14.1.4.2 Riemannian Manifold Learning, Grassman Manifold Clustering

Lin, T.[Tong], Zha, H.B.[Hong-Bin],
Riemannian Manifold Learning,
PAMI(30), No. 5, May 2008, pp. 796-809.
IEEE DOI 0803
BibRef

Lin, T.[Tong], Zha, H.B.[Hong-Bin], Lee, S.U.[Sang Uk],
Riemannian Manifold Learning for Nonlinear Dimensionality Reduction,
ECCV06(I: 44-55).
Springer DOI 0608
BibRef

Subbarao, R.[Raghav], Meer, P.[Peter],
Nonlinear Mean Shift over Riemannian Manifolds,
IJCV(84), No. 1, August 2009, pp. xx-yy.
Springer DOI 0905
BibRef
Earlier:
Discontinuity Preserving Filtering over Analytic Manifolds,
CVPR07(1-6).
IEEE DOI 0706
BibRef
Earlier:
Nonlinear Mean Shift for Clustering over Analytic Manifolds,
CVPR06(I: 1168-1175).
IEEE DOI 0606
BibRef
And:
Subspace Estimation Using Projection Based M-Estimators over Grassmann Manifolds,
ECCV06(I: 301-312).
Springer DOI 0608
BibRef
Earlier:
Heteroscedastic Projection Based M-Estimators,
EEMCV05(III: 38-38).
IEEE DOI 0507
projection based estimator to eliminate RANSAC problems. BibRef

Subbarao, R.[Raghav], Genc, Y.[Yakup], Meer, P.[Peter],
Robust unambiguous parametrization of the essential manifold,
CVPR08(1-8).
IEEE DOI 0806
BibRef
Earlier:
Nonlinear Mean Shift for Robust Pose Estimation,
WACV07(6-6).
IEEE DOI 0702
BibRef

Tan, H.L.[Heng-Liang], Ma, Z.M.[Zheng-Ming], Zhang, S.[Sumin], Zhan, Z.R.[Zeng-Rong], Zhang, B.B.[Bei-Bei], Zhang, C.G.[Cheng-Gong],
Grassmann manifold for nearest points image set classification,
PRL(68, Part 1), No. 1, 2015, pp. 190-196.
Elsevier DOI 1512
Image set classification BibRef

Zhao, K.[Kun], Alavi, A.[Azadeh], Wiliem, A.[Arnold], Lovell, B.C.[Brian C.],
Efficient clustering on Riemannian manifolds: A kernelised random projection approach,
PR(51), No. 1, 2016, pp. 333-345.
Elsevier DOI 1601
Riemannian manifolds BibRef

Liu, T., Shi, Z., Liu, Y.,
Joint Normalization and Dimensionality Reduction on Grassmannian: A Generalized Perspective,
SPLetters(25), No. 6, June 2018, pp. 858-862.
IEEE DOI 1806
geometry, image recognition, learning (artificial intelligence), optimisation, Grassmann manifold, Riemannian geometry, image-set recognition BibRef

Ali, M.[Muhammad], Gao, J.B.[Jun-Bin], Antolovich, M.[Michael],
Parametric Classification of Bingham Distributions Based on Grassmann Manifolds,
IP(28), No. 12, December 2019, pp. 5771-5784.
IEEE DOI 1909
Manifolds, Kernel, Data models, Bayes methods, Parametric statistics, Maximum likelihood estimation, Analytical models, classification BibRef

Xie, X.F.[Xiao-Feng], Yu, Z.L.[Zhu Liang], Gu, Z.H.[Zheng-Hui], Li, Y.Q.[Yuan-Qing],
Classification of symmetric positive definite matrices based on bilinear isometric Riemannian embedding,
PR(87), 2019, pp. 94-105.
Elsevier DOI 1812
Covariance feature, Dimensionality reduction, Isometric projection, Riemannian manifold, Pattern classification BibRef

Hechmi, S.[Sabra], Gallas, A.[Abir], Zagrouba, E.[Ezzeddine],
Multi-kernel sparse subspace clustering on the Riemannian manifold of symmetric positive definite matrices,
PRL(125), 2019, pp. 21-27.
Elsevier DOI 1909
Sparse subspace clustering (SSC), Riemannian kernel, Multi-kernel SSC, Face clustering BibRef

Gao, Z.[Zhi], Wu, Y.W.[Yu-Wei], Bu, X.Y.[Xing-Yuan], Yu, T.[Tan], Yuan, J.S.[Jun-Song], Jia, Y.D.[Yun-De],
Learning a robust representation via a deep network on symmetric positive definite manifolds,
PR(92), 2019, pp. 1-12.
Elsevier DOI 1905
Feature aggregation, SPD Matrix, Riemannian manifold, Deep convolutional network BibRef

Minnehan, B.[Breton], Savakis, A.[Andreas],
Deep domain adaptation with manifold aligned label transfer,
MVA(30), No. 3, April 2019, pp. 473-485.
WWW Link. 1906
BibRef
Earlier:
Manifold Guided Label Transfer for Deep Domain Adaptation,
Diff-CVML17(744-752)
IEEE DOI 1709
Feature extraction, Manifolds, Measurement, Principal component analysis, Training BibRef

Kumar, S.[Sriram], Savakis, A.[Andreas],
Learning a perceptual manifold for image set classification,
ICIP16(4433-4437)
IEEE DOI 1610
BibRef
Earlier:
Robust Domain Adaptation on the L1-Grassmannian Manifold,
DIFF-CV16(1058-1065)
IEEE DOI 1612
Biologically motivated BibRef

Yang, Z., Cheng, Y., Wu, H., Wang, H.,
Enhanced Matrix CFAR Detection With Dimensionality Reduction of Riemannian Manifold,
SPLetters(27), 2020, pp. 2084-2088.
IEEE DOI 2012
Matrix CFAR detection, Riemannian manifold, dimensionality reduction, Grassmann manifold, orthonormal constraint optimization BibRef

Chen, S., Harandi, M., Jin, X., Yang, X.,
Domain Adaptation by Joint Distribution Invariant Projections,
IP(29), 2020, pp. 8264-8277.
IEEE DOI 2008
Kernel, Covariance matrices, Training, Labeling, Estimation, Optimization, Dimensionality reduction, L²-distance, Riemannian optimization BibRef

Wei, D.[Dong], Shen, X.B.[Xiao-Bo], Sun, Q.S.[Quan-Sen], Gao, X.Z.[Xi-Zhan], Yan, W.Z.[Wen-Zhu],
Prototype learning and collaborative representation using Grassmann manifolds for image set classification,
PR(100), 2020, pp. 107123.
Elsevier DOI 2005
Image set classification, Collaborative representation, Prototype learning, Grassmann manifolds BibRef

Wang, B., Hu, Y., Gao, J., Sun, Y., Ju, F., Yin, B.,
Learning Adaptive Neighborhood Graph on Grassmann Manifolds for Video/Image-Set Subspace Clustering,
MultMed(23), 2021, pp. 216-227.
IEEE DOI 2012
Manifolds, Laplace equations, Learning systems, Videos, Clustering methods, Streaming media, adaptive neighborhood regularization BibRef

Wang, H.Y.[Hai-Yan], Han, G.Q.[Guo-Qiang], Zhang, B.[Bin], Tao, G.H.[Gui-Hua], Cai, H.M.[Hong-Min],
Multi-View Learning a Decomposable Affinity Matrix via Tensor Self-Representation on Grassmann Manifold,
IP(30), 2021, pp. 8396-8409.
IEEE DOI 2110
Tensors, Manifolds, Task analysis, Matrix decomposition, Sparse matrices, Merging, Clustering methods, Grassmann manifold BibRef

Wu, D.Y.[Dan-Yang], Dong, X.[Xia], Nie, F.P.[Fei-Ping], Wang, R.[Rong], Li, X.L.[Xue-Long],
An attention-based framework for multi-view clustering on Grassmann manifold,
PR(128), 2022, pp. 108610.
Elsevier DOI 2205
Multi-view clustering, Grassmann manifold, Principle angles, Attentive weighted-learning scheme BibRef

Chakraborty, R.[Rudrasis], Bouza, J.[Jose], Manton, J.H.[Jonathan H.], Vemuri, B.C.[Baba C.],
ManifoldNet: A Deep Neural Network for Manifold-Valued Data With Applications,
PAMI(44), No. 2, February 2022, pp. 799-810.
IEEE DOI 2201
Deep learning on geometric data, e.g. pose.Manifolds, Biomedical imaging, Neural networks, Measurement, Standards, riemannian manifolds BibRef

Chen, S.T.[Sen-Tao], Zheng, L.[Lin], Wu, H.[Hanrui],
Riemannian representation learning for multi-source domain adaptation,
PR(137), 2023, pp. 109271.
Elsevier DOI 2302
Convex optimization, Hellinger distance, Multi-source domain adaptation, Representation learning, Riemannian manifold BibRef

Yin, W.G.[Wan-Guang], Ma, Z.M.[Zheng-Ming], Liu, Q.Y.[Quan-Ying],
Discriminative subspace learning via optimization on Riemannian manifold,
PR(139), 2023, pp. 109450.
Elsevier DOI 2304
Discriminative subspace learning, Riemannian manifold optimization, Dimensionality reduction, Classification BibRef

Ben Amor, B.[Boulbaba], Arguillère, S.[Sylvain], Shao, L.[Ling],
ResNet-LDDMM: Advancing the LDDMM Framework Using Deep Residual Networks,
PAMI(45), No. 3, March 2023, pp. 3707-3720.
IEEE DOI 2302
Shape, Strain, Measurement, Kernel, Residual neural networks, Point cloud compression, Computational anatomy, Riemannian geometry BibRef

Mohammadi, M., Babai, M., Wilkinson, M.H.F.,
Generalized Relevance Learning Grassmann Quantization,
PAMI(47), No. 1, January 2025, pp. 502-513.
IEEE DOI 2412
Learning from sets of images. Manifolds, Prototypes, Vectors, Vector quantization, Face recognition, Training, Complexity theory, GLVQ classifier BibRef

Zeng, X.H.[Xian-Hua], Guo, J.[Jueqiu], Wei, Y.F.[Yi-Fan], Zhuo, Y.[Yang],
Deep hybrid manifold for image set classification,
IVC(143), 2024, pp. 104935.
Elsevier DOI 2403
The image set data is modeled through SPD manifold and Grassmann manifold. The modeled data is input into the backbone network composed of SPDNet and GrNet for initial feature extraction, and the output manifold data are input into HMAEs. SPD manifold, Grassmann manifold, Visual classification, Hybrid manifold, Neural network BibRef

Cai, L.P.[Li-Peng], Shi, J.[Jun], Du, S.[Shaoyi], Gao, Y.[Yue], Ying, S.H.[Shi-Hui],
Self-adaptive subspace representation from a geometric intuition,
PR(149), 2024, pp. 110228.
Elsevier DOI 2403
Subspace learning, Grassmannian manifold, Geometric model, Intrinsic algorithm BibRef

Tayanov, V.[Vitaliy], Krzyzak, A.[Adam], Suen, C.Y.[Ching Y.],
Analysis of Different Deep Learning Architectures to Learn Generalised Classifier Stacking on Riemannian and Grassmann Manifolds,
ICPR22(2735-2741)
IEEE DOI 2212
Manifolds, Geometry, Architecture, Stacking, Deep architecture, Predictive models BibRef

Tayanov, V.[Vitaliy], Krzyzak, A.[Adam], Suen, C.Y.[Ching Y.],
Comparison of Stacking-based Classifier Ensembles using Euclidean and Riemannian Geometries,
ICPR21(10359-10366)
IEEE DOI 2105
Geometry, Radio frequency, Manifolds, Stacking, Neural networks, Vegetation, Prediction algorithms BibRef

Piao, X.L.[Xing-Lin], Hu, Y.L.[Yong-Li], Gao, J.B.[Jun-Bin], Sun, Y.F.[Yan-Feng], Yang, X.[Xin], Yin, B.C.[Bao-Cai],
Reweighted Non-Convex Non-Smooth Rank Minimization Based Spectral Clustering on Grassmann Manifold,
ACCV20(V:562-577).
Springer DOI 2103
BibRef

Schwarz, J.[Jonathan], Draxler, F.[Felix], Köthe, U.[Ullrich], Schnörr, C.[Christoph],
Riemannian SOS-Polynomial Normalizing Flows,
GCPR20(218-231).
Springer DOI 2110
BibRef

Shao, H.[Hang], Kumar, A.[Abhishek], Fletcher, P.T.[P. Thomas],
The Riemannian Geometry of Deep Generative Models,
Diff-CVML18(428-4288)
IEEE DOI 1812
Manifolds, Jacobian matrices, Computational modeling, Measurement, Geometry, Generators, Data models BibRef

Li, Y., Lu, R.,
Riemannian Metric Learning based on Curvature Flow,
ICPR18(806-811)
IEEE DOI 1812
Manifolds, Geometry, Euclidean distance, Matrix decomposition, Machine learning algorithms, Dimensionality reduction, Riemannian curvature BibRef

Tayanov, V., Krzyzak, A., Suen, C.Y.,
Prediction-based classification using learning on Riemannian manifolds,
ICPR18(591-596)
IEEE DOI 1812
Manifolds, Measurement, Symmetric matrices, Radio frequency, Tensile stress, Decision trees, Prediction algorithms BibRef

Chen, K., Wu, X., Wang, R., Kittler, J.V.,
Riemannian kernel based Nyström method for approximate infinite-dimensional covariance descriptors with application to image set classification,
ICPR18(651-656)
IEEE DOI 1812
Manifolds, Kernel, Covariance matrices, Measurement, Feature extraction, Symmetric matrices, Task analysis, Reproducing Kernel Hilbert Space BibRef

Ilea, I.[Ioana], Bombrun, L.B.[Lionel Bombrun], Said, S.[Salem], Berthoumieu, Y.[Yannick],
Covariance Matrices Encoding Based on the Log-Euclidean and Affine Invariant Riemannian Metrics,
Diff-CVML18(506-50609)
IEEE DOI 1812
Covariance matrices, Measurement, Manganese, Encoding, Computational modeling, Feature extraction, Histograms BibRef

Lohit, S.[Suhas], Turaga, P.K.[Pavan K.],
Learning Invariant Riemannian Geometric Representations Using Deep Nets,
Manifold17(1329-1338)
IEEE DOI 1802
Train deep neural nets whose final outputs are elements on a Riemannian manifold. Face, Geometry, Lighting, Machine learning, Manifolds, Neural networks BibRef

Zheng, L.G.[Li-Gang], Qiu, G.P.[Guo-Ping], Huang, J.W.[Ji-Wu],
Clustering Symmetric Positive Definite Matrices on the Riemannian Manifolds,
ACCV16(I: 400-415).
Springer DOI 1704
BibRef

Yang, Y.X.[Yong-Xin], Hospedales, T.M.[Timothy M.],
Multivariate Regression on the Grassmannian for Predicting Novel Domains,
CVPR16(5071-5080)
IEEE DOI 1612
BibRef
Earlier:
Zero-Shot Domain Adaptation via Kernel Regression on the Grassmannian,
DIFF-CV15(xx-yy).
DOI Link 1601
BibRef

Masci, J., Boscaini, D., Bronstein, M.M., Vandergheynst, P.,
Geodesic Convolutional Neural Networks on Riemannian Manifolds,
3DRR15(832-840)
IEEE DOI 1602
Eigenvalues and eigenfunctions BibRef

Kim, K.I.[Kwang In], Tompkin, J.[James], Theobalt, C.[Christian],
Curvature-Aware Regularization on Riemannian Submanifolds,
ICCV13(881-888)
IEEE DOI 1403
Semi-supervised learning; manifold; regularization BibRef

Zheng, J.J.[Jing-Jing], Liu, M.Y.[Ming-Yu], Chellappa, R.[Rama], Phillips, P.J.[P. Jonathon],
A Grassmann manifold-based domain adaptation approach,
ICPR12(2095-2099).
WWW Link. 1302
shifts in the distribution between training and testing data BibRef

Yu, D.J.[Dong-Jun], Hancock, E.R.[Edwin R.], Smith, W.A.P.[William A. P.],
A Riemannian Self-Organizing Map,
CIAP09(229-238).
Springer DOI 0909
Generalize SOM to Riemannian space. BibRef

Goh, A.[Alvina], Vidal, R.[Rene],
Clustering and dimensionality reduction on Riemannian manifolds,
CVPR08(1-7).
IEEE DOI 0806
BibRef

Zhao, D.L.[De-Li], Lin, Z.C.[Zhou-Chen], Tang, X.[Xiaoou],
Classification via semi-Riemannian spaces,
CVPR08(1-8).
IEEE DOI 0806
BibRef
Earlier:
Contextual Distance for Data Perception,
ICCV07(1-8).
IEEE DOI 0710
Context from nearest neighbors. BibRef

Brun, A.[Anders], Westin, C.F.[Carl-Fredrik], Herberthson, M.[Magnus], Knutsson, H.[Hans],
Fast Manifold Learning Based on Riemannian Normal Coordinates,
SCIA05(920-929).
Springer DOI 0506
BibRef

Chapter on Pattern Recognition, Clustering, Statistics, Grammars, Learning, Neural Nets, Genetic Algorithms continues in
Spectral Clustering, Data Dimensionality Reduction .