Semi-supervised discriminative preference elicitation for cold-start recommendation

Abstract

Recommendation for cold users is fairly challenging because no prior rating can be used in preference prediction. To tackle this cold-start scenario, rating elicitation is usually employed through an initial interview in which users are queried by some carefully selected items. In this paper, we propose a novel framework to mine the most valuable items to construct query set using a semi-supervised discriminative selection (SSDS) model. To learn a low dimensional representation for users in item space which can reflect their tastes to a large extent, the model incorporates category labels as discriminative information. To ensure the used labels reliable as well as all users considered, the model utilizes a semi-supervised scheme leveraging expert guidance with graph regularization. Experimental results on real-world dataset MovieLens demonstrate that the proposed SSDS model outperforms traditional preference elicitation methods on top-N measures for cold-start recommendation.

Full text

Semi-Supervised Discriminative Preference Elicitation for
Cold-Start Recommendation
Xi Zhang, Jian Cheng, Ting Yuan, Biao Niu, Hanqing Lu
National Laboratory of Pattern Recognition
Institute of Automation, Chinese Academy of Sciences
Beijing, China
{xi.zhang, jcheng, tyuan, bniu, luhq}@nlpr.ia.ac.cn
ABSTRACT
Recommendation for cold users is fairly challenging because
no prior rating can be used in preference prediction. To
tackle this cold-start scenario, rating elicitation is usually
employed through an initial interview in which users are
queried by some carefully selected items. In this paper, we
propose a novel framework to mine the most valuable items
to construct query set using a semi-supervised discriminative
selection (SSDS) model. To learn a low dimensional repre-
sentation for users in item space which can reflect their tastes
to a large extent, the model incorporates category labels as
discriminative information. To ensure the used labels reli-
able as well as all users considered, the model utilizes a semi-
supervised scheme leveraging expert guidance with graph
regularization. Experimental results on real-world dataset
MovieLens demonstrate that the proposed SSDS model out-
performs traditional preference elicitation methods on top-N
measures for cold-start recommendation.
Categories and Subject Descriptors
H.3.3 [Information Search and Retrieval]: Information
filtering; H.3.5 [On-line Information Services]: Web-
based services
General Terms
Algorithms, Experimentation
Keywords
Recommender Systems, Cold-Start, Preference Elicitation
1. INTRODUCTION
With the prevalence of massive web 2.0 applications, on-
line information for a large variety of items is growing rapid-
ly. Recommender systems, as important tools for informa-
tion filtering, have received success in many famous com-
mercial websites such as Amazon, Netflix and Last.fm. Most
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of these websites are based on Collaborative Filtering(CF)
which is a widely used recommendation approach. The basic
hypothesis of CF is that similar users have similar responses
to similar items. However, it is difficult to compute similari-
ty for users without any observed rating, thus CF would fail
in this cold-start scenario. In general, recommendation for
new users is quite challenging.
Existing studies on cold-start problem mainly focus on
three different strategies. The first strategy is extracting la-
tent features via auxiliary social relations instead of directly
exploiting CF [5, 3]. The second one is mapping addition-
al attributes from user profiles into a latent feature space
such that the lacked rating records can be compensated [1].
One limitation of these methods is that the user profile and
social connection are usually personal and not always avail-
able. Hence many recommender systems resort to an alter-
native strategy named Rating Elicitation which solicits user
preference by initial interview process on some items [4, 2,
6]. On the one hand, rating elicitation admits an overal-
l tendency that the more ratings requested from users the
better recommendations are. On the other hand, different
observed rating sets might lead to significantly different rec-
ommendation performance. Consequently, for the purpose
of constructing a most valuable query set to interview cold
users, the essential goal of preference elicitation is item s-
election by making full use of available information in the
system.
In this paper, our item selection model is developed on the
basis of the following two concerns. From the perspective
of elicitation mechanism, the qualified items in query set
should largely reflect user taste on diverse items of multiple
genres. The reason is natural. If the interests on categories
are captured, it would be much easier to comprehensively
understand user preference such as to return an appealing
item list. Moreover, from the perspective of user modeling,
since there is no extra information to describe user except
observed ratings, the rating vectors can be viewed as a sort
of representation for users. The problem of item selection
is converted to the problem of learning a low dimensional
representation which can embody user preference as much
as possible.
For above two considerations, we incorporate category la-
bels as discriminative information to guide the representa-
tive item selection. Particularly, the user category labels are
inferred by rating matrix and item category relations. Here
we only utilize the category labels of partial users(experts)
to make sure labels are trustworthy. In addition, to take
advantage of unlabeled user data, a graph regularization is

employed. Therefore, a Semi-Supervised Discriminative Se-
lection(SSDS) framework is proposed for preference elicita-
tion to integrate discriminative and semi-supervised compo-
nents by combining expert guidance and graph constraint
together.
As aforementioned, the output of SSDS model is the se-
lected representative items. Ratings on them are regarded as
new descriptions of users in a low dimensional space. Final-
ly, ranking scores are generated for cold users through these
learned user representations as well as the original rating
matrix.
2. SEMI-SUPERVISED DISCRIMINATIVE
SELECTION MODEL
2.1 Problem Statement
Let U={u1,··· , un}be the user collection and V=
{v1,··· , vm}be the item collection. Normally, tradition-
al elicitation model have an observed rating matrix R=
(r1,· · · ,rn)∈Rm×nas input. Due to high data sparsity in
a real world scenario, there exists large amounts of missing
value in each column ri, and most of the items are not pop-
ular. Thereby a candidate pool Vp={v1,··· , vmp}with
mp< m is constructed by filtering out the long-tailed item-
s. Then X= (x1,··· ,xn)∈Rmp×nis the submatrix of R
where each column xicorresponds to ratings user uigiven
to candidate pool Vpand is deemed as item representation
for ui.
Suppose there are kcategories in the given dataset, C=
{c1,··· , ck}is the category label set. Let Xl= (x1,··· ,xnl)
∈Rmp×nlwith nl< n denote rating matrix for labeled user-
s. Yl∈Rnl×kdenote user-category matrix where Yl(i, j) =
1 if user uiis interested in category cj, and 0 otherwise. A
toy example of data resources is depicted in Figure 1. Note
that the labeled user set Ulis a small subset of U, which con-
sists of only active users in each category and is regarded as
informative experts.
Based on above notations, the problem of item selection
can be stated as: given rating matrix Xfor warm user set
U, rating matrix Xland label matrix Ylfor expert set Ul,
the goal is to select most representative item set Vsfrom
candidate pool Vpby building an item selection model fas
f:{Vp;Xl,Yl,X} → {Vs}
2.2 Expert-Guided Selection
In order to capture preference for cold users, an intuitive
scheme is using most discriminative items as queries which
can express users’ attitude towards items of different cate-
gories, thus user category labels are embedded into our s-
election model. Concretely, a user who has a quantity of
ratings in certain category suggests that the user may be
interested in the category. Yet, there is no sufficient rating
for most users to determine their loved categories. Instead,
labels of experts are utilized as selection guidance, and thus
the correctness of used labels can be guaranteed.
With representation matrix Xland category label matrix
Ylfor experts predefined, the selection procedure can be for-
mulated as the following ℓ2,1-norm regularized least squares
regression problem:
min
P∥XT
lP−Yl∥2
F+α∥P∥2,1(1)
......... ...
Figure 1: A toy example of data resources. X and Xl
are representation matrices for all users and experts
respectively, Ylis expert label matrix, and xn+1 is
interview result related with cold user.
where P∈Rmp×kis a mapping matrix to find a low di-
mensional subspace such that the disagreement of predicted
preference over categories and their true labels is minimized.
αis the parameter of ℓ2,1-norm regularization. ∥P∥2,1is de-
fined as
∥P∥2,1=
mp

i=1 



k

j=1
P2(i, j) =
mp

i=1
∥P(i, :)∥2(2)
where ℓ2,1-norm constrains the sparsity of item dimension
and inclines to select items by jointly considering regression
task on kcategories.
2.3 Graph-Regularized Selection
However, the supervised setting of selection model might
suffer overfitting problem for unlabeled data because of mere-
ly taking ratings of experts into account. To overcome this
limitation, unlabeled users should be concerned. To this
end, we propose a semi-supervised method to integrate graph
regularization into the above selection model, which is pre-
sented as
min
P∥XT
lP−Yl∥2
F+α∥P∥2,1
+β
i
i′
S(i, i′)∥PTxi−PTxi′∥2
2
(3)
where βis a weight to control the strength of graph regu-
larization. In particular, we construct an undirected graph
Gwith adjacency matrix Sfor both labeled and unlabeled
users. The nodes in Gcorrespond to user representation
{x1,· · · ,xn}. The adjacency matrix Sis computed by co-
sine similarity based on the following rule,
S(i, i′) = cos(xi,xi′),if xi′∈ N (xi) or xi∈ N (xi′)
0,otherwise.
(4)
where N(xi) denote the nearest neighbor set of xi. The
assumption under graph regularization in Eq.(3) is that if
two users are similar in representation space, their category
labels should also be similar.
Using Laplacian matrix LS=DS−Sin Eq.(3) where
DS(i, i) = jS(i, j) is a diagonal matrix, the SSDS model
combined expert guidance with graph regularization can be
finally written as
min
P∥XT
lP−Yl∥2
F+α∥P∥2,1+βtr(PTXLSXTP)(5)

2.4 Optimization of SSDS Algorithm
To optimize the unified objective function in Eq.(5), we
convert the first term into tr(·) and discard the constant
term tr(YT
lYl). The minimization problem becomes
J(P) = tr(PTGP −2HP) + α∥P∥2,1(6)
where G=XlXT
l+βXLSXTand H=YT
lXT
l. To obtain
the optimal solution for P, the derivative of the objective
function in Eq.(6) is set as ∂J(P)
∂P= 0. Then Pis presented
as
P= (G+αDP)−1HT(7)
where DPis a diagonal matrix with DP(i, i) = 1
2∥P(i,:)∥2. It
can be proved that G+αDPis a positive definite matrix,
thus the inverse in Eq.(7) exist. Since DPis dependent to P,
Pand DPcan be updated alternatively until convergence.
The detailed optimization algorithm for SSDS is described
in Algorithm 1.
Algorithm 1 The SSDS Algorithm
Input: {Vp,Xl,Yl,X, α, β, K }
Output: Vsincluding Kmost representative items
1: Construct Gby XlXT
l+βXLSXT;
2: Construct Hby YT
lXT
l;
3: Set t= 0 and initialize DPtas an identity matrix;
4: loop
5: Compute Pt+1 = (G+αDPt)−1HT;
6: Update the diagonal matrix DPt+1 with the i-th
diagonal element is 1
2∥Pt+1(i,:)∥2;
7: t=t+ 1;
8: end loop until convergence
9: Sort each item according to ∥P(i, :)∥2in descending or-
der and select top-K ranked ones.
3. COLD-START RECOMMENDATION
Once representative items are selected, for a new user, an
interview process is conducted by offering questions with the
learned items aiming to elicit preference efficiently. Further-
more, to recommend items, a ranking estimation method is
introduced to predict possible rankings towards the whole
item set V.
Without loss of generality, a new user can be denoted as
un+1. After interview process, one new column xn+1 is gen-
erated. Next, we place emphasis on utilizing representative
item set Vs, observed rating matrix Rand representation
vector xn+1 in cold-start recommendation. Inspired by low-
rank matrix factorization, a global optimal formulation is
developed which solves a loading matrix W∈RK×mby
min
w
1
2∥R−WT
X∥2
F+λ
2∥W∥2
F(8)
where 
X=X(Vs,:) is new matrix description for user set U
based on selected items Vs. Similarly, un+1 also has 
xn+1.
Accordingly, the solution of Wis given by
W∗= ( 
X
XT+λI)−1
XRT(9)
Where I∈RK×Kis an identity matrix. When there is a new
user, the personalized ranking score is eventually computed
by rn+1 = (W∗)T
xn+1. Notice that the loading matrix
can be pre-computed and thus our model is consistent with
online-updating principle of real-world systems.
Table 1: Comparison of Different Selection Strate-
gies for Cold-Start Recommendation(nl= 50, β = 0.1)
Methods Query# MAP NDCG Prec@5
random
K=10
0.0669 0.0465 0.0445
popular 1 0.3119 0.2027 0.1950
popular 2 0.3397 0.2136 0.2023
k-medoids 0.1971 0.1436 0.1369
SSDS 0.3516 0.2272 0.2151
random
K=20
0.1834 0.1268 0.1204
popular 1 0.3479 0.2208 0.2089
popular 2 0.3352 0.2120 0.2023
k-medoids 0.2692 0.1892 0.1803
SSDS 0.3816 0.2469 0.2320
random
K=30
0.2109 0.1467 0.1381
popular 1 0.3668 0.2302 0.2161
popular 2 0.3414 0.2140 0.2022
k-medoids 0.3454 0.2392 0.2290
SSDS 0.4122 0.2701 0.2533
4. EXPERIMENTS
4.1 Experiment Design
In order to evaluate how SSDS behaves on user cold-start
recommendation, we conduct experiments using a bench-
mark dataset MovieLens. The dataset includes one million
observed ratings ranged from 1 to 5 points which are given
by 6,040 users to 3,952 movies. Besides, category informa-
tion about movies is available. To simulate cold users, 20%
users are randomly picked from the whole user set. Then
to test the cold-start recommendation results, an 80-20 split
is used for each cold user, where 80% ratings are randomly
chosen as the response set to answer queries during inter-
view while the rest of 20% ratings is test set. The experi-
ments are set up as 5-fold cross-validation. The parameter
λin Eq.(8) and the size of the nearest neighbor set are re-
spectively determined on MovieLens data as 0.1 and 10 by
cross-validation. We also choose items owned more than 500
ratings to construct the candidate pool Vp.
4.2 Evaluation Metrics
After SSDS-based preference elicitation, ranking scores
are predicted. The performance can be measured by three
classical evaluation metrics in top-N recommendation:
Mean Average Precision(MAP). For each user, Av-
erage Precision(AP) is first defined as
AP(u) = N
i=1 prec(i)×pref(i)
# of preferred items
where prec(i) is precision and pref(i) is a binary preference
indicator at ranked position i. MAP is computed based on
AP by the following equation
MAP = 1
|U| 
u∈U
AP(u)
Normalized Discounted Cumulative Gain(NDCG).
For a ranked list of Nitem, NDCG is computed by
NDCG = 1
IDCG ×
N

i=1
2pref(i)−1
log2(i+ 1)
where IDCG is produced by a perfect ranking algorithm.

10 20 30
0.3
0.33
0.36
0.39
0.42
K
MAP
nl=20
nl=50
nl=200
nl=500
10 20 30
0.2
0.22
0.24
0.26
K
NDCG
nl=20
nl=50
nl=200
nl=500
Figure 2: Performance Variation of SSDS with re-
spect to expert number nland query number K
Precision. If an item is contained in the test set, we
consider that it is correctly predicted. Prec@N evaluates
the ratio of correctly predicted items in top-N lists. In our
work, we report results for Prec@5.
4.3 Results and Analysis
To demonstrate the effectiveness of the proposed SSDS
model, we compare it with several traditional query selection
methods for cold-start problem including random, popular,
k-medoids strategies. It is worth to notice that we combine
the same cold-start recommendation approach introduced in
Section 3 with all above selection methods. The experimen-
tal results are shown in Table 1. To make a fair comparison,
there are two different popular strategies used here. The first
one(popular 1) is a query list which is comprised of popular
items extracted from multiple categories to make sure diver-
sity of query list, while the other one(popular 2) is normal
popular set without considering category information.
Because rating elicitation aims to minimize user interac-
tion costs at the same time improving recommendation ac-
curacy, the length of the interview is the pivotal parameter
in our work. To avoid boring interviews, we vary the query
number Kfrom 10 to 30. The overall trend of recommen-
dation correctness along with the interview process can be
observed.
For all compared methods, the performance increases when
Kis expanded. This phenomenon confirms a basic fact: the
more ratings are elicited from the users, the more effective
the recommendations are. On the other hand, these method-
s are not equally efficient for learning user preference. Specif-
ically, two points could be inferred by comparing the per-
formance of these methods: 1. Random strategy performs
severely worse than other strategies, which empirically prove
the necessity of designing an appropriate selection model.
2. SSDS model yields best performance under all of the e-
valuation conditions, which verify that our semi-supervised
discriminative selection framework can do benefits on iden-
tifying more informative items than other methods and then
boost cold-start recommendation accuracy.
Additionally, to assess influence of the two fundamental
components of SSDS: expert guidance and graph regulariza-
tion, we study the impact of parameters. Correspondingly,
the two important parameters of SSDS are the number of
experts nland weight of regularization term β. Thereby,
we analyze each of them by keeping the other one fixed.
Firstly, fixed βas β= 0.1 and given the query number
K∈ {10,20,30}, the performance variation with respect
to nlis shown in Figure 2. When nlis increasing, both
MAP and NDCG first increase until reach peaks and then
drop. The main reason behind this observation is: At the
10 20 30
0.2
0.25
0.3
0.35
0.4
K
MAP
β=0
β=0.001
β=0.01
β=0.1
β=1
10 20 30
0.1
0.15
0.2
0.25
K
NDCG
β=0
β=0.001
β=0.01
β=0.1
β=1
Figure 3: Performance Variation of SSDS with re-
spect to graph weight βand query number K
beginning, adding more labeled users can provide more dis-
criminative information so as to help us finding a better user
representation in item space. Nevertheless, with the num-
ber of labeled users growing, some untrustworthy labels are
mixed into discriminative information and finally result in
the accuracy declining.
Secondly, fixed nlas nl= 50 and still given the query
number K∈ {10,20,30}, the performance variation with
respect to βis illustrated in Figure 3. βis varied from the
range {0,0.001,0.01,0.1,1}where larger βenhance the effect
of graph constraint on users who are similar in rating behav-
iors. From the figure we can see that, even though it achieves
the best point when βis at different value, it is clearly that
the performance upgrades on the basis of the model without
graph regularization(β= 0). Especially, the improvement is
significantly when the interview is short(K= 10).
5. CONCLUSIONS
In this paper, we propose a novel query selection frame-
work for preference elicitation. By using semi-supervised
and discriminative information, our model tends to select
representative item set which can describe user preference
on diverse categories comprehensively. Experimental results
on benchmark movie rating dataset show that the proposed
query selection model produces more accurate recommenda-
tion for cold users than competitors.
6. ACKNOWLEDGEMENT
This work was supported by 973 Program under Project
2010CB327905, by the National Natural Science Foundation
of China under Grant No. 61170127 and 61070104.
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