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Multilevel Low Rank Matrices and Applications
Multilevel Low Rank Matrices and Applications
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20250211152117
- ISBN
- 9798384341420
- DDC
- 330
- 서명/저자
- Multilevel Low Rank Matrices and Applications
- 발행사항
- [Sl] : Stanford University, 2024
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2024
- 형태사항
- 106 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 86-03, Section: B.
- 주기사항
- Advisor: Boyd, Stephen.
- 학위논문주기
- Thesis (Ph.D.)--Stanford University, 2024.
- 초록/해제
- 요약The purpose of this thesis is to present a new matrix format that extends low rank matrices to handle hierarchically structured data, which we refer to as the multilevel low rank (MLR) matrix. We demonstrate that this format compresses storage and supports fast linear algebraic operations.We consider two metrics for fitting MLR matrices: the Frobenius norm difference between the data matrix and the MLR, and the log-likelihood of observations for the positive semidefinite MLR. Using the Frobenius norm, we provide heuristic methods for fitting factors, rank allocation, and hierarchy. Using log-likelihood, we introduce a fast method for fitting factors in the multilevel factor model in linear time without ever forming the full covariance matrix.Through various examples, we illustrate that, in some cases, the MLR structure is advantageous for fitting data.
- 일반주제명
- Sparsity
- 일반주제명
- Decomposition
- 일반주제명
- Integral equations
- 일반주제명
- Fourier transforms
- 일반주제명
- Iterative methods
- 일반주제명
- Neural networks
- 일반주제명
- Linear algebra
- 일반주제명
- Mathematics
- 기타저자
- Stanford University.
- 기본자료저록
- Dissertations Abstracts International. 86-03B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■00520250211152117
■006m o d
■007cr#unu||||||||
■020 ▼a9798384341420
■035 ▼a(MiAaPQ)AAI31460329
■035 ▼a(MiAaPQ)Stanfordpf444cd9151
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a330
■1001 ▼aParshakova, Tetiana.
■24510▼aMultilevel Low Rank Matrices and Applications
■260 ▼a[Sl]▼bStanford University▼c2024
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2024
■300 ▼a106 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 86-03, Section: B.
■500 ▼aAdvisor: Boyd, Stephen.
■5021 ▼aThesis (Ph.D.)--Stanford University, 2024.
■520 ▼aThe purpose of this thesis is to present a new matrix format that extends low rank matrices to handle hierarchically structured data, which we refer to as the multilevel low rank (MLR) matrix. We demonstrate that this format compresses storage and supports fast linear algebraic operations.We consider two metrics for fitting MLR matrices: the Frobenius norm difference between the data matrix and the MLR, and the log-likelihood of observations for the positive semidefinite MLR. Using the Frobenius norm, we provide heuristic methods for fitting factors, rank allocation, and hierarchy. Using log-likelihood, we introduce a fast method for fitting factors in the multilevel factor model in linear time without ever forming the full covariance matrix.Through various examples, we illustrate that, in some cases, the MLR structure is advantageous for fitting data.
■590 ▼aSchool code: 0212.
■650 4▼aSparsity
■650 4▼aDecomposition
■650 4▼aIntegral equations
■650 4▼aFourier transforms
■650 4▼aIterative methods
■650 4▼aNeural networks
■650 4▼aLinear algebra
■650 4▼aMathematics
■690 ▼a0800
■690 ▼a0405
■71020▼aStanford University.
■7730 ▼tDissertations Abstracts International▼g86-03B.
■790 ▼a0212
■791 ▼aPh.D.
■792 ▼a2024
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17162966▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
