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This paper proposes a new methodology to predict and update the residual useful lifetime of a system using a sequence of degradation images. The methodology integrates tensor linear algebra with traditional location-scale regression widely used in reliability and prognosis. To address the high dimensionality challenge, the degradation image streams are first projected to a low-dimensional tensor subspace that is able to preserve their information. Next, the projected image tensors are regressed against time-to-failure via penalized location-scale tensor regression. The coefficient tensor is then decomposed using CANDECOMP/PARAFAC (CP) and Tucker decompositions, which enables parameter estimation in a high-dimensional setting. Two optimization algorithms with a global convergence property are developed for model estimation. The effectiveness of our models is validated using a simulated dataset and infrared degradation image streams from a rotating machinery.
Nitrogen dioxide (NO$_2$) is a primary constituent of traffic-related air pollution and has well established harmful environmental and human-health impacts. Knowledge of the spatiotemporal distribution of NO$_2$ is critical for exposure and risk asse
We propose a novel image set classification technique using linear regression models. Downsampled gallery image sets are interpreted as subspaces of a high dimensional space to avoid the computationally expensive training step. We estimate regression
Model fitting often aims to fit a single model, assuming that the imposed form of the model is correct. However, there may be multiple possible underlying explanatory patterns in a set of predictors that could explain a response. Model selection with
This study presents application examples of generalized spatial regression modeling for count data and continuous non-Gaussian data using the spmoran package (version 0.2.2 onward). Section 2 introduces the model. The subsequent sections demonstrate
Medical imaging studies have collected high dimensional imaging data to identify imaging biomarkers for diagnosis, screening, and prognosis, among many others. These imaging data are often represented in the form of a multi-dimensional array, called