如何使用增量 SVD 推荐系统创建推荐

Question

我正在测试一个根据 Simon Funk 算法构建的推荐系统。 （由 Timely Dev 编写。http://www.timelydevelopment.com/demos/NetflixPrize.aspx)

问题是，所有增量 SVD 算法都尝试预测 user_id 和 movie_id 的评分。但在真实的系统中，这应该为活动用户生成一个新项目列表。 我看到有些人在增量 SVD 之后使用了 kNN，但是如果我没有错过任何东西，如果我在通过增量 SVD 创建模型后使用 kNN，我会失去所有性能增益。

任何人都有增量 SVD/Simon Funk 方法的经验，并告诉我如何生成新推荐项目列表？

Answer 1

产生推荐电影的方式：

1. 取一个未看过的电影列表，
2. 将其特征向量乘以用户的特征向量。
3. 按结果降序排序并选取排名靠前的电影。

对于理论：假装只有两个维度（喜剧和戏剧）。如果我喜欢喜剧，但讨厌戏剧，我的特征向量是[1.0, 0.0]。如果你将我与以下电影进行比较：

Comedy:  [1.0, 0.0] x [1.0, 0.0] = 1
Dramedy: [0.5, 0.5] x [1.0, 0.0] = 0.5
Drama:   [0.0, 1.0] x [1.0, 0,0] = 0 

Answer 2

这是一个基于 Yelp Netflix 代码的简单 Python 代码。如果您安装 Numba，它将以 C 速度运行。

data_loader.py

import os
import numpy as np
from scipy import sparse

class DataLoader:
    def __init__(self):
        pass

    @staticmethod
    def create_review_matrix(file_path):
        data = np.array([[int(tok) for tok in line.split('\t')[:3]]
                         for line in open(file_path)])

        ij = data[:, :2]
        ij -= 1
        values = data[:, 2]
        review_matrix = sparse.csc_matrix((values, ij.T)).astype(float)
        return review_matrix

movielens_file_path = '%s/Downloads/ml-100k/u1.base' % os.environ['HOME']

my_reviews = DataLoader.create_review_matrix(movielens_file_path)

user_reviews = my_reviews[8]
user_reviews = user_reviews.toarray().ravel()
user_rated_movies,  = np.where(user_reviews > 0)
user_ratings = user_reviews[user_rated_movies]

movie_reviews = my_reviews[:, 201]
movie_reviews = movie_reviews.toarray().ravel()
movie_rated_users,  = np.where(movie_reviews > 0)
movie_ratings = movie_reviews[movie_rated_users]

user_pseudo_average_ratings = {}
user_pseudo_average_ratings[8] = np.mean(user_ratings)
user_pseudo_average_ratings[9] = np.mean(user_ratings)
user_pseudo_average_ratings[10] = np.mean(user_ratings)
users, movies = my_reviews.nonzero()

users_matrix = np.empty((3, 3))
users_matrix[:] = 0.1

movies_matrix = np.empty((3, 3))
movies_matrix[:] = 0.1

result = users_matrix[0] * movies_matrix[0]
otro = movies_matrix[:, 2]
otro[2] = 8

funk.py

# Requires Movielens 100k data 
import numpy as np, time, sys
from data_loader import DataLoader
from numba import jit
import os

def get_user_ratings(user_id, review_matrix):
    """
    Returns a numpy array with the ratings that user_id has made

    :rtype : numpy array
    :param user_id: the id of the user
    :return: a numpy array with the ratings that user_id has made
    """
    user_reviews = review_matrix[user_id]
    user_reviews = user_reviews.toarray().ravel()
    user_rated_movies, = np.where(user_reviews > 0)
    user_ratings = user_reviews[user_rated_movies]
    return user_ratings

def get_movie_ratings(movie_id, review_matrix):
    """
    Returns a numpy array with the ratings that movie_id has received

    :rtype : numpy array
    :param movie_id: the id of the movie
    :return: a numpy array with the ratings that movie_id has received
    """
    movie_reviews = review_matrix[:, movie_id]
    movie_reviews = movie_reviews.toarray().ravel()
    movie_rated_users, = np.where(movie_reviews > 0)
    movie_ratings = movie_reviews[movie_rated_users]
    return movie_ratings

def create_user_feature_matrix(review_matrix, NUM_FEATURES, FEATURE_INIT_VALUE):
    """
    Creates a user feature matrix of size NUM_FEATURES X NUM_USERS
    with all cells initialized to FEATURE_INIT_VALUE

    :rtype : numpy matrix
    :return: a matrix of size NUM_FEATURES X NUM_USERS
    with all cells initialized to FEATURE_INIT_VALUE
    """
    num_users = review_matrix.shape[0]
    user_feature_matrix = np.empty((NUM_FEATURES, num_users))
    user_feature_matrix[:] = FEATURE_INIT_VALUE
    return user_feature_matrix

def create_movie_feature_matrix(review_matrix, NUM_FEATURES, FEATURE_INIT_VALUE):
    """
    Creates a user feature matrix of size NUM_FEATURES X NUM_MOVIES
    with all cells initialized to FEATURE_INIT_VALUE

    :rtype : numpy matrix
    :return: a matrix of size NUM_FEATURES X NUM_MOVIES
    with all cells initialized to FEATURE_INIT_VALUE
    """
    num_movies = review_matrix.shape[1]
    movie_feature_matrix = np.empty((NUM_FEATURES, num_movies))
    movie_feature_matrix[:] = FEATURE_INIT_VALUE
    return movie_feature_matrix

@jit(nopython=True)
def predict_rating(user_id, movie_id, user_feature_matrix, movie_feature_matrix):
    """
    Makes a prediction of the rating that user_id will give to movie_id if
    he/she sees it

    :rtype : float
    :param user_id: the id of the user
    :param movie_id: the id of the movie
    :return: a float in the range [1, 5] with the predicted rating for
    movie_id by user_id
    """
    rating = 1.
    for f in range(user_feature_matrix.shape[0]):
        rating += user_feature_matrix[f, user_id] * movie_feature_matrix[f, movie_id]

    # We trim the ratings in case they go above or below the stars range
    if rating > 5: rating = 5
    elif rating < 1: rating = 1
    return rating

@jit(nopython=True)
def sgd_inner(feature, A_row, A_col, A_data, user_feature_matrix, movie_feature_matrix, NUM_FEATURES):
    K = 0.015
    LEARNING_RATE = 0.001
    squared_error = 0
    for k in range(len(A_data)):
        user_id = A_row[k]
        movie_id = A_col[k]
        rating = A_data[k]
        p = predict_rating(user_id, movie_id, user_feature_matrix, movie_feature_matrix)
        err = rating - p

        squared_error += err ** 2

        user_feature_value = user_feature_matrix[feature, user_id]
        movie_feature_value = movie_feature_matrix[feature, movie_id]
        #for j in range(NUM_FEATURES):
        user_feature_matrix[feature, user_id] += \
            LEARNING_RATE * (err * movie_feature_value - K * user_feature_value)
        movie_feature_matrix[feature, movie_id] += \
            LEARNING_RATE * (err * user_feature_value - K * movie_feature_value)

    return squared_error

def calculate_features(A_row, A_col, A_data, user_feature_matrix, movie_feature_matrix, NUM_FEATURES):
    """
    Iterates through all the ratings in search for the best features that
    minimize the error between the predictions and the real ratings.
    This is the main function in Simon Funk SVD algorithm

    :rtype : void
    """
    MIN_IMPROVEMENT = 0.0001
    MIN_ITERATIONS = 100
    rmse = 0
    last_rmse = 0
    print len(A_data)
    num_ratings = len(A_data)
    for feature in xrange(NUM_FEATURES):
        iter = 0
        while (iter < MIN_ITERATIONS) or  (rmse < last_rmse - MIN_IMPROVEMENT):
            last_rmse = rmse
            squared_error = sgd_inner(feature, A_row, A_col, A_data, user_feature_matrix, movie_feature_matrix, NUM_FEATURES)
            rmse = (squared_error / num_ratings) ** 0.5
            iter += 1
        print ('Squared error = %f' % squared_error)
        print ('RMSE = %f' % rmse)
        print ('Feature = %d' % feature)
    return last_rmse


LAMBDA = 0.02
FEATURE_INIT_VALUE = 0.1
NUM_FEATURES = 20

movielens_file_path = '%s/Downloads/ml-100k/u1.base' % os.environ['HOME']

A = DataLoader.create_review_matrix(movielens_file_path)
from scipy.io import mmread, mmwrite
mmwrite('./data/A', A)

user_feature_matrix = create_user_feature_matrix(A, NUM_FEATURES, FEATURE_INIT_VALUE)
movie_feature_matrix = create_movie_feature_matrix(A, NUM_FEATURES, FEATURE_INIT_VALUE)

users, movies = A.nonzero()
A = A.tocoo()

rmse = calculate_features(A.row, A.col, A.data, user_feature_matrix, movie_feature_matrix, NUM_FEATURES )
print 'rmse', rmse

Answer 3

我认为这是一个大问题，因为有很多推荐方法我认为可以称为“增量 SVD”。要回答您的具体问题：kNN 是在投影项目空间上运行的，而不是在原始空间上运行的，因此应该非常快。

Answer 4

假设您有 n 个用户和 m 个项目。经过增量 SVD 后，您将获得 k 个经过训练的特征。要获取给定用户的新项目，请将 1xk 用户特征向量和 kxm 项目特征矩阵相乘。您最终会得到该用户对每个项目的 m 个评分。然后对它们进行排序，删除已经看过的，并显示一些新的。