Aberrant Structure MRI in Parkinson’s Disease and Comorbidity with Depression Based on Multinomial Tensor Regression Analysis

Background: Depression is a prominent and highly prevalent nonmotor feature in patients with Parkinson’s disease (PD). The neural and pathophysiologic mechanisms of PD with depression (DPD) remain unclear. The current diagnosis of DPD largely depends on clinical evaluation. Methods: We proposed a new family of multinomial tensor regressions that leveraged whole-brain structural magnetic resonance imaging (MRI) data to discriminate among 196 non-depressed PD (NDPD) patients, 84 DPD patients, 200 healthy controls (HC), and to assess the special brain microstructures in NDPD and DPD. The method of maximum likelihood estimation coupled with state-of-art gradient descent algorithms was used to predict the individual diagnosis of PD and the development of DPD in PD patients. Results: The results reveal that the proposed efficient approach not only achieved a high prediction accuracy (0.94) with a multi-class AUC (0.98) for distinguishing between NDPD, DPD, and HC on the testing set but also located the most discriminative regions for NDPD and DPD, including cortical regions, the cerebellum, the brainstem, the bilateral basal ganglia, and the thalamus and limbic regions. Conclusions: The proposed imaging technique based on tensor regression performs well without any prior feature information, facilitates a deeper understanding into the abnormalities in DPD and PD, and plays an essential role in the statistical analysis of high-dimensional complex MRI imaging data to support the radiological diagnosis of comorbidity of depression with PD.

Fast Prediction of Thermal Data Stream for Direct Laser Deposition Processes Using Network-based Tensor Regression

The objective of this research is to study an effective thermal history prediction method for additive manufacturing (AM) processes using thermal image streams in a layer-wise manner. The need for immaculate integration of in-process sensing and data-driven approaches to monitor process dynamics in AM has been clearly stated in blueprint reports released by various U.S. agencies such as NIST and DoD over the past five years. Reliable physics-based models have been developed to delineate the underlying thermo-mechanical dynamics of AM processes; however, the computational cost is extremely high. We propose a tensor-based surrogate modeling methodology to predict the layer-wise relationship in the thermal history of the AM parts, which is time-efficient compared to available physics-based prediction models. We construct a network-tensor structure for freeform shapes based on thermal image streams obtained in metal-based AM process. Subsequently, we simplify the network-tensor structure by concatenating images to reach layer-wise structure. Succeeding layers are predicted based on antecedent layer using the tensor regression model. Generalized multilinear structure, called the higher-order partial least squares (HOPLS) is used to estimate the tensor regression model parameters. Through proposed method, high-dimensional thermal history of AM components can be predicted accurately in a computationally efficient manner. The proposed thermal history prediction is applied on simulated thermal images from finite element method (FEM) simulations. This shows that the proposed model can be used to enhance their performance alongside simulation-based models.

Multi-view feature selection via sparse tensor regression

In this paper, we propose a sparse tensor regression model for multi-view feature selection. Apart from the most of existing methods, our model adopts a tensor structure to represent multi-view data, which aims to explore their underlying high-order correlations. Based on this tensor structure, our model can effectively select the meaningful feature set for each view. We also develop an iterative optimization algorithm to solve our model, together with analysis about the convergence and computational complexity. Experimental results on several popular multi-view data sets confirm the effectiveness of our model.