scholarly journals Tensor-tensor algebra for optimal representation and compression of multiway data

2021 ◽  
Vol 118 (28) ◽  
pp. e2015851118
Author(s):  
Misha E. Kilmer ◽  
Lior Horesh ◽  
Haim Avron ◽  
Elizabeth Newman
Keyword(s):  
Large Datasets ◽  
High Dimensional ◽  
Tensor Algebra ◽  
Tensor Representation ◽  
Optimal Representation ◽  
Data Dimensionality Reduction ◽  
The Matrix ◽  
Optimality Properties ◽  
Value Decomposition ◽  
High Dimensional Datasets

With the advent of machine learning and its overarching pervasiveness it is imperative to devise ways to represent large datasets efficiently while distilling intrinsic features necessary for subsequent analysis. The primary workhorse used in data dimensionality reduction and feature extraction has been the matrix singular value decomposition (SVD), which presupposes that data have been arranged in matrix format. A primary goal in this study is to show that high-dimensional datasets are more compressible when treated as tensors (i.e., multiway arrays) and compressed via tensor-SVDs under the tensor-tensor product constructs and its generalizations. We begin by proving Eckart–Young optimality results for families of tensor-SVDs under two different truncation strategies. Since such optimality properties can be proven in both matrix and tensor-based algebras, a fundamental question arises: Does the tensor construct subsume the matrix construct in terms of representation efficiency? The answer is positive, as proven by showing that a tensor-tensor representation of an equal dimensional spanning space can be superior to its matrix counterpart. We then use these optimality results to investigate how the compressed representation provided by the truncated tensor SVD is related both theoretically and empirically to its two closest tensor-based analogs, the truncated high-order SVD and the truncated tensor-train SVD.

Fast Algorithms for LS and LAD-Collaborative Regression

2021 ◽  
Author(s):  
Jun Sun ◽  
Lingchen Kong ◽  
Mei Li
Keyword(s):  
Numerical Experiments ◽  
Modern Science ◽  
Alternating Direction Method ◽  
Least Square ◽  
High Dimensional ◽  
Statistical Interpretation ◽  
Absolute Deviation ◽  
Linear Rate ◽  
Alternating Direction ◽  
High Dimensional Datasets

With the development of modern science and technology, it is easy to obtain a large number of high-dimensional datasets, which are related but different. Classical unimodel analysis is less likely to capture potential links between the different datasets. Recently, a collaborative regression model based on least square (LS) method for this problem has been proposed. In this paper, we propose a robust collaborative regression based on the least absolute deviation (LAD). We give the statistical interpretation of the LS-collaborative regression and LAD-collaborative regression. Then we design an efficient symmetric Gauss–Seidel-based alternating direction method of multipliers algorithm to solve the two models, which has the global convergence and the Q-linear rate of convergence. Finally we report numerical experiments to illustrate the efficiency of the proposed methods.

scholarly journals Internet Photogrammetry for Inspection of Seaports

2017 ◽  
Vol 24 (s1) ◽  
pp. 174-181 ◽  
Author(s):  
Zygmunt Paszotta ◽  
Malgorzata Szumilo ◽  
Jakub Szulwic
Keyword(s):  
Fundamental Matrix ◽  
Laser Scanning ◽  
3D Models ◽  
Digital Cameras ◽  
Correct Orientation ◽  
The Matrix ◽  
Transport Safety ◽  
Left And Right ◽  
Value Decomposition ◽  
The Relationship

Abstract This paper intends to point out the possibility of using Internet photogrammetry to construct 3D models from the images obtained by means of UAVs (Unmanned Aerial Vehicles). The solutions may be useful for the inspection of ports as to the content of cargo, transport safety or the assessment of the technical infrastructure of port and quays. The solution can be a complement to measurements made by using laser scanning and traditional surveying methods. In this paper the authors recommend a solution useful for creating 3D models from images acquired by the UAV using non-metric images from digital cameras. The developed algorithms, created and presented software allows to generate 3D models through the Internet in two modes: anaglyph and display in shutter systems. The problem of 3D image generation in photogrammetry is solved by using epipolar images. The appropriate method was presented by Kreiling in 1976. However, it applies to photogrammetric images for which the internal orientation is known. In the case of digital images obtained with non-metric cameras it is required to use another solution based on the fundamental matrix concept, introduced by Luong in 1992. In order to determine the matrix which defines the relationship between left and right digital image it is required to have at least eight homologous points. To determine the solution it is necessary to use the SVD (singular value decomposition). By using the fundamental matrix the epipolar lines are determined, which makes the correct orientation of images making stereo pairs, possible. The appropriate mathematical bases and illustrations are included in the publication.

scholarly journals (Auto)Biographical reflections on the contributions of William F. Loomis (1940-2016) to Dictyostelium biology

2019 ◽  
Vol 63 (8-9-10) ◽  
pp. 343-357
Author(s):  
Adam Kuspa ◽  
Gad Shaulsky
Keyword(s):  
Cell Differentiation ◽  
Molecular Biology ◽  
Genetic Control ◽  
Dictyostelium Discoideum ◽  
University Of California ◽  
High Dimensional ◽  
Social Amoeba ◽  
The Social ◽  
The University ◽  
High Dimensional Datasets

William Farnsworth Loomis studied the social amoeba Dictyostelium discoideum for more than fifty years as a professor of biology at the University of California, San Diego, USA. This biographical reflection describes Dr. Loomis’ major scientific contributions to the field within a career arc that spanned the early days of molecular biology up to the present day where the acquisition of high-dimensional datasets drive research. Dr. Loomis explored the genetic control of social amoeba development, delineated mechanisms of cell differentiation, and significantly advanced genetic and genomic technology for the field. The details of Dr. Loomis’ multifaceted career are drawn from his published work, from an autobiographical essay that he wrote near the end of his career and from extensive conversations between him and the two authors, many of which took place on the deck of his beachfront home in Del Mar, California.

scholarly journals Curating Metal-Organic Frameworks to Compose Robust Gas Sensor Arrays in Dilute Conditions

2019 ◽  
Author(s):  
Arni Sturluson ◽  
Rachel Sousa ◽  
Yujing Zhang ◽  
Melanie T. Huynh ◽  
Caleb Laird ◽  
...  
Keyword(s):  
Sensor Array ◽  
Gas Sensing ◽  
Metal Organic Frameworks ◽  
Sensor Arrays ◽  
Gas Composition ◽  
Composition Space ◽  
The Matrix ◽  
Metal Organic ◽  
Analyte Detection ◽  
Value Decomposition

Metal-organic frameworks (MOFs)-- tunable, nano-porous materials-- are alluring recognition elements for gas sensing. Mimicking human olfaction, an array of cross-sensitive, MOF-based sensors could enable analyte detection in complex, variable gas mixtures containing confounding gas species. Herein, we address the question: given a set of MOF candidates and their adsorption properties, how do we select the optimal subset to compose a sensor array that accurately and robustly predicts the gas composition via monitoring the adsorbed mass in each MOF? We first mathematically formulate the MOF-based sensor array problem under dilute conditions. Instructively, the sensor array can be viewed as a linear map from <i>gas composition space</i> to <i>sensor array response space</i> defined by the matrix <b>H</b> of Henry coefficients of the gases in the MOFs. Characterizing this mapping, the singular value decomposition of <b>H </b>is a useful tool for evaluating MOF subsets for sensor arrays, as it determines the sensitivity of the predicted gas composition to measurement error, quantifies the magnitude of the response to changes in composition, and recovers which direction in gas composition space elicits the largest/smallest response. To illustrate, on the basis of experimental adsorption data, we curate MOFs for a sensor array with the objective of determining the concentration of CO<sub>2</sub> and SO<sub>2</sub> in the gas phase.

scholarly journals Probing Multiscale Disorder in Pyrochlore and Related Complex Oxides in the Transmission Electron Microscope: A Review

2021 ◽  
Vol 9 ◽  
Author(s):  
Jenna L. Wardini ◽  
Hasti Vahidi ◽  
Huiming Guo ◽  
William J. Bowman
Keyword(s):  
Complex Oxides ◽  
Atomic Scale ◽  
High Dimensional ◽  
Detection Systems ◽  
Spatially Resolved ◽  
Chemical Ordering ◽  
Transmission Electron ◽  
The Many ◽  
High Dimensional Datasets

Transmission electron microscopy (TEM), and its counterpart, scanning TEM (STEM), are powerful materials characterization tools capable of probing crystal structure, composition, charge distribution, electronic structure, and bonding down to the atomic scale. Recent (S)TEM instrumentation developments such as electron beam aberration-correction as well as faster and more efficient signal detection systems have given rise to new and more powerful experimental methods, some of which (e.g., 4D-STEM, spectrum-imaging, in situ/operando (S)TEM)) facilitate the capture of high-dimensional datasets that contain spatially-resolved structural, spectroscopic, time- and/or stimulus-dependent information across the sub-angstrom to several micrometer length scale. Thus, through the variety of analysis methods available in the modern (S)TEM and its continual development towards high-dimensional data capture, it is well-suited to the challenge of characterizing isometric mixed-metal oxides such as pyrochlores, fluorites, and other complex oxides that reside on a continuum of chemical and spatial ordering. In this review, we present a suite of imaging and diffraction (S)TEM techniques that are uniquely suited to probe the many types, length-scales, and degrees of disorder in complex oxides, with a focus on disorder common to pyrochlores, fluorites and the expansive library of intermediate structures they may adopt. The application of these techniques to various complex oxides will be reviewed to demonstrate their capabilities and limitations in resolving the continuum of structural and chemical ordering in these systems.

scholarly journals Diabetes and its Complication Prediction using Multi-Task Learning

2020 ◽  
Vol 9 (5) ◽  
pp. 1426-1430
Keyword(s):  
Risk Factors ◽  
Diabetes Patient ◽  
Prediction Performance ◽  
Multitask Learning ◽  
High Dimensional ◽  
Disease Prediction ◽  
Healthcare Applications ◽  
Future Health ◽  
High Dimensional Datasets

Diabetes is a long-term disease that ends up in multiple side-effects. It has now become a reticent exterminator in society because it doesn’t reveal any signs hitherto to the patients until it’s too late. It leads to many complications to other organs, such as kidney, cardiovascular, liver or blood pressure [1]. This work tends to apply a unique multitask learning [2] to synchronously map the relation between manifold complications wherever every task conforms to risks of modelling of complications [3]. It also uses feature selection to reduce the set of risk factors from high-dimensional datasets. Then using the concept of correlation, it finds the degree of relativity among various sideeffects. The proposed method is able to identify the possible future health hazards identified with the diabetes patient. This will enable us to explain medical conditions and can improves healthcare applications which would help to improve disease prediction performance.

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