Kolda, TG, Bader, BW Tensor decomposition and applications. Pastor Siam 51(3), 455–500 (2009).
Tucker, LR Mathematical notes on three-mode factor analysis. psychometrica 31(3), 279–311 (1966).
Kruskal, JB Ternary arrays: rank and uniqueness of trilinear decompositions with applications to arithmetic complexity and statistics. Linear algebra applications. 18(2), 95–138 (1977).
Bengio, Y., Courville, A., Vincent, P. Representation learning: A review and new perspectives. IEEE Trans. pattern anal. Mach. intelligence. 35(8), 1798–1828 (2013).
Tancik, M. et al. Fourier functions allow networks to learn high-frequency functions in low-dimensional domains. Advanced neural information processes. system. 17537–7547 (2020).
Google Scholar
Hitchcock Frank, L. Tensor or polyadic representation as a sum of products. J. Math. Physics. 6(1–4), 164–189 (1927).
Google Scholar
Acar, E., Dunlavy, DM, Kolda, TG & Mørup, M. Scalable tensor factorization for incomplete data. Kemama. intelligence. Laboratory systems. 106(1), 41–56 (2011).
Google Scholar
Oseledets, IV Tensor train decomposition. Siam J. Sci. Calculate. 33(5), 2295–2317 (2011).
Google Scholar
Cichocki, A., Rafal, Z., Shun-ichi, A. Nonnegative matrices and tensor factorization. [lecture notes]. IEEE Signal Process. Mug. twenty five(1), 142–145 (2007).
Xue, J., Zhao, Y., Tongle, W. & Chan, J. Tensor convolution-like low-rank dictionaries for high-dimensional image representation. IEEE Trans. circle system. video technology. (2024).
Wang, A. et al. The transformed low-rank parameterization helps in robust generalization of tensor neural networks. Advanced neural information processes. system. 363032–3082 (2023).
Google Scholar
Wang, A., Qiu, Y., Huang, H., Jin, Z., Zhou, G., Zhao, Q. Toward a geometric understanding of tensor learning by t-products. in 39th Annual Conference on Neural Information Processing Systems (2025).
Bagherian, M., Chehade, S., Whitney, B. & Passian, A. Classical and quantum compression for edge computing: Dimensionality reduction of ubiquitous data. computing 105(7), 1419–1465 (2023).
Google Scholar
Tenenbaum, JB, Silva, VD & Langford, JC A global geometric framework for nonlinear dimensionality reduction. science 290(5500), 2319–2323 (2000).
Google Scholar
Roweis, ST & Saul, LK Nonlinear dimensionality reduction with local linear embeddings. science 290(5500), 2323–2326 (2000).
Google Scholar
Belkin, M., Partha, N. Laplacian eigenmaps for dimensionality reduction and data representation. neural computing. 15(6), 1373–1396 (2003).
Van der Maaten, L., Hinton, G. Data visualization using t-sne. J. Mach. learn. resolution 9(11) (2008).
McInnes, L., Healy, J., Melville, J. Umap: Uniform manifold approximation and projection for dimensionality reduction, arXiv preprint arXiv:1802.03426 (2018).
Kulis, B. et al. Learning indicators: A survey. Found it. trend mach. learn. 5(4), 287–364 (2013).
Hadsell, R., Chopra, S., and LeCun, Y. Dimensionality reduction by learning invariant mappings. in 2006 ieee computer society conference on computer vision and pattern recognition (cvpr 06)1735–1742 (2006).
Schroff, F., Kalenichenko, D., and Philbin, J. Facenet: Unified embeddings for face recognition and clustering. in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognitionpp. 815–823 (2015).
Wang, H., Wang, Y., Zhou, Z., Ji, X., Gong, D., Zhou, J., Li, Z., and Liu, W. Cosface: Large margin cosine loss for deep face recognition. in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognitionpp. 5265–5274 (2018).
Faghri, F., Fleet, DJ, Kiros, JR, and Sanja, F. Vse++: Improving visual meaning embedding with hard negatives, arXiv preprint arXiv:1707.05612 (2017).
Hermans, A., Lucas, B., Bastian, L. Triplet loss defense for re-identificationarxiv preprint arxiv:1703.07737, (2017).
Wang, T. & Isola, P. Understanding contrastive representation learning through alignment and uniformity on a hypersphere 99299939 (2020).
Google Scholar
Kulkarni, N., Gupta, A., Tulsiani, S. Canonical surface mapping with geometric cycle consistency. in Proceedings of the IEEE/CVF International Conference on Computer Visionpp. 2202–2211 (2019).
Hubble, EP Extragalactic Nebula. Astrophy. J. 64321–369 (1926).
Dieleman, S., Willett, KW & Dambre, J. Rotation-invariant convolutional neural networks for galaxy morphology prediction. There’s no moon. R. Astron. society 450(2), 1441–1459 (2015).
Google Scholar
Walmsley, M. et al. Galaxy Zoo Decals: Detailed volunteer visual morphometry and deep learning of 314,000 galaxies. There’s no moon. R. Astron. society 509(3), 3966–3988 (2022).
Google Scholar
Isayev, O. et al. Universal fragment descriptors for predicting properties of inorganic crystals. nut. common. 8(1), 15679 (2017).
Xie, T. & Grossman, JC Crystal graph convolutional neural networks for accurate and interpretable prediction of material properties. Physics. Pastor Rhett. 120(14), 145301 (2018).
Google Scholar
Chen, T., Simon, K., Mohammad, N., and Geoffrey, H. A simple framework for contrastive learning of visual representations. in International conference on machine learningpp. 1597–1607 (2020).
Oord, A., Li, Y., Vinyals, O. Representation learning with contrastive predictive coding, arXiv preprint arXiv:1807.03748 (2018).
Bagherian, M. Tensor denoising with dual Schatten norms. Optimal. Let. 18(5), 1285–1301 (2024).
Google Scholar
Bagherian, M., Kim, RB, Jiang, C., Sartor, MA, Derksen, H., and Najarian, K. Combination matrix and binding tensor matrix completion methods for predicting drug-target interactions. Easy. bioinf. twenty two(2), 2161–2171 (2021).
Bagherian, M., Tarzanagh, D.A., Ivo, D., & Welch, J.D. A bilevel optimization method for tensor recovery under metric learning constraints. arXiv preprint arXiv:2209.00545 (2022).
Hiller, C.J. & Lim, L.-H. Most tensor problems are np-hard. JACM 60(6), 1–39 (2013).
Google Scholar
Wu, C.-Y., Manmatha, R., Smola, A. J., Krahenbuhl, P. Sampling is important in deep embedding learning. in Proceedings of the IEEE International Conference on Computer Vision2840–2848 (2017).
Mo, S., Sun, Z., and Li, C. Rethinking prototype contrastive learning with alignment, uniformity, and correlation, arXiv preprint (2022).
Kurt, H., Stinchcombe, MB, Halbert, W. Multilayer feedforward networks are general-purpose approximators. neural network 2(5), 359–366 (1989).
Google Scholar
Mohri, M., Rostamizadeh, A., Talwalkar, A. (MIT Press, Fundamentals of Machine Learning, 2018).
Shalev-Shwartz, S., Ben-David, S. Understanding machine learning: From theory to algorithms. (Cambridge University Press, 2014).
Weinberger, K.Q., Blitzer, J., Saul, L. Distance metric learning for large margin nearest neighbor classification. Advanced neural information processes. system. 18 (2005).
Bottou, L., Curtis, FE, Jorge, N. Optimization techniques for large-scale machine learning. Pastor Siam 60(2), 223–311 (2018).
Lee, JD, Simchowitz, M., Jordan, MI, Recht, B. Gradient descent converges only to the minimizer. in Conference on learning theorypp. 1246–1257 (2016).
Hein, M., Audibert, J.-Y., and von Luxburg, U. Graphing the Laplacian and its convergence in random neighborhood graphs. J. Mach. learn. resolution (2007).
Robbins, H. & Monro, S. Stochastic approximation methods. Ann. Mathematics. statistics 1400–407 (1951).
Google Scholar
Karl Pearson, FRS iii. On the straight line and plane closest to a system of points in space. Rondo. edinburgh dublin philos. Mug. J.Sci. 2(11), 559–572 (1901).
Kullback, S., Leibler, R.A. On information and sufficiency. Ann. Mathematics. statistics twenty two(1), 79–86 (1951).
Wang, X., Han, X., Huang, W., Dong, D., Scott, M.R. Multiple similarity loss with general pair weighting for deep metric learning. in Proceedings of the ieee/cvf conference on computer vision and pattern recognition.5022–5030 (2019).
Kingma, DP, and Welling, M. Variational Bay automatic encoding, arXiv preprint arXiv:1312.6114. (2013).
Xie, J., Girshick, R., and Farhadi, A. Unsupervised deep embedding for clustering analysis. in International conference on machine learning478–487 (2016).
Huang, G.B., Marwan, M., Tamara, B., Learned-Miller, E. Labeled faces in the wild: A database for studying face recognition in unconstrained environments. in Workshop on faces in real images: detection, alignment, and recognition(2008).
Pedregosa, F. et al. Scikitlearn: Machine learning in Python. J. Mach. learn. resolution 122825–2830 (2011). Dataset: Olivetti Faces, available at https://scikit-learn.org/stable/modules/generated/sklearn.datasets.fetch_oliveetti_faces.html.
Di Martino, A. et al. Strengthening connectome research in autism using autism brain imaging data exchange ii. Science. data 4170010 (2017).
Google Scholar
Dektor, A., Rodgers, A., Venturi, D. Rank-adaptive tensor methods for high-dimensional nonlinear pdes. J.Sci.Calculate. 88(2), 36 (2021).
Google Scholar
Sedigin, F., Cicciocchi, A., Huang, A.-H. Adaptive rank selection for tensor ring decomposition. IEEE J. Select. top. signal process. 15(3), 454–463 (2021).
Google Scholar
Vaswani, A. et al. All you need is attention. Advanced neural information processes. system. 30 (2017).
