数据挖掘有个常见的应用场景，即顾客在购买一件商品时，商家可以趁机了解他们还想买什么，以便把多数顾客意愿同时购买的商品放到一起以提高销售量。当商家收集到足够多的数据时，就可以对其进行亲和性分析，以确定哪些商品合适放在一起销售
什么是亲和性：
亲和性分析根据样本个体（物体）之间的相似度，确定他们关系的亲疏。亲和性分析的应用场景如下：
- 向网站用户提供多样化的服务或投放定向广告；
- 为了向用户推荐电影或者商品，儿卖给他们一些与之相关的小玩意；
- 根据基因寻找亲缘关系的人
商品推荐：
我们一起看下简单的商品推荐服务，他背后的思路其实很好理解：人们之前经常同时购买两件商品，以后也很可能同时购买，该想法很简单吧，可这就是很多商品推荐服务的基础；
为了简化代码，我们只考虑一次购买两件商品的请客。例如，人们去了超市既买了面包又买了牛奶。作为数据挖掘的例子，我们希望看到下面的规则：
如果一个人买了商品X，那么他很可能购买商品Y
多件商品的规则会更为复杂，比如购买了香肠和汉堡的顾客比起其他顾客更有可能购买番茄酱。本次不探讨这样的规则。
加载数据：
In [2]: import numpy as np
In [3]: path = 'D:\\books\\affinity_dataset.txt'
In [4]: data = np.loadtxt(path)
In [5]: n_samples,n_features = data.shape
In [6]: n_samples
Out[6]: 100
In [7]: n_features
Out[7]: 5
In [8]: print("This dataset has {0} samples and {1} features".format(n_samples, n_features))
This dataset has 100 samples and 5 features
#查看数据
In [11]: print(data[:5])
[[0. 0. 1. 1. 1.]
[1. 1. 0. 1. 0.]
[1. 0. 1. 1. 0.]
[0. 0. 1. 1. 1.]
[0. 1. 0. 0. 1.]]
输出的结果中，从横向和竖向我们可以，横着看，每次只看一行，第一行（0,0,1,1,1）表示第一条交易数据所包含的商品，竖着看，每一列代表一种商品。在我们的例子中，这五种商品分别包含面包、牛奶、奶酪、苹果和香蕉；从第一条交易数据，我们可以看到顾客买了奶酪，香蕉和苹果，但是没买面包和牛奶；
每个特征只有两种可能，1或0，表示是否购买了某种商品，而不是购买商品的数量；1表示至少购买了一个单位的该商品，0表示顾客没有购买该商品；
实现简单的排序规则：
正如前面所说，我们要找出“如果顾客买了商品X，那么他们可能愿意购买商品Y”这样的规则，简单粗暴的做法是，找出数据集中所有同事购买的两件商品。找出规则后，还需要判断其优劣势；我们挑好用的规则用：
规则的优劣势有多重衡量方法，常用的是支持度(support)和置信度(confidence)
- 支持度指数集中规则应验的次数：支持度衡量的是给定规则的应验比例；
- 置信度衡量的是规则准确率如何，即符合给定条件（即规则的“如果”语句所表示的前提条件）的所有规则里，跟当前结论一致的比例有多大；计算方法为首先统计当前规则出现的次数，再用他来除以（“如果”语句）相同规则的数量
接下来我们通过一个例子来说明支持度和置信度的计算方法；我们来看一下“如果顾客购买了苹果，他们也会购买香蕉”这条的支持度和置信度；
In [12]: fearures = ['beard','milk','cheese','apple','bananas']
In [13]: num_apple_purchases = 0
#First ,how many rows contain our premise:that a person is buying apples
In [14]: for sample in data:
...: if sample[3] == 1: #this person bought apples
...: num_apple_purchases += 1
...:
In [15]: print("{0} people bought Apples".format(num_apple_purchases))
36 people bought Apples
同理，检测sample[4]的值是否为1，就能确定顾客有没有买香蕉，
我们需要统计数据集中所有规则的相关数据，首先分别为规则应验和规则无效这两种情况创建字典。字典的键是由条件和结论组成的元组，元组元素为特征在特征列表中的索引值，不要用实际特征名；
In [16]: rule_valid = 0
In [17]: rule_invalid = 0
In [19]: for sample in data:
...: if sample[3] == 1: #this person bought apples
...: if sample[4] == 1: #this person bought both apples and bananas
...: rule_valid += 1
...: else:
...: rule_invalid += 1
...:
In [20]: print("{0} cases of the rule being valid were discovered".format(rule_valid))
21 cases of the rule being valid were discovered
In [21]: print("{0} cases of the rule being invalid were discovered".format(rule_invalid))
15 cases of the rule being invalid were discovered
我们可以计算支持度和置信度了；
# Now we have all the information needed to compute Support and Confidence
In [22]: support = rule_valid # The Support is the number of times the rule is discovered.
In [23]: confidence = rule_valid / num_apple_purchases
In [24]: print("The support is {0} and the confidence is {1:.3f}.".format(support, confidence))
The support is 21 and the confidence is 0.583.
# Confidence can be thought of as a percentage using the following:
In [25]: print("As a percentage, that is {0:.1f}%.".format(100 * confidence))
As a percentage, that is 58.3%.
为了计算所有规则的置信度和支持度，首先要创建几个字典，用来存放计算结果。这里使用defaultdict。
from collections import defaultdict
# Now compute for all possible rules
valid_rules = defaultdict(int)
invalid_rules = defaultdict(int)
num_occurences = defaultdict(int)
for sample in X:
for premise in range(n_features):
if sample[premise] == 0: continue
# Record that the premise was bought in another transaction
num_occurences[premise] += 1
for conclusion in range(n_features):
if premise == conclusion: # It makes little sense to measure if X -> X.
continue
if sample[conclusion] == 1:
# This person also bought the conclusion item
valid_rules[(premise, conclusion)] += 1
else:
# This person bought the premise, but not the conclusion
invalid_rules[(premise, conclusion)] += 1
support = valid_rules
confidence = defaultdict(float)
for premise, conclusion in valid_rules.keys():
confidence[(premise, conclusion)] = valid_rules[(premise, conclusion)] / num_occurences[premise]
for premise, conclusion in confidence:
premise_name = features[premise]
conclusion_name = features[conclusion]
print("Rule: If a person buys {0} they will also buy {1}".format(premise_name, conclusion_name))
print(" - Confidence: {0:.3f}".format(confidence[(premise, conclusion)]))
print(" - Support: {0}".format(support[(premise, conclusion)]))
print("")
Rule: If a person buys bread they will also buy milk
- Confidence: 0.519
- Support: 14
Rule: If a person buys milk they will also buy cheese
- Confidence: 0.152
- Support: 7
Rule: If a person buys apples they will also buy cheese
- Confidence: 0.694
- Support: 25
Rule: If a person buys milk they will also buy apples
- Confidence: 0.196
- Support: 9
Rule: If a person buys bread they will also buy apples
- Confidence: 0.185
- Support: 5
Rule: If a person buys apples they will also buy bread
- Confidence: 0.139
- Support: 5
Rule: If a person buys apples they will also buy bananas
- Confidence: 0.583
- Support: 21
Rule: If a person buys apples they will also buy milk
- Confidence: 0.250
- Support: 9
Rule: If a person buys milk they will also buy bananas
- Confidence: 0.413
- Support: 19
Rule: If a person buys cheese they will also buy bananas
- Confidence: 0.659
- Support: 27
Rule: If a person buys cheese they will also buy bread
- Confidence: 0.098
- Support: 4
Rule: If a person buys cheese they will also buy apples
- Confidence: 0.610
- Support: 25
Rule: If a person buys cheese they will also buy milk
- Confidence: 0.171
- Support: 7
Rule: If a person buys bananas they will also buy apples
- Confidence: 0.356
- Support: 21
Rule: If a person buys bread they will also buy bananas
- Confidence: 0.630
- Support: 17
Rule: If a person buys bananas they will also buy cheese
- Confidence: 0.458
- Support: 27
Rule: If a person buys milk they will also buy bread
- Confidence: 0.304
- Support: 14
Rule: If a person buys bananas they will also buy milk
- Confidence: 0.322
- Support: 19
Rule: If a person buys bread they will also buy cheese
- Confidence: 0.148
- Support: 4
Rule: If a person buys bananas they will also buy bread
- Confidence: 0.288
- Support: 17
def print_rule(premise, conclusion, support, confidence, features):
premise_name = features[premise]
conclusion_name = features[conclusion]
print("Rule: If a person buys {0} they will also buy {1}".format(premise_name, conclusion_name))
print(" - Confidence: {0:.3f}".format(confidence[(premise, conclusion)]))
print(" - Support: {0}".format(support[(premise, conclusion)]))
print("")
premise = 1
conclusion = 3
print_rule(premise, conclusion, support, confidence, features)
Rule: If a person buys milk they will also buy apples
- Confidence: 0.196
- Support: 9
# Sort by support
from pprint import pprint
pprint(list(support.items()))
[((0, 1), 14),
((1, 2), 7),
((3, 2), 25),
((1, 3), 9),
((0, 2), 4),
((3, 0), 5),
((4, 1), 19),
((3, 1), 9),
((1, 4), 19),
((2, 4), 27),
((2, 0), 4),
((2, 3), 25),
((2, 1), 7),
((4, 3), 21),
((0, 4), 17),
((4, 2), 27),
((1, 0), 14),
((3, 4), 21),
((0, 3), 5),
((4, 0), 17)]
排序：
from operator import itemgetter
sorted_support = sorted(support.items(), key=itemgetter(1), reverse=True)
for index in range(5):
print("Rule #{0}".format(index + 1))
(premise, conclusion) = sorted_support[index][0]
print_rule(premise, conclusion, support, confidence, features)
Rule #1
Rule: If a person buys cheese they will also buy bananas
- Confidence: 0.659
- Support: 27
Rule #2
Rule: If a person buys bananas they will also buy cheese
- Confidence: 0.458
- Support: 27
Rule #3
Rule: If a person buys apples they will also buy cheese
- Confidence: 0.694
- Support: 25
Rule #4
Rule: If a person buys cheese they will also buy apples
- Confidence: 0.610
- Support: 25
Rule #5
Rule: If a person buys bananas they will also buy apples
- Confidence: 0.356
- Support: 21
