### Python 实现协同过滤算法代码示例 #### 用户基础的协同过滤(User-Based Collaborative Filtering) 用户基础的协同过滤依赖于找到具有相似偏好的其他用户，并基于这些用户的偏好向目标用户推荐项目。 ```python from math import sqrt import numpy as np def similarity_score(person1, person2): both_viewed = {} # To get items rated by both persons for item in dataset[person1]: if item in dataset[person2]: both_viewed[item] = 1 number_of_ratings = len(both_viewed) # If no ratings in common, return 0 if number_of_ratings == 0: return 0 # Add up all the preferences of each user person1_preferences_sum = sum([dataset[person1][item] for item in both_viewed]) person2_preferences_sum = sum([dataset[person2][item] for item in both_viewed]) # Sum up the squares of preferences of each user person1_square_preferences_sum = sum([pow(dataset[person1][item], 2) for item in both_viewed]) person2_square_preferences_sum = sum([pow(dataset[person2][item], 2) for item in both_viewed]) # Sum up the product value of both preferences for each item product_sum_of_both_users = sum([dataset[person1][item] * dataset[person2][item] for item in both_viewed]) # Calculate the pearson correlation score numerator_value = product_sum_of_both_users - (person1_preferences_sum*person2_preferences_sum/number_of_ratings) denominator_value = sqrt((person1_square_preferences_sum - pow(person1_preferences_sum, 2)/number_of_ratings) * \ (person2_square_preferences_sum - pow(person2_preferences_sum, 2)/number_of_ratings)) if denominator_value == 0: return 0 else: r = numerator_value / denominator_value return r def most_similar_users(person, number_of_users): scores = [(similarity_score(person, other_person), other_person) for other_person in dataset if other_person != person] # Sort list so highest scores appear at top scores.sort() scores.reverse() return scores[:number_of_users] def user_reommendations(person): totals = {} simSums = {} for other in dataset: if other == person: continue sim = similarity_score(person,other) if sim <= 0: continue for item in dataset[other]: if item not in dataset[person] or dataset[person][item] == 0: totals.setdefault(item, 0) totals[item] += dataset[other][item]*sim simSums.setdefault(item, 0) simSums[item] += sim rankings = [(total/simSums[item], item) for item, total in totals.items()] rankings.sort(reverse=True) recommendations = [recommend_item for _, recommend_item in rankings] return recommendations ``` 这段代码实现了基于用户的协同过滤，其中`similarity_score()`函数用来计算两个用户间的皮尔逊相关系数作为相似度得分；`most_similar_users()`返回与指定用户最接近的一组用户列表；而`user_recommendations()`则利用上述信息给出针对特定用户的个性化推荐[^4]。 #### 物品基础的协同过滤(Item-Based Collaborative Filtering) 物品基础的方法侧重于寻找那些经常一起被评价的商品或服务。这种方法通常更稳定也更容易扩展至大规模数据集上。 ```python def compute_deviations(): deviations = {} frequency = {} for ratings in data.values(): for rating_item_i, rating_value_i in ratings.items(): deviations.setdefault(rating_item_i, {}) frequency.setdefault(rating_item_i, {}) for rating_item_j, rating_value_j in ratings.items(): if rating_item_i != rating_item_j: deviations[rating_item_i].setdefault(rating_item_j, []) frequency[rating_item_i].setdefault(rating_item_j, []) deviations[rating_item_i][rating_item_j].append(rating_value_i-rating_value_j) frequency[rating_item_i][rating_item_j]+=1 for rating_item_i, neighbors in deviations.items(): for rating_item_j, diff in neighbors.items(): n = frequency[rating_item_i][rating_item_j] deviations[rating_item_i][rating_item_j]=sum(diff)/n return deviations, frequency def slope_one_recommendations(user_ratings): recommendations = {} frequency = {} dev, freq = compute_deviations() for unrated_item in dev.keys(): if unrated_item not in user_ratings and any(nbr in user_ratings for nbr in dev[unrated_item]): avg_diffs = [] num_rat = [] for i_rated_item in user_ratings: if i_rated_item in dev[unrated_item]: avg_diffs.append(dev[unrated_item][i_rated_item]+user_ratings[i_rated_item]) num_rat.append(freq[unrated_item][i_rated_item]) est_rating=np.average(avg_diffs, weights=num_rat) recommendations[unrated_item]=est_rating sorted_recommendations=sorted(recommendations.items(), key=lambda kv:(kv[1], kv[0]), reverse=True) return dict(sorted_recommendations) ``` 此部分展示了如何构建简单的斜率一(Slope One)[^4]类型的物品间偏差模型来进行预测和推荐。这里的关键在于先通过已有评分记录算出各对商品之间的平均差异(`compute_deviations()`)，再依据这个结果为未打过分的产品估算可能分数(`slope_one_recommendations()`)。