Tensor Array Research Articles

Simultaneous clustering and estimation of networks in multiple graphical models.

Gaussian graphical models are widely used to study the dependence structure among variables. When samples are obtained from multiple conditions or populations, joint analysis of multiple graphical models are desired due to their capacity to borrow strength across populations. Nonetheless, existing methods often overlook the varying levels of similarity between populations, leading to unsatisfactory results. Moreover, in many applications, learning the population-level clustering structure itself is of particular interest. In this article, we develop a novel method, called Simultaneous Clustering and Estimation of Networks via Tensor decomposition (SCENT), that simultaneously clusters and estimates graphical models from multiple populations. Precision matrices from different populations are uniquely organized as a three-way tensor array, and a low-rank sparse model is proposed for joint population clustering and network estimation. We develop a penalized likelihood method and an augmented Lagrangian algorithm for model fitting. We also establish the clustering accuracy and norm consistency of the estimated precision matrices. We demonstrate the efficacy of the proposed method with comprehensive simulation studies. The application to the Genotype-Tissue Expression multi-tissue gene expression data provides important insights into tissue clustering and gene coexpression patterns in multiple brain tissues.

TENSOR REGRESSION FOR INCOMPLETE OBSERVATIONS WITH APPLICATION TO LONGITUDINAL STUDIES.

Multivariate longitudinal data are frequently encountered in practice such as in our motivating longitudinal microbiome study. It is of general interest to associate such high-dimensional, longitudinal measures with some univariate continuous outcome. However, incomplete observations are common in a regular study design, as not all samples are measured at every time point, giving rise to the so-called blockwise missing values. Such missing structure imposes significant challenges for association analysis and defies many existing methods that require complete samples. In this paper we propose to represent multivariate longitudinal data as a three-way tensor array (i.e., sample-by-feature-by-time) and exploit a parsimonious scalar-on-tensor regression model for association analysis. We develop a regularized covariance-based estimation procedure that effectively leverages all available observations without imputation. The method achieves variable selection and smooth estimation of time-varying effects. The application to the motivating microbiome study reveals interesting links between the preterm infant's gut microbiome dynamics and their neurodevelopment. Additional numerical studies on synthetic data and a longitudinal aging study further demonstrate the efficacy of the proposed method.

Generalized Co-clustering Analysis via Regularized Alternating Least Squares

Biclustering is an important exploratory analysis tool that simultaneously clusters rows (e.g., samples) and columns (e.g., variables) of a data matrix. Checkerboard-like biclusters reveal intrinsic associations between rows and columns. However, most existing methods rely on Gaussian assumptions and only apply to matrix data. In practice, non-Gaussian and/or multi-way tensor data are frequently encountered. A new CO-clustering method via Regularized Alternating Least Squares (CORALS) is proposed, which generalizes biclustering to non-Gaussian data and multi-way tensor arrays. Non-Gaussian data are modeled with single-parameter exponential family distributions and co-clusters are identified in the natural parameter space via sparse CANDECOMP/PARAFAC tensor decomposition. A regularized alternating (iteratively reweighted) least squares algorithm is devised for model fitting and a deflation procedure is exploited to automatically determine the number of co-clusters. Comprehensive simulation studies and three real data examples demonstrate the efficacy of the proposed method. The data and code are publicly available at https://github.com/reagan0323/CORALS.

Systolic Tensor Array: An Efficient Structured-Sparse GEMM Accelerator for Mobile CNN Inference

Convolutional neural network (CNN) inference on mobile devices demands efficient hardware acceleration of low-precision (INT8) general matrix multiplication (GEMM). The systolic array (SA) is a pipelined 2D array of processing elements (PEs), with very efficient local data movement, well suited to accelerating GEMM, and widely deployed in industry. In this letter, we describe two significant improvements to the traditional SA architecture, to specifically optimize for CNN inference. First, we generalize the traditional scalar PE, into a Tensor-PE, which gives rise to a family of new Systolic Tensor Array (STA) microarchitectures. The STA family increases intra-PE operand reuse and datapath efficiency, resulting in circuit area and power dissipation reduction of as much as 2.08× and 1.36× respectively, compared to the conventional SA at iso-throughput with INT8 operands. Second, we extend this design to support a novel block-sparse data format called density-bound block (DBB). This variant (STA-DBB) achieves a 3.14× and 1.97× improvement over the SA baseline at iso-throughput in area and power respectively, when processing specially-trained DBB-sparse models, while remaining fully backwards compatible with dense models.

Modified tensor method to power flow analysis

This study introduces a modified tensor-based power flow method designed using complex voltages represented in their rectangular form. Tensor-based methods employ the second-order Taylor series expansion of the power flow equations to estimate a correction vector to be added to the iterative increments of the Newton-Raphson method. In the proposed approach, the estimation of the correction vector is improved by taking advantage of a relation between the Jacobian and tensor arrays and symmetries between matrix-vector products involving Jacobian matrices. Result analysis highlights the efficiency and robustness of the proposed method in comparison with the original tensor-based approach using test systems and an actual system.

Tensor DoA Estimation With Directional Elements

Directivity gain patterns are treated as a physical diversity for tensor array processing, replacing space diversity, in addition to time and space shift diversities. We show that the tensor formulation allows to estimate directions of arrival under the assumption of unknown gain patterns, improving the performance of the omnidirectional case. We propose a trilinear model where one dimension of the multiway data array is fully provided by gain patterns, allowing tensor approaches even when space diversity is missing due to sensor overlap.

Multivariate Surprisal Analysis of Gene Expression Levels

We consider here multivariate data which we understand as the problem where each data point i is measured for two or more distinct variables. In a typical situation there are many data points i while the range of the different variables is more limited. If there is only one variable then the data can be arranged as a rectangular matrix where i is the index of the rows while the values of the variable label the columns. We begin here with this case, but then proceed to the more general case with special emphasis on two variables when the data can be organized as a tensor. An analysis of such multivariate data by a maximal entropy approach is discussed and illustrated for gene expressions in four different cell types of six different patients. The different genes are indexed by i, and there are 24 (4 by 6) entries for each i. We used an unbiased thermodynamic maximal-entropy based approach (surprisal analysis) to analyze the multivariate transcriptional profiles. The measured microarray experimental data is organized as a tensor array where the two minor orthogonal directions are the different patients and the different cell types. The entries are the transcription levels on a logarithmic scale. We identify a disease signature of prostate cancer and determine the degree of variability between individual patients. Surprisal analysis determined a baseline expression level common for all cells and patients. We identify the transcripts in the baseline as the “housekeeping” genes that insure the cell stability. The baseline and two surprisal patterns satisfactorily recover (99.8%) the multivariate data. The two patterns characterize the individuality of the patients and, to a lesser extent, the commonality of the disease. The immune response was identified as the most significant pathway contributing to the cancer disease pattern. Delineating patient variability is a central issue in personalized diagnostics and it remains to be seen if additional data will confirm the power of multivariate analysis to address this key point. The collapsed limits where the data is compacted into two dimensional arrays are contained within the proposed formalism.

Multidimensional tensor array analysis of multiphase flow during a hydrodynamic ram event

Flow visualization is necessary to characterize the fluid flow properties during a hydrodynamic ram event. The multiphase flow during a hydrodynamic ram event can make traditional image processing techniques such as contrast feature detection and PIV difficult. By stacking the imagery to form a multidimensional tensor array, feature detection to determine flow field velocities are visualized.

Three-Dimensional Sparse Turntable Microwave Imaging Based on Compressive Sensing

In this letter, we propose a fast reconstruction algorithm for 3-D turntable microwave imaging from sparse measurements. A conventional Fourier-transform-based 3-D microwave imaging method collects data over densely azimuth-elevation samples and needs a large amount of data storage and long collection time. To reduce the cost of data acquisition, the proposed method exploits the sparsity in the image domain to achieve 3-D microwave imaging by utilizing sparse measurements. For this aim, the signal model is first represented as a tensor array, and then, a novel sparse reconstruction algorithm called 3-D-SL0 is applied to recover the 3-D scattering reflectivity, i.e., a 3-D image. Simulation results are finally shown to investigate the validity of the proposed method.

Exponential family tensor factorization: an online extension and applications

In this paper, we propose a new probabilistic model of heterogeneously attributed multi-dimensional arrays. The model can manage heterogeneity by employing individual exponential family distributions for each attribute of the tensor array. Entries of the tensor are connected by latent variables and share information across the different attributes through the latent variables. The assumption of heterogeneity makes a Bayesian inference intractable, and we cast the EM algorithm approximated by the Laplace method and Gaussian process. We also extended the proposal algorithm for online learning. We apply our method to missing-values prediction and anomaly detection problems and show that our method outperforms conventional approaches that do not consider heterogeneity.

Seismic moments of Taiwan’s earthquakes evaluated from a regional broadband array

Abstract We have taken the seismic moment (M o) values of 79 earthquakes occurring in the Taiwan region that have been published in the Global centroid-moment tensor (CMT) and regional Broadband Array in Taiwan for Seismology (BATS) catalogues for the period 1996–2005 and compared the values determined from the global and regional networks, respectively. M oG and M oB are used to denote the M o values published in the Global CMT and regional BATS catalogues, respectively. Our results show that M oB linearly correlates with M oG and that M oB is, on average, approximately equal to 0.37M oG. This difference may be caused by the use of shorter period seismic waves in BATS for estimating M oB. The moment magnitude evaluated from regional BATS seismograms is about 0.3 less than that estimated from global data.

Bio-Image Warehouse System: Concept and Implementation of a Diagnosis-Based Data Warehouse for Advanced Imaging Modalities in Neuroradiology

Advanced neuroimaging techniques, such as functional magnetic resonance imaging (fMRI), chemical shift spectroscopy imaging (CSI), diffusion tensor imaging (DTI), and perfusion-weighted imaging (PWI) create novel challenges in terms of data storage and management: huge amounts of raw data are generated, the results of analysis may depend on the software and settings that have been used, and most often intermediate files are inherently not compliant with the current DICOM (digital imaging and communication in medicine) standard, as they contain multidimensional complex and tensor arrays and various other types of data structures. A software architecture, referred to as Bio-Image Warehouse System (BIWS), which can be used alongside a radiology information system/picture archiving and communication system (RIS/PACS) system to store neuroimaging data for research purposes, is presented. The system architecture is conceived with the purpose of enabling to query by diagnosis according to a predefined two-layered classification taxonomy. The operational impact of the system and the time needed to get acquainted with the web-based interface and with the taxonomy are found to be limited. The development of modules enabling automated creation of statistical templates is proposed.

Analytical solution for the electric potential in arbitrary anisotropic layered media applying the set of Hankel transforms of integer order

ABSTRACTThe analytical solution and algorithm for simulating the electric potential in an arbitrarily anisotropic multilayered medium produced by a point DC source is here proposed. The solution is presented as a combination of Hankel transforms of integer order and Fourier transforms based on the analytical recurrent equations obtained for the potential spectrum. For the conversion of the potential spectrum into the space domain, we have applied the algorithm of the Fast Fourier Transform for logarithmically spaced points. A comparison of the modelling results with the power‐series solution for two‐layered anisotropic structures demonstrated the high accuracy and computing‐time efficiency of the method proposed.The results of the apparent‐resistivity calculation for both traditional pole‐pole and tensor arrays above three‐layered sequence with an azimuthally anisotropic second layer are presented. The numerical simulations show that both arrays have the same sensitivity to the anisotropy parameters. This sensitivity depends significantly on the resistivity ratio between anisotropic and adjacent layers and increases for the models with a conductive second layer.