Paper:
Unorganized Malicious Attacks Detection
Recommender systems have attracted much attention during the past decade. Many attack detection algorithms have been developed for better recommendations, mostly focusing on shilling attacks, where an attack organizer produces a large number of user profiles by the same strategy to promote or demote an item. This work considers another different attack style: unorganized malicious attacks, where attackers individually utilize a small number of user profiles to attack different items without organizer. This attack style occurs in many real applications, yet relevant study remains open. We formulate the unorganized malicious attacks detection as a matrix completion problem, and propose the Unorganized Malicious Attacks detection (UMA) algorithm, based on the alternating splitting augmented Lagrangian method. We verify, both theoretically and empirically, the effectiveness of the proposed approach.

Review:
This paper proposes a new kind of attack on recommender systems that the authors call unorganized malicious attacks. In these attacks, each item can only attacked by a limited number of users. The authors propose an algorithm for solving it and show global convergence of it. Finally, the authors evaluate their algorithm on two (semi-)synthetic tasks and one real-world one.  My main issues with this paper are that (i) assumptions are not well motivated and justified, (ii) the theoretical results are not well aligned with the task of finding malicious users and (iii) the empirical evaluation does not have any recent baselines. With all the major revisions needed, I vote to reject this submission. Below are my detailed comments.  Significance. The paper lacks proper motivation and justification for the scenario of malicious unorganized attacks that is studied in it. Why is this scenario more important or realistic than shilling attacks? To what degree does it generalize those? I think answering those questions right away in the introduction would strengthen the paper tremendously. Moreover, especially the formulation of the optimization problem (lines 148-159) needs proper justification. For example, why do we care about the rank function? Moving on to the theoretical results, I don't really feel there are connected well to the problem of finding malicious users, e.g., users with |Y_ij| != 0. The results give us convergence in terms of the Frobenius norm on Y, but I would like to see convergence in terms of the L_1 norm here.   Quality. Regarding the empirical evaluation, I am not convinced that the baselines offer a fair comparison. Especially the N-P and k-means based methods are very simple. The most recent baseline is 5 years old which would need some justification. I would also expect to see Maximum-margin matrix factorization as a baseline here.   Originality. This work is based on standard approaches for matrix completion and convex analysis. The main novelty is the introduction of the attack matrix Y. Hence, I would consider the work in this paper to be incremental overall.  Clarity. I had a hard time reading through the paper because relevant information was scattered throughout and it also lacked a clear focus. I would rewrite the paper so that it is clear from the very begining that the problem you are trying to solve is to find users that were part of an unorganized malicious attack. This will make the theory and introduction easier to write. Right now, it's not clear what exactly the problem is that the authors seek out to solve. For example, in the introduction the paper says "in this paper, we investigate a new attack model" -- yes, but what is the goal? There are also various typos ("recommender system has" -> "recommender systems have", "there are many works" -> "there is much work", "is a (or partial) matrix" -> "is a partial matrix" etc.) that should be fixed. Moreover, the first paragraph in the introduction is   unnecessarily broad and should be more focused, then the last paragraph can be omitted since it is already clear from the section headings what follows. The problem formulation should follow right after the introduction, I would move related work to the end. I would also start with the new unorganized attack scenario and then later talk about the other attack strategies. Section 3 should also be written to make the assumptions and model more prominent.  Author rebuttal: Thank you for clarifying my concerns. However, the revisions needed / proposed would be substantial, and the paper would need another round of reviewing. Hence, I still vote to reject this paper.