Robust Stochastic Principal Component Analysis
نویسندگان
چکیده
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 PCA – the stochastic power method, incremental PCA and online PCA using matrix-exponentiated-gradient (MEG) updates. For robust online PCA we also give a sub-linear convergence guarantee. Our numerical results demonstrate the superiority of the the robust online method over the other robust stochastic methods and the advantage of robust methods over their non-robust counterparts in the presence of outliers in artificial and real scenarios.
منابع مشابه
An application of principal component analysis and logistic regression to facilitate production scheduling decision support system: an automotive industry case
Production planning and control (PPC) systems have to deal with rising complexity and dynamics. The complexity of planning tasks is due to some existing multiple variables and dynamic factors derived from uncertainties surrounding the PPC. Although literatures on exact scheduling algorithms, simulation approaches, and heuristic methods are extensive in production planning, they seem to be ineff...
متن کاملRobust Principal Component Analysis and Fractal Methods to Delineate Mineralization-Related Hydrothermally-Altered Zones from ASTER Data: A Case Study of Dehaj Terrain, Central Iran
The Dehaj area, located in the southern part of the Urumieh-Dokhtar magmatic belt, is a well-endowed terrain hosting a number of world-class porphyry copper deposits. These deposits are all hosted in an acidic to intermediate volcano-plutonic sequence greatly affected by various types of the hydrothermal alterations, whether argillic, phyllic or propylitic. Although there are a handful of hithe...
متن کاملRobust Functional Principal Components : a Projection - Pursuit Approach
In many situations, data are recorded over a period of time and may be regarded as realizations of a stochastic process. In this paper, robust estimators for the principal components are considered by adapting the projection pursuit approach to the functional data setting. Our approach combines robust projection–pursuit with different smoothing methods. Consistency of the estimators are shown u...
متن کاملStochastic Parallel Block Coordinate Descent for Large-Scale Saddle Point Problems
We consider convex-concave saddle point problems with a separable structure and non-strongly convex functions. We propose an efficient stochastic block coordinate descent method using adaptive primal-dual updates, which enables flexible parallel optimization for large-scale problems. Our method shares the efficiency and flexibility of block coordinate descent methods with the simplicity of prim...
متن کاملNo Spurious Local Minima in Nonconvex Low Rank Problems: A Unified Geometric Analysis
In this paper we develop a new framework that captures the common landscape underlying the common non-convex low-rank matrix problems including matrix sensing, matrix completion and robust PCA. In particular, we show for all above problems (including asymmetric cases): 1) all local minima are also globally optimal; 2) no highorder saddle points exists. These results explain why simple algorithm...
متن کامل