Evidence map›Paper›PMID 34776610›Full record

ArticleSIAM journal on matrix analysis and applications : a publication of the Society for Industrial and Applied Mathematics2021

ORTHOGONAL TRACE-SUM MAXIMIZATION: APPLICATIONS, LOCAL ALGORITHMS, AND GLOBAL OPTIMALITY.

Joong-Ho Won, Hua Zhou, Kenneth Lange

Abstract read
PubMed Full text at PMC Publisher
In one paragraph

Article in SIAM journal on matrix analysis and applications : a publication of the Society for Industrial and Applied Mathematics, 2021. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 1 paper.

0numbers the graph read from it
0cells of the map it votes in
1citing papers in PubMed
–field-weighted citation impact
1 · What the graph read from it

What it found

Each row is one number read from the abstract, on the scale the paper reported it, with its interval. Left of the dashed line favours the treatment, right favours the comparator. Under each row is the sentence it came from. New to these charts? A ten-minute tutorial.

The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.

2 · The registry

The trial behind it

Trials whose registry record cites this paper, or whose number appears in the abstract. A trial that started after this paper was published is citing it as background, not reporting it.

Neither the registry nor the abstract names a trial number. If this is a trial report, that itself is worth knowing.

3 · Its place in the literature

Who cites it

1 citing paper in PubMed.

  1. ORTHOGONAL TRACE-SUM MAXIMIZATION: TIGHTNESS OF THE SEMIDEFINITE RELAXATION AND GUARANTEE OF LOCALLY OPTIMAL SOLUTIONS.SIAM journal on optimization : a publication of the Society for Industrial and Applied Mathematics · 2022
    Article
4 · The record

Corrections and comments

PubMed lists nothing against this paper. Absence here is not a guarantee, only a check that was made.

5 · Who and what money

Authors and funding

3 authors.

Joong-Ho WonDepartment of Statistics, Seoul National University, Seoul 08826, Korea.
Hua ZhouDepartment of Biostatistics, University of California, Los Angeles, CA 90095-1766 USA.
Kenneth LangeDepartments of Computational Medicine, Human Genetics, and Statistics, University of California, Los Angeles, CA 90095 USA.

Funding

Genomics, GPUs, and Next Generation Computational StatisticsR01HG006139 · NHGRI · UNIVERSITY OF CALIFORNIA LOS ANGELES · PI SOBEL, ERIC · 2011 to 2023
$5.1M
Modeling, Inference, and Optimization for Genomic and Biomedical Big DataR35GM141798 · NIGMS · UNIVERSITY OF CALIFORNIA LOS ANGELES · PI LANGE, KENNETH L · 2021 to 2025
$2.7M
NHGRI NIH HHS R01 HG006139NIGMS NIH HHS R35 GM141798
6 · The paper itself

Abstract

This paper studies the problem of maximizing the sum of traces of matrix quadratic forms on a product of Stiefel manifolds. This orthogonal trace-sum maximization (OTSM) problem generalizes many interesting problems such as generalized canonical correlation analysis (CCA), Procrustes analysis, and cryo-electron microscopy of the Nobel prize fame. For these applications finding global solutions is highly desirable, but it has been unclear how to find even a stationary point, let alone test its global optimality. Through a close inspection of Ky Fan's classical result [

Indexed as

15B1049K3049M2065K0590C26canonical correlation analysiscryo-EMKurdyka–Łojasiewicz inequalityMAXBETMAXDIFFMM algorithmProcrustes analysissemidefinite programmingStiefel manifold

Identifiers

PMID34776610
PMCPMC8589322

What OpenQuestion holds

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Registered trials

None linked

Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.