DeepAI

# Nonnegative matrix factorization with side information for time series recovery and prediction

Motivated by the reconstruction and the prediction of electricity consumption, we extend Nonnegative Matrix Factorization (NMF) to take into account side information (column or row features). We consider general linear measurement settings, and propose a framework which models non-linear relationships between features and the response variables. We extend previous theoretical results to obtain a sufficient condition on the identifiability of the NMF in this setting. Based the classical Hierarchical Alternating Least Squares (HALS) algorithm, we propose a new algorithm (HALSX, or Hierarchical Alternating Least Squares with eXogeneous variables) which estimates the factorization model. The algorithm is validated on both simulated and real electricity consumption datasets as well as a recommendation dataset, to show its performance in matrix recovery and prediction for new rows and columns.

• 2 publications
• 18 publications
• 16 publications
• 2 publications
• 5 publications
10/05/2016

### Recovering Multiple Nonnegative Time Series From a Few Temporal Aggregates

Motivated by electricity consumption metering, we extend existing nonneg...
06/29/2019

### Fast Convolutive Nonnegative Matrix Factorization Through Coordinate and Block Coordinate Updates

Identifying recurring patterns in high-dimensional time series data is a...
07/28/2014

### Algorithms, Initializations, and Convergence for the Nonnegative Matrix Factorization

It is well known that good initializations can improve the speed and acc...
09/27/2018

### Supervised Nonnegative Matrix Factorization to Predict ICU Mortality Risk

ICU mortality risk prediction is a tough yet important task. On one hand...
08/11/2021

### The Lawson-Hanson Algorithm with Deviation Maximization: Finite Convergence and Sparse Recovery

In this work we apply the "deviation maximization", a new column selecti...
07/12/2020

### An Alternating Rank-K Nonnegative Least Squares Framework (ARkNLS) for Nonnegative Matrix Factorization

Nonnegative matrix factorization (NMF) is a prominent technique for data...
04/08/2021

### Archetypal Analysis for Sparse Nonnegative Matrix Factorization: Robustness Under Misspecification

We consider the problem of sparse nonnegative matrix factorization (NMF)...