协同过滤算法.txt

"""
协同过滤算法
"""
from abc import ABCMeta, abstractmethod
import numpy as np
from collections import defaultdict


class CF_base(metaclass=ABCMeta):
    def __init__(self, k=3):
        self.k = k
        self.n_user = None
        self.n_item = None

    @abstractmethod
    def init_param(self, data):
        pass

    @abstractmethod
    def cal_prediction(self, *args):
        pass

    @abstractmethod
    def cal_recommendation(self, user_id, data):
        pass

    def fit(self, data):
        # 计算所有用户的推荐物品
        self.init_param(data)
        all_users = []
        for i in range(self.n_user):
            all_users.append(self.cal_recommendation(i, data))
        return all_users


class CF_knearest(CF_base):
    """
    基于物品的K近邻协同过滤推荐算法
    """

    def __init__(self, k, criterion='cosine'):
        super(CF_knearest, self).__init__(k)
        self.criterion = criterion
        self.simi_mat = None
        return

    def init_param(self, data):
        # 初始化参数
        self.n_user = data.shape[0]
        self.n_item = data.shape[1]
        self.simi_mat = self.cal_simi_mat(data)
        return

    def cal_similarity(self, i, j, data):
        # 计算物品i和物品j的相似度
        items = data[:, [i, j]]
        del_inds = np.where(items == 0)[0]
        items = np.delete(items, del_inds, axis=0)
        if items.size == 0:
            similarity = 0
        else:
            v1 = items[:, 0]
            v2 = items[:, 1]
            if self.criterion == 'cosine':
                if np.std(v1) > 1e-3:  # 方差过大，表明用户间评价尺度差别大需要进行调整
                    v1 = v1 - v1.mean()
                if np.std(v2) > 1e-3:
                    v2 = v2 - v2.mean()
                similarity = (v1 @ v2) / np.linalg.norm(v1, 2) / np.linalg.norm(v2, 2)
            elif self.criterion == 'pearson':
                similarity = np.corrcoef(v1, v2)[0, 1]
            else:
                raise ValueError('the method is not supported now')
        return similarity

    def cal_simi_mat(self, data):
        # 计算物品间的相似度矩阵
        simi_mat = np.ones((self.n_item, self.n_item))
        for i in range(self.n_item):
            for j in range(i + 1, self.n_item):
                simi_mat[i, j] = self.cal_similarity(i, j, data)
                simi_mat[j, i] = simi_mat[i, j]
        return simi_mat

    def cal_prediction(self, user_row, item_ind):
        # 计算预推荐物品i对目标活跃用户u的吸引力
        purchase_item_inds = np.where(user_row > 0)[0]
        rates = user_row[purchase_item_inds]
        simi = self.simi_mat[item_ind][purchase_item_inds]
        return np.sum(rates * simi) / np.linalg.norm(simi, 1)

    def cal_recommendation(self, user_ind, data):
        # 计算目标用户的最具吸引力的k个物品list
        item_prediction = defaultdict(float)
        user_row = data[user_ind]
        un_purchase_item_inds = np.where(user_row == 0)[0]
        for item_ind in un_purchase_item_inds:
            item_prediction[item_ind] = self.cal_prediction(user_row, item_ind)
        res = sorted(item_prediction, key=item_prediction.get, reverse=True)
        return res[:self.k]


class CF_svd(CF_base):
    """
    基于矩阵分解的协同过滤算法
    """

    def __init__(self, k=3, r=3):
        super(CF_svd, self).__init__(k)
        self.r = r  # 选取前k个奇异值
        self.uk = None  # 用户的隐因子向量
        self.vk = None  # 物品的隐因子向量
        return

    def init_param(self, data):
        # 初始化，预处理
        self.n_user = data.shape[0]
        self.n_item = data.shape[1]
        self.svd_simplify(data)
        return data

    def svd_simplify(self, data):
        # 奇异值分解以及简化
        u, s, v = np.linalg.svd(data)
        u, s, v = u[:, :self.r], s[:self.r], v[:self.r, :]  # 简化
        sk = np.diag(np.sqrt(s))  # r*r
        self.uk = u @ sk  # m*r
        self.vk = sk @ v  # r*n
        return

    def cal_prediction(self, user_ind, item_ind, user_row):
        rate_ave = np.mean(user_row)  # 用户已购物品的评价的平均值(未评价的评分为0)
        return rate_ave + self.uk[user_ind] @ self.vk[:, item_ind]  # 两个隐因子向量的内积加上平均值就是最终的预测分值

    def cal_recommendation(self, user_ind, data):
        # 计算目标用户的最具吸引力的k个物品list
        item_prediction = defaultdict(float)
        user_row = data[user_ind]
        un_purchase_item_inds = np.where(user_row == 0)[0]
        for item_ind in un_purchase_item_inds:
            item_prediction[item_ind] = self.cal_prediction(user_ind, item_ind, user_row)
        res = sorted(item_prediction, key=item_prediction.get, reverse=True)
        return res[:self.k]


if __name__ == '__main__':
    # data = np.array([[4, 3, 0, 5, 0],
    #                  [4, 0, 4, 4, 0],
    #                  [4, 0, 5, 0, 3],
    #                  [2, 3, 0, 1, 0],
    #                  [0, 4, 2, 0, 5]])
    data = np.array([[3.5, 1.0, 0.0, 0.0, 0.0, 0.0],
                     [2.5, 3.5, 3.0, 3.5, 2.5, 3.0],
                     [3.0, 3.5, 1.5, 5.0, 3.0, 3.5],
                     [2.5, 3.5, 0.0, 3.5, 4.0, 0.0],
                     [3.5, 2.0, 4.5, 0.0, 3.5, 2.0],
                     [3.0, 4.0, 2.0, 3.0, 3.0, 2.0],
                     [4.5, 1.5, 3.0, 5.0, 3.5, 0.0]])
    # cf = CF_svd(k=1, r=3)
    cf = CF_knearest(k=1)
    print(cf.fit(data))