all frequent itemsets.
    min_support: The minimum support.
  Returns:
    L: The list of Lk.
    support_data: A dictionary. The key is frequent itemset and the value is support.
  """
  support_data = {}
  C1 = create_C1(data_set)
  L1 = generate_Lk_by_Ck(data_set, C1, min_support, support_data)
  Lksub1 = L1.copy()
  L = []
  L.append(Lksub1)
  for i in range(2, k+1):
    Ci = create_Ck(Lksub1, i)
    Li = generate_Lk_by_Ck(data_set, Ci, min_support, support_data)
    Lksub1 = Li.copy()
    L.append(Lksub1)
  return L, support_data


def generate_big_rules(L, support_data, min_conf):
  """
  Generate big rules from frequent itemsets.
  Args:
    L: The list of Lk.
    support_data: A dictionary. The key is frequent itemset and the value is support.
    min_conf: Minimal confidence.
  Returns:
    big_rule_list: A list which contains all big rules. Each big rule is represented
            as a 3-tuple.
  """
  big_rule_list = []
  sub_set_list = []
  for i in range(0, len(L)):
    for freq_set in L[i]:
      for sub_set in sub_set_list:
        if sub_set.issubset(freq_set):
          conf = support_data[freq_set] / support_data[freq_set - sub_set]
          big_rule = (freq_set - sub_set, sub_set, conf)
          if conf >= min_conf and big_rule not in big_rule_list:
            # print freq_set-sub_set, " => ", sub_set, "conf: ", conf
            big_rule_list.append(big_rule)
      sub_set_list.append(freq_set)
  return big_rule_list


if __name__ == "__main__":
  """
  Test
  """
  data_set = load_data_set()
  L, support_data = generate_L(data_set, k=3, min_support=0.2)
  big_rules_list = generate_big_rules(L, support_data, min_conf=0.7)
  for Lk in L:
    print "="*50
    print "frequent " + str(len(list(Lk)[0])) + "-itemsets\t\tsupport"
    print "="*50
    for freq_set in Lk:
      print freq_set, support_data[freq_set]
  print
  print "Big Rules"
  for item in big_rules_list:
    print item[0], "=>", item[1], "conf: ", item[2]