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Grassmann discriminant analysis: a unifying view on subspace-based learning

Authors:

Daniel D. LeeAuthors Info & Claims

ICML '08: Proceedings of the 25th international conference on Machine learning

Pages 376 - 383

https://doi.org/10.1145/1390156.1390204

Published: 05 July 2008 Publication History

Abstract

In this paper we propose a discriminant learning framework for problems in which data consist of linear subspaces instead of vectors. By treating subspaces as basic elements, we can make learning algorithms adapt naturally to the problems with linear invariant structures. We propose a unifying view on the subspace-based learning method by formulating the problems on the Grassmann manifold, which is the set of fixed-dimensional linear subspaces of a Euclidean space. Previous methods on the problem typically adopt an inconsistent strategy: feature extraction is performed in the Euclidean space while non-Euclidean distances are used. In our approach, we treat each sub-space as a point in the Grassmann space, and perform feature extraction and classification in the same space. We show feasibility of the approach by using the Grassmann kernel functions such as the Projection kernel and the Binet-Cauchy kernel. Experiments with real image databases show that the proposed method performs well compared with state-of-the-art algorithms.

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Cited By

Xu HZhang CHuang LTao JZheng J(2025)A Discriminative Prediction Strategy Based on Multi-View Knowledge Transfer for Dynamic Multi-Objective OptimizationProcesses10.3390/pr1303074413:3(744)Online publication date: 4-Mar-2025
https://doi.org/10.3390/pr13030744
Maswanganyi RTu COwolawi PDu S(2025)Single-Source and Multi-Source Cross-Subject Transfer Based on Domain Adaptation Algorithms for EEG ClassificationMathematics10.3390/math1305080213:5(802)Online publication date: 27-Feb-2025
https://doi.org/10.3390/math13050802
Fei YLiu YJia CLi ZWei XChen M(2025)A Survey of Geometric Optimization for Deep Learning: From Euclidean Space to Riemannian ManifoldACM Computing Surveys10.1145/370849857:5(1-37)Online publication date: 24-Jan-2025
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Index Terms

Grassmann discriminant analysis: a unifying view on subspace-based learning
1. Computing methodologies
  1. Machine learning
  2. Modeling and simulation
    1. Model development and analysis
      1. Model verification and validation

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Information

Published In

cover image ACM Other conferences

ICML '08: Proceedings of the 25th international conference on Machine learning

July 2008

1310 pages

ISBN:9781605582054

DOI:10.1145/1390156

General Chair:
William Cohen
Carnegie Mellon University
,
Program Chairs:
Andrew McCallum
University of Massachusetts Amherst
,
Sam Roweis
University of Toronto and Google

Copyright © 2008 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Pascal
University of Helsinki
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Google Inc.
NSF
Machine Learning Journal/Springer
Microsoft Research: Microsoft Research
Intel: Intel
Yahoo!
Helsinki Institute for Information Technology
IBM: IBM

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 05 July 2008

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ICML '08

Sponsor:

Microsoft Research
Intel
IBM

ICML '08: The 25th Annual International Conference on Machine Learning held in conjunction with the 2007 International Conference on Inductive Logic Programming

July 5 - 9, 2008

Helsinki, Finland

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Overall Acceptance Rate 140 of 548 submissions, 26%

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Cited By

Xu HZhang CHuang LTao JZheng J(2025)A Discriminative Prediction Strategy Based on Multi-View Knowledge Transfer for Dynamic Multi-Objective OptimizationProcesses10.3390/pr1303074413:3(744)Online publication date: 4-Mar-2025
https://doi.org/10.3390/pr13030744
Maswanganyi RTu COwolawi PDu S(2025)Single-Source and Multi-Source Cross-Subject Transfer Based on Domain Adaptation Algorithms for EEG ClassificationMathematics10.3390/math1305080213:5(802)Online publication date: 27-Feb-2025
https://doi.org/10.3390/math13050802
Fei YLiu YJia CLi ZWei XChen M(2025)A Survey of Geometric Optimization for Deep Learning: From Euclidean Space to Riemannian ManifoldACM Computing Surveys10.1145/370849857:5(1-37)Online publication date: 24-Jan-2025
https://dl.acm.org/doi/10.1145/3708498
Mohammadi MBabai MWilkinson M(2025)Generalized Relevance Learning Grassmann QuantizationIEEE Transactions on Pattern Analysis and Machine Intelligence10.1109/TPAMI.2024.346631547:1(502-513)Online publication date: Jan-2025
https://doi.org/10.1109/TPAMI.2024.3466315
Dou ZRen HMa YGao YHuang GMa X(2025)One-step Multi-view Spectral Clustering with Subspaces Fusion on Grassmann manifoldNeurocomputing10.1016/j.neucom.2025.129568626(129568)Online publication date: Apr-2025
https://doi.org/10.1016/j.neucom.2025.129568
Yu NChen LYi X(2025)Enhancing explainability via distinguishable feature learning based on causality in image classificationDisplays10.1016/j.displa.2024.10293387(102933)Online publication date: Apr-2025
https://doi.org/10.1016/j.displa.2024.102933
Cevikalp HTurgut KTopal C(2025)Discriminative Frontal Face Synthesis by Using Attention and Metric LearningJournal of Signal Processing Systems10.1007/s11265-025-01942-1Online publication date: 4-Feb-2025
https://doi.org/10.1007/s11265-025-01942-1
Li BWang TRan R(2025)Discriminant locality preserving projection on Grassmann Manifold for image-set classificationThe Journal of Supercomputing10.1007/s11227-024-06904-181:2Online publication date: 17-Jan-2025
https://doi.org/10.1007/s11227-024-06904-1
Wang GGu Y(2024)Multi-Task Scenario Encrypted Traffic Classification and Parameter AnalysisSensors10.3390/s2410307824:10(3078)Online publication date: 12-May-2024
https://doi.org/10.3390/s24103078
Wang RHu CChen ZWu XSong XLarson K(2024)A Grassmannian manifold self-attention network for signal classificationProceedings of the Thirty-Third International Joint Conference on Artificial Intelligence10.24963/ijcai.2024/564(5099-5107)Online publication date: 3-Aug-2024
https://dl.acm.org/doi/10.24963/ijcai.2024/564
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