Online Robust PCA via Stochastic Optimization Supplementary Material
نویسندگان
چکیده
For the data projection r and noise estimation e, we can get the closed-form solutions for them respectively, as shown in Algorithm 1.1. In particular, the closed-form solution to a projection to 1-ball in updating e involves a soft thresholding operator S λ [·] Hale et al. (2008), which is defined as:
منابع مشابه
Online Robust PCA via Stochastic Optimization
Robust PCA methods are typically based on batch optimization and have to load all the samples into memory during optimization. This prevents them from efficiently processing big data. In this paper, we develop an Online Robust PCA (OR-PCA) that processes one sample per time instance and hence its memory cost is independent of the number of samples, significantly enhancing the computation and st...
متن کاملA Combined Stochastic Programming and Robust Optimization Approach for Location-Routing Problem and Solving it via Variable Neighborhood Search algorithm
The location-routing problem is one of the combined problems in the area of supply chain management that simultaneously make decisions related to location of depots and routing of the vehicles. In this paper, the single-depot capacitated location-routing problem under uncertainty is presented. The problem aims to find the optimal location of a single depot and the routing of vehicles to serve th...
متن کاملRobust Stochastic Principal Component Analysis
We consider the problem of finding lower dimensional subspaces in the presence of outliers and noise in the online setting. In particular, we extend previous batch formulations of robust PCA to the stochastic setting with minimal storage requirements and runtime complexity. We introduce three novel stochastic approximation algorithms for robust PCA that are extensions of standard algorithms for...
متن کاملAn Online Q-learning Based Multi-Agent LFC for a Multi-Area Multi-Source Power System Including Distributed Energy Resources
This paper presents an online two-stage Q-learning based multi-agent (MA) controller for load frequency control (LFC) in an interconnected multi-area multi-source power system integrated with distributed energy resources (DERs). The proposed control strategy consists of two stages. The first stage is employed a PID controller which its parameters are designed using sine cosine optimization (SCO...
متن کاملApplication of Stochastic Optimal Control, Game Theory and Information Fusion for Cyber Defense Modelling
The present paper addresses an effective cyber defense model by applying information fusion based game theoretical approaches. In the present paper, we are trying to improve previous models by applying stochastic optimal control and robust optimization techniques. Jump processes are applied to model different and complex situations in cyber games. Applying jump processes we propose some m...
متن کامل