A Generalized Robust Minimization Framework for Low-Rank Matrix Recovery

This paper considers the problem of recovering low-rank matrices which are heavily corrupted by outliers or large errors. To improve the robustness of existing recovery methods, the problem is solved by formulating it as a generalized nonsmooth nonconvex minimization functional via exploiting the Schatten p-norm (0 < p ≤1) and Lq(0 < q ≤1) seminorm. Two numerical algorithms are provided based on the augmented Lagrange multiplier (ALM) and accelerated proximal gradient (APG) methods as well as efficient root-finder strategies. Experimental results demonstrate that the proposed generalized approach is more inclusive and effective compared with state-of-the-art methods, either convex or nonconvex

Minimal Shrinkage for Noisy Data Recovery Using Schatten-p Norm Objective

Abstract. Noisy data recovery is an important problem in machine learning field, which has widely applications for collaborative prediction, recommendation systems, etc. One popular model is to use trace norm model for noisy data recovery. However, it is ignored that the reconstructed data could be shrank (i.e., singular values could be greatly suppressed). In this paper, we present novel noisy data recovery models, which replaces the standard rank constraint (i.e., trace norm) using Schatten-p Norm. The proposed model is attractive due to its suppression on the shrinkage of singular values at smaller parameter p. We analyze the optimal solution of proposed models, and characterize the rank of optimal solution. Efficient algorithms are presented, the convergences of which are rigorously proved. Extensive experiment results on 6 noisy datasets demonstrate the good performance of proposed minimum shrinkage models.

Distributed Anomaly Detection Using Minimum Volume Elliptical Principal Component Analysis

Principal component analysis and the residual error is an effective anomaly detection technique. In an environment where anomalies are present in the training set, the derived principal components can be skewed by the anomalies. A further aspect of anomaly detection is that data might be distributed across different nodes in a network and their communication to a centralized processing unit is prohibited due to communication cost. Current solutions to distributed anomaly detection rely on a hierarchical network infrastructure to aggregate data or models; however, in this environment, links close to the root of the tree become critical and congested. In this paper, an algorithm is proposed that is more robust in its derivation of the principal components of a training set containing anomalies. A distributed form of the algorithm is then derived where each node in a network can iterate towards the centralized solution by exchanging small matrices with neighboring nodes. Experimental evaluations on both synthetic and real-world data sets demonstrate the superior performance of the proposed approach in comparison to principal component analysis and alternative anomaly detection techniques. In addition, it is shown that in a variety of network infrastructures, the distributed form of the anomaly detection model is able to derive a close approximation of the centralized model

The use of machine learning algorithms in recommender systems: A systematic review

The final publication is available at Elsevier via https://doi.org/10.1016/j.eswa.2017.12.020 © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/Recommender systems use algorithms to provide users with product or service recommendations. Recently, these systems have been using machine learning algorithms from the field of artificial intelligence. However, choosing a suitable machine learning algorithm for a recommender system is difficult because of the number of algorithms described in the literature. Researchers and practitioners developing recommender systems are left with little information about the current approaches in algorithm usage. Moreover, the development of recommender systems using machine learning algorithms often faces problems and raises questions that must be resolved. This paper presents a systematic review of the literature that analyzes the use of machine learning algorithms in recommender systems and identifies new research opportunities. The goals of this study are to (i) identify trends in the use or research of machine learning algorithms in recommender systems; (ii) identify open questions in the use or research of machine learning algorithms; and (iii) assist new researchers to position new research activity in this domain appropriately. The results of this study identify existing classes of recommender systems, characterize adopted machine learning approaches, discuss the use of big data technologies, identify types of machine learning algorithms and their application domains, and analyzes both main and alternative performance metrics.Natural Sciences and Engineering Research Council of Canada (NSERC) Ontario Research Fund of the Ontario Ministry of Research, Innovation, and Scienc