Exploiting Data Sparsity in Secure Cross-Platform Social Recommendation
Authors: Jamie Cui
Chaochao Chen
Lingjuan Lyu
Carl Yang
Wang Li
Venue: NeurIPS 2021 Poster (2021)
Keywords: Social Recommendation
secure machine learning
MPC
PIR

Abstract: Social recommendation has shown promising improvements over traditional systems since it leverages social correlation data as an additional input. Most existing work assumes that all data are available to the recommendation platform. However, in practice, user-item interaction data (e.g.,rating) and user-user social data are usually generated by different platforms, and both of which contain sensitive information.  Therefore, "How to perform secure and efficient social recommendation across different platforms, where the data are highly-sparse in nature" remains an important challenge. In this work, we bring secure computation techniques into social recommendation, and propose S3Rec, a sparsity-aware secure cross-platform social recommendation framework. As a result, our model can not only improve the recommendation performance of the rating platform by incorporating the sparse social data on the social platform, but also protect data privacy of both platforms. Moreover, to further improve model training efficiency, we propose two secure sparse matrix multiplication protocols based on homomorphic encryption and private information retrieval. Our experiments on two benchmark datasets demonstrate the effectiveness of S3Rec.

Exploiting Data Sparsity in Secure Cross-Platform Social Recommendation
Jamie Cui', Chaochao Chen Lingjuan Lyu', Carl Yang", and Li Wang'
Ant Group
Zhejiang University
Sony Al
Emory University
"Corresponding author, email: zjuccezzj.. edu.
Abstract
Social recommendation has shown promising improvements over traditional sys- tems since it leverages social correlation data an additional input. Most existing works assume that data are available to the recommendation platform. However, in practice, user-item interaction data (e.g., rating) and aser-user social data usually generated by different platforms, both which contain sensitive infor- mation. Therefore, How to perform secure and efficient social recommendation across different platforms, where the data are highly-sparse in nature remains an important challenge. In this work, we bring secure computation techniques into social recommendation, and propose Ree, a sparsity-awar secure cross- platform social recommendation framework. As result, Rec not only improve the recommendation performance of the rating platform by incorporating the sparse social data the social platform, but also protect data privacy of both platforms. Moreover, to further improve model training efficiency, we propose two secure sparse matrix multiplication protocols based on homomorphic encryption and private information retrieval. Our experiments on two benchmark datasets demon- strate that S Ree improves the computation time and communication size of the state-of-te state-of-the-ee the-hht-t art model by about 40x and 423x in average, respectively.
Introduction
The recent advances of social recommendation have achieved remarkable performances in recommen- dation tasks [2, 288. Unlike traditional methods, social recommendation leverages user-item rating data (e.g. from Netflix) with user-user social data (e.g. from Facebook) to facilitate model training. The intuition behind this setup is that Facebook's social data is much better than Netflix's social data in both quantity and quality, and those social data Facebook can help improve Netflix's recommendation performance. However, the cross-platform nature, the high sparsity and sensitivity of recommendationsscciaa data make social recommendation hard-to-deploy in the real world [5). In summary, the main problem we are facing is,
How perform secure and efficient social recommendation across different platforms, where the data are highly-sparse in nature?
Specifically, we focus on the problem of collaborative social recommendation in the two-party model, where one party (denoted as Pσ) a rating platform that holds user-item rating data, and the other party (denoted as Pi) is a social platform that holds user-user social data. We also assume that the adversaries are ceni-honest, which is commonly used in the secure computation literature [9] That
35th Conference on Neural Information Processing Systems (NcurIPS 2021).

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is to say, the adversary will not deviate from the pre-defined protocol, but will try to learn as much information as possible from its received messages.
Choices of privacy enhancing techniques. Currently, many anonymization techniques have been used in publishing recommendation data, such as k-anonymity and differential privacy [I.. On the other hand, cryptographic methods like secure multiparty computation (MPC) [T] and homomorphic encryption (HE) have been proposed to enable calculation on the protected data. Since k k-anonymity has been demonstrated risky in practice (e.g., the re-identification attack on Netflix Prize dataset (22). and differential privacy introduces random noises to the dataset which eventually affects model accuracy [O), we consider they are not the ideal choice for our framework. Instead, we choose combination of cryptographic tools (i.e., MPC and HE, but mainly MPC) which allows multiple parties to jointly compute a function depending on their private inputs while providing security guarantees.
Choices of social recommendation model. In literature, many social recommendation models have been proposed 88 [8 27 using matrix factorization or neural networks. Existing MPC-based neural network protocols [2 29 usually suffer from accuracy loss and inefficiency due to their approximation of non-linear operations. Especially for the case of social recommendation, training data could exceed to millions, and this makes NN-based model a less ideal choice. Therefore, choose the classic social recommendation model, Soreg [18. as a typical example, and present how to build secure and efficient version of Soreg under cross-domain social recommendation scenario.
Dealing with sparse data in secure machine learning. One important property of social recom- mendation data is its high sparsity. Take LibraryThing dataset (32 for example, its social matrix density is less than 0.02%. Recently. Schoppmann et al. introduced the ROOM framework [26) for secure computation over sparse data. However, their solution only works on column-sparse or row-sparse data, and in addition, it requires secure matrix multiplication protocol (for instance, based on Beaver's multiplication triple). Chen et al. proposed a secure protocol for a sparse matrix multiplies dense matrix (6). which combines homomorphic encryption and secret sharing, but it only works well when the dense matrix is small. Different from their work, in this paper, we propose a PlR-based matrix multiplication which does not reply on pre-generated correlated randomness.
Our framework. In this paper, we propose Ree, a sparsity-aware secure cross-platform social recommendation framework. Starting with the classic Soreg model, we observe that the training process of Soreg involves two types of calculation terms: (1) the rating term which could be calculated by Po locally, and (2) the social term which needs to be calculated by Po and P1 collaboratively. Therefore, the key Rec designing secure and efficient protocols for calculating the social term.
To begin with, we first let both parties perform local calculation. Then both parties invoke a secure social term calculation protocol and let Po finally receive the plaintext social term, and update the model accordingly. In this way, the security of our protocol relies significantly on the secure social term calculation protocol (for simplicity, we refer this protocol as the 'ST-MPC' protocol), and propose a secure instantiation and prove its security. Similarly, the efficiency of ReRec relies heavily on the performance of ST-MPC, and at the core, it relies on the efficiency of matrix multiplication protocol. The naïve secure matrix multiplication protocol is traditionally evaluated through Beaver's triples B., and has Okkm² asymptotic communication complexity, where l is the dimension of latent factors and m is the number of users. To improve the communication efficiency, we propose two secure sparse matrix multiplication protocols for ST-MPC, based on two sparsity settings: (I) insensitive sparsity, which is weaker variant of matrix multiplication where we assume both parties know the locations of non-zero values in the sparse matrix, and (2) sensitive sparsity, which is also weaker variant of matrix multiplication, but stronger than (1), and we assume 'only' the number of zeros is public. Nevertheless, we present secure constructions for MatrixMul in both cases by leveraging two cryptography primitives called Private Information Retrieval (PIR) [I] and Homomorphic Encryption (HE) [24). PIR can hide the locations of the non-zero values in the sparse matrix while HE enables additions and multiplications on ciphertexts. To this end, we drop the communication complexity of secure MatrixMul to ((k)) for the insensitive sparsity case and to ((kkm) for the sensitive sparsity case, where a denotes the density of user social matrix.
Summary of our experimental results. We conduct experiments on two popularly used dataset, i.e. Epinions [19 and LibraryThing (32] The results demonstrate that (1) S Rec achieves the same

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performance as existing social recommendation models, and (2) Ree improves the computation time and communication size the state-of-the-ar (SeSoRec) by about 40 and 423x in average.
Contributions. We summarize our main contributions below: (1) We propose ReR, privacy- preserving cross-platform social recommendation framework, which relies on a general protocol for calculating the social term securely: (2) We propose two secure sparse matrix multiplication protocols based on different sparsity visibility, ie.. insensitive sparsity and sensitive sparsity. We prove that both protocols are secure under semi-honest adversaries; and (3) We empirically evaluate the performance of ReR on benchmark datasets.
2 Tools and Recommendation Model
Notation.
We use [n] to denote the set {1, n), and [x| to denote the bit length of x. In terms of MPC, denote secret shared value of in NN as [-:], where N is positive integer. Also, let
[or]o denote Po's share, and [>r]] denote Pi 's share, where [x] = [x]o + [<]] E NN_ We also use
denote the assignment of variables, e.g., 27
2.1 Tools
In this section, we introduce several secure computation tools used in our work.
Multi-Party Computation (MPC). MPC is cryptographic tool which enables multiple par- ties (say, n parties) to jointly compute function f(, Tn.)........ where 2; is i-th party's 's private in- put. MPC protocols ensure that, at the end of the protocol, parties eventually learn nothing but their own input and the function output. MPC has been widely-used in secure machine learn- ing systems such PrivColl [31] and CrypT- Flow [15]. most of which support a wide range of linear (e.g. addition, multiplication) and non- linear functions (e.g. equality test, comparison). Here, present three popular MPC protocols (addition, multiplication, and matrix multiplica- tion), which will later in our protocol,
MatrixMul(X, Y)
(Offline) Generate km Beaver's triples
1: Vas, E X, Po invokes [[r,,]] + Shr(a:.)
2: Vy.. Y, Pi invokes [v.s] < Shr(w
foreach i E [k]..j [m]] let [[.,]] = 0,
4: foreach a [m]] E [m].
5: |tmp] + Mul[[ [yne])
6: |a.,] + Add[[tmp]] (2s.))
7: endfor
8: endfor
return [2]
Add [ı]]: Take two shares as inputs from both parties, Poc locally calculate and return [x]b [y]s.
Figure 1: Secure matrix multiplication protocol, where Shr a secret sharing algorithm.
Mul([=]] [v]): Take shares as inputs from both parties, then evaluate using Beaver's Triples 3
Homomorphic Encryption (HE) scheme. HE is essentially a specific type of encryption scheme which allows manipulation encrypted data. More specifically, HE involves key pair (pk, sk), where the public key pk is used for encryption and the secret key sk is used for decryption. In this work, use an additive HE scheme (i.c., Paillier (24) which allows the following operations:
Encpk(ar) + Encpx(y): addition between two ciphertexts, returns Encpk (x + y);
Enc,k(x)) @ yt multiplication between ciphertext and plaintext, returns EEncpk (x y).
Private Information Retrieval (PIR). Now, we introduce single-server PIR 1 In this setting, we assume there is server and a client, where the server holds database DB fdi,....dy with elements, and client wants to retrieve DB, while hiding the query index from the server. Roughly, PIR protocol consists of tuple of algorithm (PIR. Quer,, PIR. ReR.Resp,,,e, PIR Extract). First, the client generates query <- PIR. PIR. Query(i) from an index and then sends query g to the server. The server then is able to generate response +- PIR. Rew.RnseepDnD.... q) based on the query and

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database DB, and returns 7 to the client. Finally, the client extracts the result from server's 's response DB, PIR.Extract(r).
Client
Server
q f PIR.Query(i)
PIR. Response(DDD
DB, PIR.Extract(r)
Figure 2: An overview of Private Information Retrieval (PIR).
2.2 Recommendation model
Recall that we assume there are two platforms, rating platform Po. and a social platform P1. We assume Po holds a private rating matrix R E Rmxx,, and P1 holds private user social matrix S Rmxxm where and m denote the number of items and their common users, respectively, Also, we denote the user latent factor matrix U RR and item latent factor matrix V E Rkxn where & is the dimension of latent factors. We further define an indication matrix I m where 1 denotes whether user has rated item
Existing work [27] summarizes factorization based social recommendation models as the combination of "basic factorization model" and "social information model". To date, different kinds of social information models have been proposed [I8] [4] and their common intuition is that users with social relations tend to have similar preferences. In this work, we focus on the classic social recommendation model, i.e., Soreg 18] which aims to learn U and by minimizing the following objective function,
Tas (ris
u. Vv
V.
uu. u. 11
=1
1=1
J=1
(1) where the first term is the basic factorization model, the last term is the social information model, and the middle two terms are regularizers, || 1 & is the Frobenius norm, À and y are hyper-parameten If we denote
m as diagonal matrix with diagonal element dp = >/ 8b,c and mm
as a diagonal matrix with diagonal element e; Σm Sb,i. The gradients of L in Eq. with respect to U and V are,
OC π
(R--U')) 01 +AU
2 UDD" + -US"
Rating term: compated by Po locally
Social term: computed by and collaboratively
ac = u ((- (R-UTV) o1 +
0V
Rating term: computed by locally
3
Framework
We summarize our proposed Re framework in Figure To begin with, we assume that party Po holds the rating matrix and P1 holds the social matrix S. At first, Po randomly initializes U + R&xm and V 4 V Rxn, Then, for each iteration (while the model dose not coverage), we let Po and P1 jointly evaluate the social term defined in Eq 2 Po then locally calculates the rating term in Eq 2 and Eq 3. well as OC/OU and aL/Ov. Party Po then locally updates U and V accordingly and ends the iteration.
Communication efficiency. In our framework, the only communication between two parties occurs in the ST-MPC protocol. Since we choose additive secret sharing, the Add protocol contains only local computation, we claim that the communication efficiency of Re significantly relies on the efficiency of matrix multiplication protocol. We give popular MatrixMul protocol in Figure

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Global Parameter: Regularization strength and learning rate
Input: Private rating matrix R from platform Po. private social matrix S from platform P1.
Output: Platform Po receives the user latent matrix and item latent matrix
Platform Po initializes U and
ST-MPC(> U, E.
while not coverage,
1: Roo + MatrixMul(7U/2.) E²)
: Po and P1 securely calculate social term f-
4: Po locally computes the rating terms
2: [R]] + MatrixMul(-qU.S"
5: Po locally updates U by U + U 0./0/0
[R] [do([ [R.])
6: Po locally updates V by V +- V 0C/OVV
return Rec([R]] to
endwhile
return
platform Pb
Our proposed Ree framework, where MatrixMul stands for secure matrix multiplication protocol, Add stands for secure add protocol, Rec stands for reconstruction protocol for secret sharing.
Figure 3:
and analyze its efficiency in our framework. The protocol in Figure | requires km log2 N bit online communication, where m the number of users and k is the dimension of latent factors. As for the usual case where the number of users is 10*, k 10, and log,v 64, one invocation of MatrixMul protocol would have a total communication of around 7.4GB. Considering 100 iterations of framework, this leads to 1491GB communication, which is impractical. Fortunately, the social matrices (D, E, and S) are highly sparse in social recommendation. In the following section, we propose PIR-based sparse matrix multiplication protocol with better communication efficiency.
3.1 Secure sparse matrix multiplication
Essentially, any matrix could be represented by value vector and location vector, where the value vector contains all non-zero values and the location vector contains locations of those values. That is, sparse matrix Y E Rm can be represented by pair of vectors (ly E No Uy RR), where t is the number of non-zero values in Y.
Dense-sparse matrix multiplication. Considering the case where X E & is the dense matrix from Po and Y mm the sparse matrix from Pl. Now we consider the following two cases.
filter with by
T2
(
Case I: insensitive sparsity, i.e., insensitive ly and sensitive Vy. This refers to the case where the locations zero values are public contain sensitive information. Take the social matrices (D and E) for example, both of them are diagonal, and thus the location vector is insensitive while the value vector is still sensitive.
Many Mul() and Add()
T4
T2
P
35.
Our protocol mainly works follows. First, Po and P: parse X and Y into two tables Тe and Tg separately, where the value set
filter with
Figure 4: Matrix multiplication
of each bin in T. is subset of one row in X, that is, (i) C Ti Similarly, bin set Ty is a subset of one column Y, (1) Vn,i. The intuition behind is to use bins to contain only necessary values needed caleulate the output value (which means filter out the zero multiplies in each bin). Take the first bin for example (that is, T₂ (0) and (0)), for j E [m], (o) contains all Tog where Vj.0 is non-zero value, and (0) contains result, perform the secure inner product protocol on T, (0) and TV, (0). and denote the result as [|] We show the high level idea in Figure By doing this, our protocol concretely consumes klty] Beaver's triples and therefore has Okklt, online communication complexity. Figure 5 shows the technical details our proposed protocol for case For Line ST-MPC (Figure clearly both parties know that D and E are diagonal matrices, that is, |,y = m. Therefore, proposed protocol in Figure can drop the complexity from Okk?² to Okk)).
with insensitive sparsity.
non-zero 3/.0- In order to get the final
5

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MatrixMul(X, Y) with insensitive sparsity
(Offfine) Generate km Beaver's triples
1: V(i,j) E ly, Pi pushes Vi,i into Ty()
2: for [k] do
Pi lets Tú =
Va [m] E [m], (f, a) E by, Po pushes Za,a into T=(a)
5: for E [m]] do
6: Both parties let = = O, then, for all values e E Ta (2),, T,))
7: Po invokes [o] < Shr(e), Pi invokes [o] + Shr(u)
8: [=t]] = Add(Mul([e)) [u]]), (asil))
endfor
10: endfor
MatrixMul(X, Y) with sensitive sparsity
(Offline) Po generates additive HE key pair (pk, then sends pk P1 1: e [k]..j [m], Po lets ei, = Enc(pk, oxs); and
encrypted matrix
2: v(i,j) E Ly, Pi pushes Yr.y into T, (f), also, Pi invokes qu f PIR.Query(i + jkb
3: Pi sends the query set (denoted as q) Po
4: Vis.y E q. Po invokes rı + Responsee (..)) (...)
Po sends the response (denoted
Pt
6: Vra,y E r, Pi invokes cs,y +- PIR.Exxract(rr.) and pushes es,j to (i)
7: for i E [k],J E [m]] do
8: Pa lets Brg Encpx(0)
9: Vo E (1),, u E Tú (J), Po invokes Pr,, = 8 3r,5
10 Po samples random numbers Ii, +- Rs, then lets.r.; = gi.s + St.5
Po sends B.,j to P1. then lets[2;,5]o Ji.j
endfor
13:
Pedecrypts receving messages and lets [ (ec)(
14:
return [Z]
Figure 5: Dense-sparse MatrixMul(X, Y) with insensitive and sensitive sparsity protocols, where have X k Y Rmxm
Lemma 1.
The first protocol Figure is secure against semi-honest adversary if we assume the existence of secure addition and multiplication semi-honest MPC protocols.
Proof. Please find the proof in the Technical Appendix.
Case 2: sensitive sparsity, i.e., sensitive ly and sensitive by. For general case, where both the location vector and the value vector contain sensitive information. Take the social matrix S for instance, its location vector indicates the existence of social relation between two users, its value vector further shows the strength of their relation, and both of which are sensitive.
In this case, both the dense matrix X and the entire sparse matrix Y are sensitive. Following the idea in case 1, the matrix multiplication protocol should first generate T,, T, according to Vg. By and ly, and then perform the inner product multiplication for each aligned bins in Tr, Ty Still, P1 Ty according to its own inputs Uy. lg- However, Po cannot generate Tx directly, since Ug is kept by itself while is held by Pt. We make communication and computation trade-off by leveraging PIR techniques, and as result, our PIR-based approach has lower concrete communication, and overall faster than the baseline protocol.
generate
We show the high-level idea of our PIR-based protocol in Figure O obliviously filter each bin in T, since both value vector and location vector sensitive. In summary,
The intuition behind is to let Pi

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first Po encrypts all the values in T.. the encrypted table is denoted as Te. Then P1 and Po invoke PIR protocol, where Po acts as server and sets T. as PIR database, Pi acts as client and parses L, to many PIR queries. At the end of PIR protocol, P1 receives the encrypted and filtered table T Afterwards Pi performs secure inner product evaluation. By doing this, the communication complexity drops from O Okm²²) to O(akm), compared with the simple solution. The details of our protocol are shown in Figure [ For Line 2 in ST-MPC (Figure (3). the social matrix (S) is sparse in nature, and thus our proposed protocol in Figure can significantly improve its efficiency. In summary, with our proposed two secure MatrixMul protocols, one can securely calculate the social term efficiently. For instance, again considering the social recommendation with zo 10 users, our proposal only requires total of = 3.6GB communication for each iteration.
Lemma 2. The second protocol in Figure secure against semi-honest adversary with the leakage ofyy if we assume the existence of secure PIR protocol.
Proof. Please find the proof in the Technical Appendix.
3.2 Security discussions of the social term
In Ree, two parties jointly calculate the social term *U("" E²)/2 US and then reveal the social term to Po (see Eq. (2). The security of Ree relies on whether Po can resolve the social matrix S" given its own inputs U and the social term. We claim that this is difficult because, the number of equations T (#epochh, 100 in our experiments) is much smaller than that of the variables (#user, much more than 100 in practice), which indicates that there are infinite solutions for this. In practice, T < can be easily satisfied for both the social platform and the rating platform. The reasons are two-folds. First, our proposed framework is secure against semi-honest adversary (which is a popular threat model in the secure computation literature), i.e., both platforms will strictly follow the protocol execution. Second, the number of items whose size/scale is usually large and cublicly-knoww in practice. Therefore, both platforms can agree on an iteration number T such that T < n, before running our proposed framework. Each platform can shut down the program if reaches the pre-defined number of iterations. Moreover, the reveal of the social term to Po could be avoided by taking the whole model training procedure as an MPC functionality and designing a complicated protocol for it. Inevitably, such protocol introduces impractical communication costs, and we leave how to solve this efficiently as a future work.
encrypt matrix E <- Enc(X)
PIR
TV
(+)
P
Many 1 and @
T
T T,(
filter with
Figure 6: Matrix multiplication with sensitive sparsity.
Experiments
Our experiments intend to answer the following questions. Q1: How do the social recommendation models using both rating data on Po and social data on P1 outperform the model that only uses rating data on Po (Section 4 Q2: How does our model perform compared with SeSoRec (Section 4 Q3: How does the social data sparsity affect the performance of SeSoRec and our model (Section 4
Implementation and setup. We run our experiments on a machine with 4-Core 2.4GHz Intel Core i5 with 16G memory, we compile our program using a modern C++ compiler (with support for C++ standard 17). In addition, our tests were run in local network, with RJ 3ms network latency. For additive HE scheme, we choose the implementation of libpaillier]] Also, we use -eal- with same parameter setting as the original paper (. For security, we choose 128-bit computational security and 40-bit statistical security as recommended by NIST (2). Similarly we leverage the generic ABY library to implement SeSoRec [5] and MPC building blocks such as addition, multiplication, and truncation. In particular, we choose 64-bit secret sharing in all our experiments.
with
libpaillier: http://assc.cc.utxxx.cccciu PSea--PIR: https://gttuub.coom/mii http://hhhh...cmmimmiiooooo//ssa MIT license
GPL license
ABY: https:/githhb.cooo//ccccyppppppp LGPL license
7

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Dataset. We choose two popular benchmark datasets to evaluate the performance of our proposed
model, i.e., Epinions [99 and LibraryThing (Lthing) [22. both of which are popularly used for
evaluating social recommendation tasks. Following existing work [S], we remove the users and items that have less than 15 interactions for both datasets. We summarize the statistics of both datasets after
process in Table ! Notice that we assume users' rating data are located at Po. users' social data are located at Pt. and Po and Pi share the same user set.
Table 1: Dataset statistics.
Dataset
Huser
#item
#rating
rating density
#social relation
social density
Epinions
11,500
7,596
283,319 529,992
0.32% 0.24%
275,117 44,710
0.21% %
Lthing
15,039
14,957
0.02%
Comparison Methods. We compare Ree with the following classic and state-of-the-art models:
-MF [20) is classic matrix factorization model that only uses rating data on Po. i.e., when y for ReRe
-ooreg [18] is a classic social recommendation model, which does not consider data privacy and assumes both rating data and social data are available on Po.
SeSoRec tries to solve the privacy-pres preeeerigg cross-platform social recommendation problem, but suffers from security and efficiency problem.
Slyper-parametert For all the model, during comparison, we set k 10. We tune learning rate and regularizer parameter X in {10-3 3, 3,10 10-2,... ..... 10'} } to achieve their best values. We also report the effect of K on model performance.
Metrics. We will evaluate both accuracy and efficiency of our proposed model. For accuracy, we choose Root Mean Square Error (RMSE) as the evaluation metric. since ratings range in [0, 5]. For efficiency, we report the computation time (in seconds) and the communication size between Po and Pi (in gigabytes), if has, for all the models. We use five-fold cross- cross-validation during experiments.
Performance Comparison. We first compare the model performances in terms of accuracy (RMSE) and efficiency (total time and communication). Table 2 shows the time and communication for each epoch, where time is shown in seconds, and communication is shown in GB.
From those Tables, find that: (1) the use of social information can indeed improve the recom- mendation performance of the rating platform, e.g., 1.193 vs. 1.062 and 0.927 vs. 0.098 in terms of RMSE Epinions and Lthing, respectively. This result is consistent with existing work from [18 5): (2) despite the same RMSE as SeSoRec and Soreg, Ree significantly improves the efficiency of SeSoRec, especially on the more sparse Lthing dataset, reducing the total time for one epoch from around 4.5 hours to around 4.5 minutes, and reducing the total communication from nearly 1.3TB to around 2.2GB. This yields an improvement of 18.57x faster, and 224.8x X less communication on Epinions and 61.37% x faster and 620.2x less communication on Lthing, respectively.
Effect of Social Data Sparsity. Next, we try to study the effect of social data sparsity on training efficiency. In order to do this, we sample the social relation of both datasets with a rate of 0.8, 0.6, and 0.4. As the result, the RMSEs of both SeSoRec and Se decrease to 1.0932, 1.1373, 1.1751 on Epinions dataset, and 0.9112, 0.9187, 0.9210 on Lthing dataset. The rational behind is that recommendation performance decreases with the number of social relations. We also report the efficiency of both models on Epinions and Lthing datasets in Table From it, we can find that the computation time and communication size of SeSoRec are constant no mater what the sample rate is. In contrast, the computation time and communication size of Re decrease linearly with sample rate. This result benefits from that Ree can deal with sparse social data with our proposed sparse matrix multiplication protocols.
Effeet of For efficiency, we report the running time and communication size of SeSoRec and PriorRec w.r.t & in Table where we use the Epinions dataset. From it, we can get that in average, Ree improves SeSoRec 18.6x in terms of total running time and 225x in terms of communication. More specifically, we observe that (1) the total running time of both SeSoRec and PriorRec increase
8

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Table 2: Comparison results of different models in terms of model accuracy (in RMSE), running time (in seconds), and communication size (in GB), on Epinions and Lthing datasets.
Epinions dataset
Lthing dataset
Models
MF
Soreg
SeSoRee
S Rec
MF
Soreg
SeSoRec
Ree
RMSE Offline Time
1.193
1.062
1.062
1.062
0.927
0.908
0,908
0.908
7,271
10.86
14,450
8.912
Total Time
3.846
40.50
7.799
419.9
9.596
57.76
16,084
262.1
Offline Comm.
788.3
1,348
Total Comm
798.6
3.552
1,365
2.201
Table 3: Comparison results by varying social data sparsity on Epinions and Lthing datasets.
Epinions 0.6
Lthing
Metric
Models
0.4
0.8
0.4
0.6
0.8
SesoRec
7,799
7,799
7,799
16,084
16,084
16,084
Total time (Seconds)
Ree
366.3
381.2
401.8
194
217
238
(Ipprovemen))
(21.29%)
(20.46x)
(19.41x)
(82.91x)
(74. (2x.12x)
(67.58x)
SesoRec
798
798
798
1,366
1,366
1,366
Total communication (GB)
Re
3.12
3.29
3.46
1.62
1.82
2.01
(Improvement)
(255k)
(243x)
(231x)
(843x)
(751x)
(680x)
Table 4: Effect of & running time and communication size Epinions dataset.
SeSoRec k = 15
Rec
Models
k = 10
k = 20
k = 10
h: = 15
k = 20
Offline Time
7,271
12,651
17,676
10.86
9.667
9.815
Total Time
7,799
13,565
19,585
419.9
449.6
527.4
Offline Comm.
788.3
1,182
1,577
0
0
0.
Total Comm. 798.6
1,198
1,597
3.552
3,552
3,552
with k, but the increase rate of Re slower than that of SeSoRec; (2) the communication size of SeSoRec increases with k in contrast, the communication size of S'Rec is constant. This result demonstrates that our proposed Ree has better scalability than SeSoRec in terms of both running time and communication size.
5 Related Work
Traditional recommender systems that only consider user-item rating information suffer from severe data sparsity problem 20
the one hand, researchers extensively incorporate other kinds of infor- mation, e.g., social 27 review 225] location [16], and time [7), to further improve recommendation performance. On the other hand, existing studies begin to explore information on multiple platforms or domains to address the data sparsity problem in recommender systems, i.e., cross-plates coos-ppltffomm and cross-domain recommendation problem in practice.
However, most of them cannot solve the data isolation
So far, there has been several work that may applied for mendations. For example, 23 applied garbled circuits for secure matrix factorization, and it has high security low efficiency, Chai al. [4] adopted homomorphic encryption for federated matrix factorization, but assumes the existence of a semi-honest server and is not provable secure. [13 uses differential privacy to protect user location privacy using transfer learning technique, which not provable secure and does not suitable to problem. The most similar work to ours is SeSoRec (5).
cross-domain recom-

---

however, it suffers from two main shortcomings: (1) as admitted by SeSoRec, it improves efficiency by sacrificing security. That is, it reveals the sum of two rows or two columns of the input matrix. We emphasis that this raises serious security concern in the social recommendation since one may infer detailed social relations from the element wise sum of two rows/columns of the user social matrix, especially when social relations are binary values; (2) SeSoRec treats the social data as dense matrix and thus still has serious efficiency issue under the practical sparse social data setting.
Conclusion
This paper aims to solve the data isolation problem in cross-platform social recommendation. To do this, we propose ReR, a sparsity-aware secure cross-platform social recommendation framework. Ree conducts social recommendation task and preserves data privacy at the same time. We also propose two secure sparse matrix multiplication protocols to improve the model training efficiency. Experiments conducted on two datasets demonstrate that Ree improves the computation time and communication size by around x0x and x23x on average, compared with the state-of-the work.
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11


Reviews:
[{"review_id": "uva3k19Fu7b", "reviewer": "Reviewer_d4vk", "summary": "This paper studies how to bring secure computation to social recommendation system, by leveraging the distributed (or sparse) data on different platforms while preserving their data privacy. The authors analysis the conventional recommender algorithm's demand on social terms, and propose two secure sparse matrix multiplication methods to conduct the computation. They compare their proposed method with two classical baselines with regards to accuracy, running time and communication size, showing competitive performance and more efficient computation.", "questions": "", "limitations": "", "rating": 7, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "Strength:\n* The paper proposed an efficient approach to social recommendation.\n\nWeakness:\n* Experiment. Since the main claim of the paper is its efficiency, in terms of social recommendation, large scale experiments are expected. However the paper only presents results on small scale datasets. Large scale results on datasets such as Amazon produce review are more convincing.\n* Recommendation model. As the proposed computation method seems not tied to a specific recommendation model. More results on modern recommendation models will help the argument, such as \"Deep Learning Recommendation Model for Personalization and Recommendation Systems\" and \"Collaborative filtering and deep learning based recommendation system for cold start items\".", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "Yes", "review_text": "", "extra_scores": {"ethical_concerns": "No", "needs_ethics_review": "No", "ethics_review_area": "", "time_spent_reviewing": "4"}, "extra_text": {}}, {"review_id": "WP7XMo5jGEl", "reviewer": "Reviewer_Maoq", "summary": "This paper proposes a secure and efficient cross-platform social recommendation algorithm. It solves a standard matrix factorization problem using network information, in which one platform has the rating data and another has the social information. \n", "questions": "", "limitations": "", "rating": 4, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "Strengths: \n\nThe paper is well-written ad easy to follow. \n\nComments: \n\n(1) My first comment on the paper is about the problem setup. I think the paper needs justifications to (1) demonstrate the practicality (how reasonable it is). Specifically, I wonder how reasonable it is to assume that two stakeholders store social and rating information separately. Realistic examples will be helpful to demonstrate the actual value of the problem formulation. I think it is more reasonable to assume that two platforms have the same information on items, e.g., Spotify, youtube, and pandora have information on similar music. \n\n(2)  Still related to the problem setup, I think there are security issues related to the problem setup. Why and how can two platforms match this sensitive information on user identity? To do so requires the platform to know some identifiable information and that they will be able to communicate through this unique identifier. \n\n(3) There are other matrix factorization methods, such as svd++ and different deep learning-based approaches. I suspect that even without social information, these methods may be able to achieve better performance. If this is the case, it is not clear this stylized extension on matrix factorization to obtain security is useful or not. I think the experiment section can be enriched by comparing with more benchmarks (without network information).\n\n(4) Regarding the communication mechanism in section 3.1, it is unclear how it can communicate the gradients in the second part of eq (2) without security concern. Specifically, for each iteration, there are no gradients and n(n-1)/2 entries. Suppose there are T iterations in total, when k * T ≥ (n-1)/2, it is possible for P0 to recover social influence in P1. There may be things I miss; please correct me if I am wrong.", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "None. ", "review_text": "", "extra_scores": {"ethical_concerns": "The authors have adequately addressed the limitations and there is no potential negative societal impact of their work. ", "needs_ethics_review": "No", "ethics_review_area": "", "time_spent_reviewing": "3.5"}, "extra_text": {}}, {"review_id": "BaC8ZgOEuEK", "reviewer": "Reviewer_2odS", "summary": "In this paper, the authors focus on improving the efficiency of a specific problem: secure cross-platform social recommendation. They exploit the sparsity of social data by proposing two novel and secure protocols for matrix multiplication. They also provide theoretical results of both the efficiency and security of their protocols. Also, in experiments, the proposed framework --- S^3^Rec improves the communication and computation efficiency of prior work by approximately 40x and 423x.", "questions": "", "limitations": "", "rating": 9, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "Data security and privacy is a hot and important research topic. Build secure recommendation models across domains is of great impact in practice. The idea of exploiting data sparsity in secure cross-platform social recommendation is new. Their proposed secure matrix multiplication protocols are novel to me (in the sense that there seem no existing PIR-based sparse matrix multiplication protocols), and the efficiency improvement brought by those two protocols is quite promising.\n\nThis work is technically written with thorough theoretical analysis. In particular, they include detailed security proof. Most of the arguments presented in this work are supported by either solid technical analysis or experiment results. \n\nThis paper is well-organized, and it clearly states the main problem in the introduction section, while some technical details are pretty dense and required patient reading, especially for the readers who are not experts in S&P area.\n\nTo the best of my knowledge, this paper is the first work exploiting the data sparsity in secure cross-platform social recommendation, and their experiments show remarkable improvements (in terms of efficiency) over the prior framework. Although the adopted social recommendation model is a little out-of-date, I believe it points out the feasibility and practicability of large-scale secure social recommendation.\n\nHowever, I do have some questions about this paper:\n\n1. Is it possible to use a similar method to improve efficiency on more complicated secure social recommendation models? For example, use secure sparse matrix multiplication protocol on a NN-based recommendation model.\n2. Can we replace PIR with other cryptographic primitives in a secure sparse matrix multiplication protocol?\n\nAnd there are some typos:\n\n1. line 305, there has been several works -> work\n2. line 106, we present three popular MPC protocols -> two\n\nMinor concerns:\n\nThe authors could state more applications of their secure sparse matrix multiplication protocols, as it shows the generalization of their proposed protocols. Also, I personally recommend the authors try to apply more complex social recommendation models such as the nn-models. Though it's known to be difficult to implement MPC-NN protocol, the authors can discuss (in theory) the impact of exploiting data sparsity in NN-based social recommendation models.\n\nIn summary, I think the problem this paper aims to solve is important, the proposed technical solution is novel, and the experimental results are impressive. I strongly support the acceptance of this paper. \n", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "See main review", "review_text": "", "extra_scores": {"needs_ethics_review": "No", "ethics_review_area": "", "time_spent_reviewing": "10"}, "extra_text": {}}, {"review_id": "20cb4OwtIf", "reviewer": "Reviewer_FftY", "summary": "In this paper, the authors study the problem of social recommendation, i.e., rating prediction with a user-item rating matrix and a user-user social relation matrix. Specifically, the authors propose a novel privacy-aware method, i.e., sparsity-aware secure cross-platform social recommendation (S^3Rec).  The main idea of S^3Rec is to compute the social term in the objective function of a classic social recommendation method (see Eq.(1)) by two different parties (or platforms) in a privacy-aware manner via homomorphic encryption and private information retrieval.", "questions": "", "limitations": "", "rating": 7, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "1 Originality: \nThe proposed method, i.e., sparsity-aware secure cross-platform social recommendation (S^3Rec), is new since no previous work use homomorphic encryption (HE) and private information retrieval (PIR) in such a way for jointly computing the social term in a social recommendation method. Moreover, the difference between the proposed method and the most closely related work, i.e., SeSoRec [5], is also well identified, i.e., security and efficiency.\n\n2 Quality:\nThe proposed model is technically sound, which is also supported by the empirical studies, i.e., the proposed methods is efficient and accurate.\n\n3 Clarity:\nOverall, the paper is well presented and is easy to follow. The motivations on leveraging the social connections for rating prediction in a privacy-aware manner are well justified. Sufficient details of the protocals are also included.\n\n4 Significance: \nThe authors have conducted extensive empirical studies, including 2 datasets, as well as studies about the effectiveness of method with different levels of sparsites. For rating prediction, the basic MF model is known not the state-of-the-art. For social recommendation, SoRec is also no the state-of-the-art. Moreover, it is not clear whether the proposed framework S^3Rec can be applied to more advanced social recommendation methods.\n", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "Yes.", "review_text": "", "extra_scores": {"needs_ethics_review": "No", "ethics_review_area": "", "time_spent_reviewing": "2"}, "extra_text": {}}]

Author rebuttal:

Meta-review: The reviews were generally positive about the motivation for the problem, novelty of the techniques, and execution of the paper. They identified a few areas for potential improvement, including expanding the scope of the experiments and handling more state-of-the-art recommendation systems. These concerns were adequately addressed in author feedback. The authors convincingly explained how their techniques would generalize to other methods based on sparse matrix multiplication, and gave an analysis for SVD++ as a specific example. I recommend the paper for acceptance.

My personal enthusiasm for the paper is a touch lower than that of the reviewers because the MPC-based security guarantees of the framework hold at a per-iteration level, rather than giving an end-to-end guarantee for the whole training process. (That is, allowing each party to learn the full sequence of social updates is potentially more disclosive than allowing each party to learn the final model.) This is a weaker guarantee, and less technically interesting to achieve. Nevertheless, the security obtained does still appear to be new and meaningful.

Comment for the authors: Please precisely define the MPC-hybrid and PIR-hybrid with leakage models in which the protocols are proved secure.
Decision: Accept (Poster)