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Collaborative Denoising Auto-Encoders

for Top-N Recommender Systems

Yao Wu Christopher DuBois Alice X. Zheng Martin Ester

Simon Fraser University Dato Inc. Dato Inc. Simon Fraser University

Burnaby, BC, Canada Seattle, WA, USA Seattle, WA, USA Burnaby, BC, Canada

wuyao[email protected] [email protected] alicez@dato.com [email protected]

ABSTRACT

Most real-world recommender services measure their performance

based on the top-N results shown to the end users. Thus, advances

in top-N recommendation have far-ranging consequences in prac-

tical applications. In this paper, we present a novel method, called

Collaborative Denoising Auto-Encoder (CDAE), for top-N recom-

mendation that utilizes the idea of Denoising Auto-Encoders. We

demonstrate that the proposed model is a generalization of several

well-known collaborative ﬁltering models but with more ﬂexible

components. Thorough experiments are conducted to understand

the performance of CDAE under various component settings. Fur-

thermore, experimental results on several public datasets demon-

strate that CDAE consistently outperforms state-of-the-art top-N

recommendation methods on a variety of common evaluation met-

rics.

Categories and Subject Descriptors

H.3.3 [Information Search and Retrieval]: Information Filtering

Keywords

Recommender Systems; Collaborative Filtering; Denoising Auto-

Encoders

1. INTRODUCTION

In recent years, recommender systems have become widely uti-

lized by businesses across industries. Given a set of users, items,

and observed user-item interactions, these systems can recommend

other items that the users might like. Personalized recommendation

is one of the key applications of machine learning in e-commerce

and beyond. Many recommendation systems use Collaborative Fil-

tering (CF) methods to make recommendations. In production, rec-

ommender systems are often evaluated based on the performance of

the top-N recommendations, since typically only a few recommen-

dations are shown to the user each time. Thus, top-N recommenda-

tion methods are of particular interest.

In this paper, we present a new model-based collaborative ﬁlter-

ing (CF) method for top-N recommendation called Collaborative

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WSDM’16, February 22–25, 2016, San Francisco, CA, USA.

 2015 Copyright held by the owner/author(s). Publication rights licensed to ACM.

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DOI: http://dx.doi.org/10.1145/2835776.2835837

Denoising Auto-Encoder (CDAE). CDAE assumes that whatever

user-item interactions are observed are a corrupted version of the

user’s full preference set. The model learns latent representations

of corrupted user-item preferences that can best reconstruct the full

input.

In other words, during training, we feed the model a sub-

set of a user’s item set and train the model to recover the whole

item set; at prediction time, the model recommends new items to

the user given the existing preference set as input. Training on cor-

rupted data effectively recovers co-preference patterns. We show

that this is an effective approach for collaborative ﬁltering.

Learning from intentionally corrupted input has been widely stud-

ied. For instance, Denoising Auto-Encoders [24] train a one-hidden-

layer neural network to reconstruct a data point from the latent rep-

resentation of its partially corrupted version. However, to our best

knowledge, no previous work has explored applying the idea to rec-

ommender systems.

CDAE generalizes several previously proposed, state-of-the-art

collaborative ﬁltering models (see Section 3.2). But its structure

is much more ﬂexible. For instance, it is easy to incorporate non-

linearities into the model to achieves better top-N recommendation

results. We investigate the effects of various choices for model

components and compare their performance against prior approaches

on three real world data sets. Experimental results show that CDAE

consistently outperforms state-of-the-art top-N recommendation meth-

ods by a signiﬁcant margin on a number of common evaluation

metrics.

Our contributions can be summarized as follows:

• We propose a new model CDAE, which formulates the top-

N recommendation problem using the Auto-Encoder frame-

work and learns from corrupted inputs. Compared to related

methods, CDAE is novel in both model deﬁnition and objec-

tive function.

• We demonstrate that CDAE is a generalization of several

state-of-the-art methods but with a more ﬂexible structure.

• We conduct thorough experiments studying the impact of the

choices of different components in CDAE, and show that

CDAE outperforms state-of-the-art methods on three real

world data sets.

The rest of the paper is organized as follows. Section 2 provides

the problem deﬁnition, background, and useful notations. Section 3

describes our proposed model and learning algorithm in detail. We

We follow the typical top-N recommendation setup and consider

only user-item interaction data in this paper. Handling of additional

data, such as user/item features and contextual information, is left

as future work.

153

discuss related work on applying neural network methods to recom-

mender systems in Section 4. Experimental results for the compo-

nents analysis and performance comparisons are presented in Sec-

tion 5. We conclude with a summary of this work and discussion

of future work in Section 6.

2. PROBLEM DEFINITION

Given a set of users U = {u = 1, ..., U }, a set of items I =

{i = 1, ..., I}, and a log of the users’ past preferences of items

O = (u, i, y

), our goal is to recommend to each user u a list of

items that will maximize her/his satisfaction. In many cases, the

log contains only implicit feedback where all the y

are 1; the rest

of the triples are assumed missing. We use

O to denote the set of

unobserved, missing triples, and O

an augmented user-item pairs

dataset that includes some data sampled from

O. (We discuss O

in more detail in the subsection on objective functions.) Let O

denote the set of item preferences in the training set for a particular

user u, and

the unobserved preferences of user u. Items in

are the candidates to be recommended to user u. The goal of the

recommender is to pick for each user u a subset of items from the

candidate set, the predicted values of which are most likely to be 1.

In some cases, y

are numeric ratings in the range of, say, [1, 5]

or binary values {0, 1}. For simplicity, we only consider the case

of implicit feedback in this paper. Numeric ratings can be handled

with slight modiﬁcations to our method.

In the rest of the paper, we use u to index a user, and i and j

to index items. Vectors and matrices are denoted by bold symbols,

where symbols in lower case (e.g., x) represent vectors and sym-

bols in upper case (e.g., X) represent matrices. Unless stated dif-

ferently, x

also represents a vector where i is used to distinguish

different vectors. We denote the i-th row of matrix X by X

and

its (i, j)-th element by X

2.1 Overview of Model-based Recommenders

Most machine learning models can be speciﬁed through two com-

ponents: model deﬁnition and objective function during training.

The model deﬁnition formulates the relationship between the in-

put (e.g., user ids, item ids, interactions, other features, etc.) and

output (ratings or implicit feedback of items). The objective func-

tion is what the training process optimizes to ﬁnd the best model

parameters.

Recommender Models

In general, recommender models are deﬁned as

ˆy

= F

(u, i), (1)

where ˆy

is the predicted preference of user u on item i, and θ

denotes the model parameters we need to learn from training data.

Different choices of the function F

correspond to different as-

sumptions about how the output depends on the input. Here we

review 4 common recommender models.

Latent Factor Model (LFM). LFM models the preference ˆy

the dot product of latent factor vectors v

and v

, representing the

user and the item, respectively [9, 17].

ˆy

= F

LF M

(u, i) = v

(2)

In addition, hierarchical latent factor models [1, 32] and the factor-

ization machine [14] can model interactions between user or item

side features.

To simplify notation, we assume that the latent factors are padded

with a constant to model the bias.

Similarity Model (SM). The Similarity model [8] models the user’s

preference for item i as a weighted combination of the user’s pref-

erence for item j and the item similarity between i and j. It is a

natural extension of an item-based nearest neighbor model. The

difference is that SM does not use predeﬁned forms of item simi-

larity (e.g., Jaccard, Cosine). Instead, it learns a similarity matrix

from data [12].

ˆy

= F

(u, i) =

j∈O

\{i}

· S

(3)

Factorized Similarity Model (FSM). The problem with the Sim-

ilarity Model is that the number of parameters is quadratic in the

number of items, which is usually impractical. A straightforward

solution is to factorize the similarity matrix into two low rank ma-

trices [8, 7].

ˆy

= F

F SM

p,q

(u, i) =





j∈O

\{i}

· p





(4)

LFSM (LFM+FSM). The above models can also be combined.

For example, combining LFM and FSM results in the model SVD++

[8], which proved to be one of the best single models for the Netﬂix

Prize.

ˆy

= F

LF SM

p,q

(u, i) =





j∈O

\{i}

· p

+ p





(5)

Objective Functions for Recommenders

Objective functions for training recommender models can be roughly

grouped into two groups: point-wise and pair-wise.

Pair-wise ob-

jectives approximates ranking loss by considering the relative order

of the predictions for pairs of items. Point-wise objectives, on the

other hand, only depend on the accuracy of the prediction of in-

dividual preferences. Pair-wise functions are usually considered

to be more suitable for optimizing top-N recommendation perfor-

mance. However, as we demonstrate in our experiments, this is not

necessarily the case for all data sets.

Regardless of the choice of a pair-wise or point-wise objective

function, it is critical to properly take into account unobserved feed-

back within the model. Models that only consider the observed

feedback fail to account for the fact that ratings are not missing at

random. These models are not suitable for top-N recommenders

[13, 23].

Let `(·) denote a loss function and Ω(θ) a regularization term

that controls model complexity and encodes any prior information

such as sparsity, non-negativity, or graph regularization. We can

write the general forms of objective functions for recommender

training as follows.

Point-wise objective function.

(u,i)∈O

point

, ˆy

) + λΩ(θ). (6)

Here O

denotes an augmented dataset that includes unobserved

user-item pairs. The problem with using only observed user-item

pairs is that, when users provide only implicit “like”s without ex-

plicit ratings, all the observed values y

are equal to 1. In this case,

directly optimizing the point-wise objective function over O leads

Some models use list-wise objective functions [28, 22], but they

are not as widely adopted as point-wise and pair-wise objectives.

154

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