scholarly journals Low-Rank Approximations of Nonseparable Panel Models

2021 ◽  
Author(s):  
Iván Fernández-Val ◽  
Hugo Freeman ◽  
Martin Weidner
Keyword(s):  
Voter Turnout ◽  
Matrix Completion ◽  
Principal Component ◽  
Low Rank ◽  
Estimation Methods ◽  
Difference In Differences ◽  
Panel Models ◽  
Large Panels ◽  
Low Rank Approximations ◽  
The U.S

Abstract We provide estimation methods for nonseparable panel models based on low-rank factor structure approximations. The factor structures are estimated by matrix-completion methods to deal with the computational challenges of principal component analysis in the presence of missing data. We show that the resulting estimators are consistent in large panels, but suffer from approximation and shrinkage biases. We correct these biases using matching and difference-in-differences approaches. Numerical examples and an empirical application to the effect of election day registration on voter turnout in the U.S. illustrate the properties and usefulness of our methods.

scholarly journals Low-Rank and Sparse Recovery of Human Gait Data

Sensors ◽  
2020 ◽  
Vol 20 (16) ◽  
pp. 4525
Author(s):  
Kaveh Kamali ◽  
Ali Akbar Akbari ◽  
Christian Desrosiers ◽  
Alireza Akbarzadeh ◽  
Martin J.-D. Otis ◽  
...  
Keyword(s):  
Matrix Completion ◽  
Principal Component ◽  
Reconstruction Error ◽  
Human Motion ◽  
Optical Tracking ◽  
Training Data ◽  
Low Rank ◽  
Human Gait ◽  
Group Sparsity ◽  
Model Combining

Due to occlusion or detached markers, information can often be lost while capturing human motion with optical tracking systems. Based on three natural properties of human gait movement, this study presents two different approaches to recover corrupted motion data. These properties are used to define a reconstruction model combining low-rank matrix completion of the measured data with a group-sparsity prior on the marker trajectories mapped in the frequency domain. Unlike most existing approaches, the proposed methodology is fully unsupervised and does not need training data or kinematic information of the user. We evaluated our methods on four different gait datasets with various gap lengths and compared their performance with a state-of-the-art approach using principal component analysis (PCA). Our results showed recovering missing data more precisely, with a reduction of at least 2 mm in mean reconstruction error compared to the literature method. When a small number of marker trajectories is available, our findings showed a reduction of more than 14 mm for the mean reconstruction error compared to the literature approach.

scholarly journals Principal Component Analysis and Its Derivation From Singular Value Decomposition

2019 ◽  
Vol 8 (2) ◽  
pp. 183
Author(s):  
Orumie, Ukamaka Cynthia ◽  
Ogbonna Onyinyechi
Keyword(s):  
Principal Component Analysis ◽  
Singular Value Decomposition ◽  
Principal Component ◽  
Component Analysis ◽  
Singular Value ◽  
Low Rank ◽  
Singular Value Decomposition Method ◽  
Daunting Task ◽  
Low Rank Approximations ◽  
Value Decomposition

Generally, today data analysts and researchers are often faced with a daunting task of reducing high dimensional datasets as large volume of data can be easily generated given the explosive activities of the internet. The most widely used tools for data reduction is the principal component analysis. Merely in some cases, the singular value decomposition method is applied. The study examined the application and theoretical framework of these methods in terms of its linear algebra foundation. The study discovered that the SVD method is a more robust and general method for a change of basis and low rank approximations. But.in terms of application, the PCA method is easy to interpret as illustrated in the work.

Genetic Analysis of Chinese Cucumber Collections in the U.S. National Germplasm Collection

HortScience ◽  
1998 ◽  
Vol 33 (3) ◽  
pp. 534e-534 ◽  
Author(s):  
J. Staub ◽  
Felix Sequen ◽  
Tom Horejsi ◽  
Jin Feng Chen
Keyword(s):  
Genetic Diversity ◽  
Principal Component Analysis ◽  
Genetic Variation ◽  
Genetic Analysis ◽  
Allelic Variation ◽  
Germplasm Collection ◽  
Principal Component ◽  
Isozyme Loci ◽  
National Plant Germplasm System ◽  
The U.S

Genetic variation in cucumber accessions from China was assessed by examining variation at 21 polymorphic isozyme loci. Principal component analysis of allelic variation allowed for the depiction of two distinct groupings of Chinese accessions collected in 1994 and 1996 (67 accessions). Six isozyme loci (Gpi, Gr, Mdh-2, Mpi-2, Pep-gl, and Pep-la) were important in elucidating these major groups. These groupings were different from a single grouping of Chinese 146 accessions acquired before 1994. Allelic variation in Chinese accessions allowed for comparisons with other accessions in the U.S. National Plant Germplasm System (U.S. NPGS) collection grouped by continent and sub-continent. When Chinese accessions taken collectively were compared with an array of 853 C. sativus U.S. NPGS accessions examined previously, relationships differed between accessions grouped by country or subcontinent. Data indicate that acquisition of additional Chinese and Indian cucumber accessions would be strategically important for increasing genetic diversity in the U.S. NPGS cucumber collection.

scholarly journals Robust Principal Component Analysis-Based Infrared Small Target Detection

2019 ◽  
Vol 33 ◽  
pp. 9925-9926
Author(s):  
Qiwei Chen ◽  
Cheng Wu ◽  
Yiming Wang
Keyword(s):  
Iteration Process ◽  
Principal Component ◽  
Component Analysis ◽  
Low Rank ◽  
Small Target ◽  
Frame Sequence ◽  
Augmented Lagrange Multiplier ◽  
Small Targets ◽  
Infrared Small Target ◽  
Augmented Lagrange Multiplier Method

A method based on Robust Principle Component Analysis (RPCA) technique is proposed to detect small targets in infrared images. Using the low rank characteristic of background and the sparse characteristic of target, the observed image is regarded as the sum of a low-rank background matrix and a sparse outlier matrix, and then the decomposition is solved by the RPCA. The infrared small target is extracted from the single-frame image or multi-frame sequence. In order to get more efficient algorithm, the iteration process in the augmented Lagrange multiplier method is improved. The simulation results show that the method can detect out the small target precisely and efficiently.

scholarly journals Clipped Matrix Completion: A Remedy for Ceiling Effects

2019 ◽  
Vol 33 ◽  
pp. 5151-5158
Author(s):  
Takeshi Teshima ◽  
Miao Xu ◽  
Issei Sato ◽  
Masashi Sugiyama
Keyword(s):  
Matrix Completion ◽  
Low Rank ◽  
Trace Norm ◽  
Minimization Algorithm ◽  
Benchmark Data ◽  
Hinge Loss ◽  
Norm Minimization ◽  
Rank Matrix ◽  
Recovery Error ◽  
Low Rank Matrix

We consider the problem of recovering a low-rank matrix from its clipped observations. Clipping is conceivable in many scientific areas that obstructs statistical analyses. On the other hand, matrix completion (MC) methods can recover a low-rank matrix from various information deficits by using the principle of low-rank completion. However, the current theoretical guarantees for low-rank MC do not apply to clipped matrices, as the deficit depends on the underlying values. Therefore, the feasibility of clipped matrix completion (CMC) is not trivial. In this paper, we first provide a theoretical guarantee for the exact recovery of CMC by using a trace-norm minimization algorithm. Furthermore, we propose practical CMC algorithms by extending ordinary MC methods. Our extension is to use the squared hinge loss in place of the squared loss for reducing the penalty of overestimation on clipped entries. We also propose a novel regularization term tailored for CMC. It is a combination of two trace-norm terms, and we theoretically bound the recovery error under the regularization. We demonstrate the effectiveness of the proposed methods through experiments using both synthetic and benchmark data for recommendation systems.

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