用Python实现svd++推荐算法

在SVD的基础上在用户特征矩阵上加入用户的偏好。某个用户对某个电影进行了评分，那么说明他看过这部电影，那么这样的行为事实上蕴含了一定的信息，因此我们可以这样来理解问题：评分的行为从侧面反映了用户的喜好，可以将这样的反映通过隐式参数的形式体现在模型中，从而得到一个更为精细的模型，便是 SVD++.
预测评分为：

目标函数：

参数更新式：


# -*- coding:utf-8 -*-

from __future__ import division, print_function

import numpy as np
from algorithm.estimator import Estimator


class SVDPlusPlus(Estimator):
    """
    属性
    ---------
    n_factors : 隐式因子数
    n_epochs : 迭代次数
    lr : 学习速率
    reg : 正则因子
    """

    def __init__(self, n_factors=20, n_epochs=20, lr=0.007, reg=.002):
        self.n_factors = n_factors
        self.n_epochs = n_epochs
        self.lr = lr
        self.reg = reg

    def train(self, train_dataset):
        user_num = train_dataset.matrix.shape[0]
        item_num = train_dataset.matrix.shape[1]
        self.train_dataset = train_dataset

        #global mean
        self.global_mean = train_dataset.global_mean

        #user bias
        self.bu = np.zeros(user_num, np.double)

        #item bias
        self.bi = np.zeros(item_num, np.double)

        #user factor
        self.p = np.zeros((user_num, self.n_factors), np.double) + .1

        #item factor
        self.q = np.zeros((item_num, self.n_factors), np.double) + .1

        #item preference facotor
        self.y = np.zeros((item_num, self.n_factors), np.double) + .1

        for current_epoch in range(self.n_epochs):
            print(" processing epoch {}".format(current_epoch))
            for u, i, r in train_dataset.all_ratings():
                #用户u点评的item集
                Nu = train_dataset.get_user(u)[0]
                I_Nu = len(Nu)
                sqrt_N_u = np.sqrt(I_Nu)

                #基于用户u点评的item集推测u的implicit偏好
                y_u = np.sum(self.y[Nu], axis=0)

                u_impl_prf = y_u / sqrt_N_u

                #预测值
                rp = self.global_mean + self.bu[u] + self.bi[i] + np.dot(self.q[i], self.p[u] + u_impl_prf)

                #误差
                e_ui = r - rp

                #sgd
                self.bu[u] += self.lr * (e_ui - self.reg * self.bu[u])
                self.bi[i] += self.lr * (e_ui - self.reg * self.bi[i])
                self.p[u] += self.lr * (e_ui * self.q[i] - self.reg * self.p[u])
                self.q[i] += self.lr * (e_ui * (self.p[u] + u_impl_prf) - self.reg * self.q[i])
                for j in Nu:
                    self.y[j] += self.lr * (e_ui * self.q[j] / sqrt_N_u - self.reg * self.y[j])

    def predict(self, u, i):
        Nu = self.train_dataset.get_user(u)[0]
        I_Nu = len(Nu)
        sqrt_N_u = np.sqrt(I_Nu)
        y_u = np.sum(self.y[Nu], axis=0) / sqrt_N_u

        est = self.global_mean + self.bu[u] + self.bi[i] + np.dot(self.q[i], self.p[u] + y_u)
        return est

代码原地址添加链接描述