深度解析推荐系统：网络与信息过滤的综合概述

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"recommender systems.pdf - 最权威的推荐系统综述，涵盖了推荐系统的理论、方法和应用，适合深入理解该领域" 推荐系统是信息过滤的一种有效手段，它在互联网爆炸性增长的背景下显得尤为重要。随着网络内容的海量增加，用户面临着如何在众多信息中找到自己真正感兴趣和有价值内容的挑战。推荐系统通过分析用户的个性化需求，基于用户的行为历史、兴趣偏好、社交网络关系等数据，提供个性化的信息推荐，从而帮助用户筛选出符合其需求的信息。推荐系统的研究主要分为基于内容的推荐、协同过滤、混合推荐等多种方法。基于内容的推荐系统依赖于对物品内容的理解，通过比较用户过去喜欢的物品与待推荐物品之间的相似度来做出预测。协同过滤则依赖于用户的行为模式，包括用户-用户协同过滤（找出具有相似行为模式的用户，将他们喜欢的物品推荐给其他用户）和物品-物品协同过滤（根据用户对物品的评价，推荐相似物品给用户）。混合推荐系统结合多种推荐策略，旨在提高推荐的准确性和多样性。网络在推荐系统中的作用不容忽视，它们可以是用户-用户网络、物品-物品网络，甚至是用户-物品网络。这些网络结构提供了丰富的信息，帮助理解用户行为和物品间的关联。例如，社交网络中的朋友关系可以揭示用户的共同兴趣，物品的关联网络可以揭示隐藏的模式和趋势。此外，复杂网络理论也被应用于推荐系统，以揭示网络中的非线性特征和复杂性。推荐系统的评估通常包括准确性、覆盖率、多样性、新颖性和用户满意度等多个指标。准确性和覆盖率衡量推荐的精确性和广度，多样性关注推荐结果的多样性，新颖性鼓励推荐未被广泛认知的新物品，而用户满意度则直接反映了用户对推荐结果的接受程度。推荐系统在电商、音乐、电影、新闻等多个领域都有广泛应用。例如，电商平台如亚马逊会根据用户的购买历史和浏览行为推荐商品；音乐平台如Spotify通过分析用户的听歌习惯推荐歌曲。然而，推荐系统也面临着冷启动问题（新用户或新物品缺乏历史数据）、数据稀疏性问题以及隐私保护等挑战。未来，推荐系统将继续发展，结合深度学习、多模态数据和更高级的网络分析技术，以实现更智能、更精准的个性化推荐。同时，考虑用户实时动态、情境感知和社交影响等因素，推荐系统将进一步提升用户体验，促进人与信息的有效连接。

L. Lü et al. / Physics Reports 519 (2012) 1–49 9

Fig. 4. Illustration of a recommender system consisted of five users and four books. The basic information contained by every recommender system is

the relations between users and objects that can be represented by a bipartite graph. This illustration also exhibits some additional information frequently

exploited in the design of recommendation algorithms, including user profiles, object attributes and object content.

max

(u) = 2k(u), while the minimal coordination number is z

min

(u) = 2n for n(n − 1) < k(u) ≤ n

and z

min

(u) = 2n + 1

for n

< k(u) ≤ n(n + 1), with n some integer. Obviously, a local tree structure leads to maximal coordination number,

while the maximum overlap corresponds to the minimal coordination number. Therefore, they define the hyperedge density

as [86]:

(u) =

max

(u) − z(u)

max

(u) − z

min

(u)

, 0 ≤ D

(u) ≤ 1. (7)

The definition of hyperedge density for resources and tags is similar. Empirical analysis indicates a high clustering behavior

under both metrics [82,86]. The study of hypergraph for the collaborative tagging networks has just been unfolding, and how

to properly quantify the clustering behavior, the correlations and similarities between nodes, and the community structure

is still an open problem.

(iv) average distance: defined as the average shortest path length between two random nodes in the whole network.

3.3. Recommender systems

A recommender system uses the input data to predict potential further likes and interests of its users. Users’ past

evaluations are typically an important part of the input data. Let M be the number of users and let N be the number of

all objects that can be evaluated and recommended. Note that object is simply as a generic term which can represent books,

movies, or any other kind of consumed content. To stay in line with standard terminology, we sometimes use item which has

the same meaning. To make the notation more clear, we restrict to Latin indices i and j when enumerating the users and to

Greek indices α and β when enumerating the objects. Evaluation/rating of object α by user i is denoted as r

iα

. This evaluation

is often numerical in an integer rating scale (think of Amazon’s five stars)—in this case we speak of explicit ratings. Note that

the common case of binary ratings (like/dislike or good/bad) also belongs to this category. When objects are only collected

(as in bookmark sharing systems) or simply consumed (as in online newspaper or magazine without rating systems) or

when ‘‘like’’ is the only possible expression (as on Facebook), we are left with unary ratings. In this case, r

iα

= 1 represents

a collected/consumed/liked object and r

iα

= 0 represents a non-existing evaluation (see Fig. 4). Inferring users’ confidence

levels of ratings is not a trivial task, especially from the binary or unary ratings. Accessorial information about users’ behavior

may be helpful, for example, the users’ confidence levels can be estimated by their watching time of television shows and

with the help of this information, the quality of recommendation can be improved [95]. Even if we have explicit ratings, it

does not mean we know how and why people vote with these ratings—do they have standards of numerical ratings or they

just use ratings to present orders? Recent evidence [96] to some extent supports the latter ansatz.

The goal of a recommender system is to deliver lists of personalized ‘‘recommended’’ objects to its users. To this end,

evaluations can be predicted or, alternatively, recommendation scores can be assigned to objects yet unknown to a given

user. Objects with the highest predicted ratings or the highest recommendation scores then constitute the recommendation

list that is presented to the target user. There is an extensive set of performance metrics that can be used to evaluate the

resulting recommendation lists (see Section 3.4). The usual classifications of recommender systems is as follows [15]:

1. Content-based recommendations: Recommended objects are those with content similar to the content of previously

preferred objects of a target user. We present them in Section 4.2.3.

10 L. Lü et al. / Physics Reports 519 (2012) 1–49

Table 2

Recommendation process in a nutshell: to estimate the potential favorable opinion

of Carol about Casablanca, one can use the similarity of her with those of Alice.

Alternatively, one can note that ratings of Titanic and Casablanca follow a similar

pattern, suggesting that people who liked the former might also like the latter.

Alice Bob Carol

Titanic 5 1 5

2001: A Space Odyssey 1 5 2

Casablanca 4 2 ?

2. Collaborative recommendations: Recommended objects are selected on the basis of past evaluations of a large group of

users. An example is given in Table 2. They can be divided into:

(a) Memory-based collaborative filtering: Recommended objects are those that were preferred by users who share similar

preferences as the target user, or, those that are similar to the other objects preferred by the target user. We present

them in Sections 4 (Standard similarity-based methods) and 7 (methods employing social filtering).

(b) Model-based collaborative filtering: Recommended objects are selected on models that are trained to identify patterns

in the input data. We present them in Sections 5 (dimensionality reduction methods) and 6 (diffusion-based

methods).

3. Hybrid approaches: These methods combine collaborative with content-based methods or with different variants of other

collaborative methods. We present them in Section 8.4.

3.4. Evaluation metrics for recommendation

Given a target user i, a recommender system will sort all i’s uncollected objects and recommend the top-ranked objects.

To evaluate recommendation algorithms, the data is usually divided into two parts: The training set E

and the probe set

. The training set is treated as known information, while no information from the probe set is allowed to be used for

recommendation. In this section we briefly review basic metrics that are used to measure the quality of recommendations.

How to choose a particular metric (or metrics) to evaluate recommendation performance depends on the goals that the

system is supposed to fulfill. Of course, the ultimate evaluation of any recommender system is given by the judgment of its

users.

3.4.1. Accuracy metrics

Rating accuracy metrics. The main purpose of recommender systems is to predict users’ future likes and interests. A

multitude of metrics exist to measure various aspects of recommendation performance. Two notable metrics, Mean Absolute

Error (MAE) and Root Mean Squared Error (RMSE), are used to measure the closeness of predicted ratings to the true ratings.

If r

iα

is the true rating on object α by user i,

iα

is the predicted rating and E

is the set of hidden user–object ratings, MAE

and RMSE are defined as

MAE =



(i,α)∈E

iα

−

iα

|, (8)

RMSE =





(i,α)∈E

iα

−

iα

)



1/2

. (9)

Lower MAE and RMSE correspond to higher prediction accuracy. Since RMSE squares the error before summing it, it tends

to penalize large errors more heavily. As these metrics treat all ratings equally no matter what their positions are in the

recommendation list, they are not optimal for some common tasks such as finding a small number of objects that are likely

to be appreciated by a given user (Finding Good Objects). Yet, due to their simplicity, RMSE and MAE are widely used in the

evaluation of recommender systems.

Rating and ranking correlations. Another way to evaluate the prediction accuracy is to calculate the correlation between

the predicted and the true ratings. There are three well-known correlation measures, namely the Pearson product-moment

correlation [97], the Spearman [98] correlation and Kendall’s Tau [99]. The Pearson correlation measures the extent to which

a linear relationship is present between the two sets of ratings. It is defined as

PCC =



(

−

r)(r

−





(

−





−

, (10)

where r

and

are the true and predicted ratings, respectively. The Spearman correlation coefficient ρ is defined in the

same manner as the Pearson correlation, except that r

and

are replaced by the ranks of the respective objects. Similarly

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深度解析推荐系统：网络与信息过滤的综合概述

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