Recovering Multiple Nonnegative Time Series From a Few Temporal\n Aggregates

2016/10/05 by Jiali Mei, Yohann de Castro, Mei, Jiali +4
Computer Science · Engineering · #Blind Source Separation Techniques #Control Systems and Identification #FOS: Computer and information sciences #Machine Learning (stat.ML) #Sparse and Compressive Sensing Techniques

paper · pdf · doi:10.48550/arxiv.1610.01492

openalex publication_date 2016/10/05 · openalex created_date 2016/10/14 · openalex updated_date 2026/07/28

Abstract

Motivated by electricity consumption metering, we extend existing nonnegative\nmatrix factorization (NMF) algorithms to use linear measurements as\nobservations, instead of matrix entries. The objective is to estimate multiple\ntime series at a fine temporal scale from temporal aggregates measured on each\nindividual series. Furthermore, our algorithm is extended to take into account\nindividual autocorrelation to provide better estimation, using a recent convex\nrelaxation of quadratically constrained quadratic program. Extensive\nexperiments on synthetic and real-world electricity consumption datasets\nillustrate the effectiveness of our matrix recovery algorithms.\n

Citations

• Low-Rank Matrix Recovery from Row-and-Column Affine Measurements
• Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization
• High-dimensional Time Series Prediction with Missing Values
• Algorithms for nonnegative matrix factorization with the beta-divergence

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