Multiple Tensor-On-Tensor Regression: An Approach for Modeling Processes with Heterogeneous Sources of Data

• Activity Number: 390 - Advanced Fault Detection and Attribution in Large and Complex Data Streams
• Type: Topic Contributed
• Date/Time: Tuesday, July 30, 2019 : 2:00 PM to 3:50 PM
• Sponsor: Quality and Productivity Section
• Author(s): Kamran Paynabar* and Mostafa Resisi and Hao Yan and Jianjun Shi
• Companies: Georgia Institute of Technology and Georgia Tech and Arizona State University and Georgia Tech
• Keywords: Tensor; low-dimensional learning; high-dimensional data

Abstract

In recent years, measurement or collection of heterogeneous sets of data such as those containing scalars, waveform signals, images, and even structured point clouds, has become more common. However, available methods mainly focus on the scalars and profiles and do not provide a general framework for integrating different sources of data to construct a model. This paper addresses the problem of estimating a process output by a set of heterogeneous process variables. We introduce a general multiple tensor-on-tensor regression approach in which each set of input data and output measurements are represented by tensors. We formulate a linear regression model between the input and output tensors and estimate the parameters by minimizing a least square loss function. In order to avoid overfitting, we decompose the model parameters using several basis matrices that span the input and output spaces, and provide efficient optimization algorithms for learning the basis and coefficients. Through several simulation and case studies, we evaluate the performance of the proposed method. The results show the advantage of our method over some benchmarks in terms of the mean square prediction error.