背景介紹

當顧客在購買一件商品時，商家可以趁機了解他們還想買什么，以便把多數顧客愿意同時購買的商品放到一起銷售以提升銷售額。當商家收集到足夠多的數據時，就可以對其進行親和性分析，以確定哪些商品適合放在一起出售。
什么是親和性呢，簡單的說就是物品之間的相似性或者說是相關性。比如說，一個去商場購物，買了蘋果的同時也買了香蕉，如果又買蘋果又買香蕉的人比較多，那么我們把蘋果和香蕉擺放在一起來銷售，往往可以提高銷量。這背后的思想就是人們經常購買同一件商品，下次大概率還是會繼續購買。看似簡單的思想，的確是很多線上和線下商品推薦服務的基礎。
之前的商品推薦工作，常常是人工在線下來完成的，費時費力，也沒有很好地精準度?，F在我們可以用數據驅動的方式來自動完成。節約成本，也提高了效率，下面我們來看看如何來做。

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數據準備和介紹

import numpy as np dataset_filename = "affinity_dataset.txt" X = np.loadtxt(dataset_filename) n_samples, n_features = X.shape print("This dataset has {0} samples and {1} features".format(n_samples, n_features))

結果是：This dataset has 100 samples and 5 features

我們來解釋下這個數據，看看顧客在前五次交易中都買了什么

print(X[: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.]]

豎著看，每一列分別表示一種商品的購買情況。分別是面包、牛奶、奶酪、蘋果和香蕉。舉個例子，第一行表示一個顧客，買了奶酪、蘋果和香蕉。而沒有買別的商品。每一行表示的是一次顧客購買行為。

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數據處理

我們把數據特征打上標簽，方便后面做處理：

# The names of the features, for your reference. features = ["bread", "milk", "cheese", "apples", "bananas"]

我們下面來做一個顧客既買蘋果又買香蕉的支持度和置信度，這里支持度指的是，對于總體而言，有多少樣本符合這個規則。置信度是：支持度/總體，比如說對于這個規則而言總是是買蘋果也買香蕉+買蘋果不買香蕉的總人數的和。即，只要他買蘋果，就算做是總體中的一員。

# How many of the cases that a person bought Apples involved the people purchasing Bananas too? # Record both cases where the rule is valid and is invalid. rule_valid = 0 rule_invalid = 0 for sample in X:if sample[3] == 1: # This person bought Applesif sample[4] == 1:# This person bought both Apples and Bananasrule_valid += 1else:# This person bought Apples, but not Bananasrule_invalid += 1 print("{0} cases of the rule being valid were discovered".format(rule_valid)) print("{0} cases of the rule being invalid were discovered".format(rule_invalid))

輸出結果是

21 cases of the rule being valid were discovered 15 cases of the rule being invalid were discovered

根據排列組合的知識，我們知道如果5種商品兩兩隨機組合的話，一共有10種組合方式（C25C52），我們計算所有組合的置信度，并把排名前三的打印出來：

import numpy as np dataset_filename = "affinity_dataset.txt" X = np.loadtxt(dataset_filename) n_samples, n_features = X.shape print("This dataset has {0} samples and {1} features".format(n_samples, n_features))# The names of the features, for your reference. features = ["bread", "milk", "cheese", "apples", "bananas"]from collections import defaultdict # Now compute for all possible rules valid_rules = defaultdict(int) invalid_rules = defaultdict(int) num_occurences = defaultdict(int) #num_occurances represents the same number of rulesfor sample in X: # (sample means record of buying fruit)for premise in range(n_features):if sample[premise] == 0: continue# Record that the premise was bought in another transactionnum_occurences[premise] += 1for conclusion in range(n_features):'''根據排列組合的規則，我這里希望按照1,2,3,4； 2，3,4； 3,4；4這樣的順序進行比較。這樣的話，比較10次，就遍歷完所有的情況?；诖?#xff0c;有了最外層的if...else語句第一句話是為了讓他按照我前面說的那個順序走，后面的判斷語句，保證不遍歷超出范圍'''conclusion = conclusion + premise if conclusion < n_features:if premise == conclusion: # It makes little sense to measure if X -> X.continueif sample[conclusion] == 1:# This person also bought the conclusion itemvalid_rules[(premise, conclusion)] += 1else:# This person bought the premise, but not the conclusioninvalid_rules[(premise, conclusion)] += 1else:continuesupport = valid_rules confidence = defaultdict(float) for premise, conclusion in valid_rules.keys():confidence[(premise, conclusion)] = valid_rules[(premise, conclusion)] / num_occurences[premise]

最后我們來進行排序操作，打印前三個結果。先來看一下我們處理之后的結果都是什么樣子的

# 用于打印 Python 數據結構. 當你在命令行下打印特定數據結構時你會發現它很有用(輸出格式比較整齊, 便于閱讀). 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)]

我們給輸出定義一個函數形式，方面后面進行輸出：
因為我們之前寫了一個feature列表，這樣的話就很容易鎖定到具體產品信息，只用一個列表就可以搞定，不用定義字典（這是一個不錯的思路）

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("")

示例輸出：

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

然后進行排序操作，我們按照置信度大小進行排序，降序：

# sort and print the first three resultfrom operator import itemgetter sorted_confidence = sorted(confidence.items(), key=itemgetter(1), reverse=True) for index in range(3):print("Rule #{0}".format(index + 1))(premise, conclusion) = sorted_confidence[index][0]print_rule(premise, conclusion, support, confidence, features)

結果如下：
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 bread they will also buy bananas
- Confidence: 0.630
- Support: 17

Rule #3
Rule: If a person buys cheese they will also buy apples
- Confidence: 0.610
- Support: 25

從排序結果來看，“顧客買蘋果，也會買奶酪”和“顧客買奶酪，也會買香蕉”，這兩條規 則的支持度和置信度都很高。超市經理可以根據這些規則來調整商品擺放位置。例如，如果本周蘋果促銷，就在旁邊擺上奶酪。或許可以提高超市銷量哦。

參考資料：
《python數據挖掘入門與實踐》
數據集

總結

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