NonnegativeRank · Geometry of Nonnegative Rank
„Хоризонт 2020“ — Действия „Мария Склодовска-Кюри“
- Период
- 2017-09-01 → 2019-08-31
- Финансиране от ЕС
- 166 603 €
- Участници
- 2
- Схема
- MSCA-IF-GF
Линиите свързват координатора с партньорите.
Накратко на български
Неотрицателният ранг изследва геометрията на матрици и тензори, което помага при компресирането на изображения и анализа на документи. Разбирането на тези структури подобрява теорията и алгоритмите в статистиката, машинното обучение и обработката на аудио сигнали.
Кратко обяснение, генерирано от езиков модел по текста на CORDIS. Оригиналът е по-долу.
Резултати накратко
Geometry of Nonnegative Rank
This project is centered on nonnegative rank - a notion that modifies the definition of matrix rank. Our goal is to do basic research aimed at better understanding the geometry of matrices and tensors of nonnegative rank at most r. Nonnegative rank appears in various applications such as statistics, machine learning, audio processing, image compression and document analysis. Understanding the geometry of nonnegative rank is fundamental in its own right and important for the theory and algorithms behind the applications. The overall objectives of this project are investigation of zero patterns in nonnegative matrix factorizations, understanding the boundaries and semialgebraic descriptions of the set of matrices and tensors of nonnegative rank r for small r, and implications of this theory to applications in statistics and other fields. We concluded that tools from (algebraic) geometry, rigidity theory and optimization are essential for studying nonnegative rank and related notions, and that especially the study of uniqueness and identifiability aspects benefits enormously from geometric tools.
Текст от CORDIS, на английски · Данни: CORDIS, © Европейски съюз
Цел на проекта
This proposal is centered on nonnegative rank - a notion that modifies the definition of matrix rank. This project is basic research aimed to better understand the geometry of matrices and tensors of nonnegative rank at most r, how this knowledge can be employed to improve exact and numerical nonnegative matrix algorithms, obtain an algorithm for nested polytopes in dimension three, and address questions about mixture models in statistics. Computing and understanding nonnegative rank is truly interdisciplinary. Completing this project requires techniques from polyhedral geometry, real algebraic geometry, optimization, statistics, symbolic algebra, and numerics.
Оригинален текст от CORDIS (на английски).
Участници
- SORBONNE UNIVERSITE · ParisКоординаторФранция
- MASSACHUSETTS INSTITUTE OF TECHNOLOGY · CambridgeСъединени щати
Връзки
Данни: CORDIS, © Европейски съюз