亲和性分析

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：

1. 向网站用户提供多样化的服务或投放定向广告；
2. 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；
3. 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