Curvature corrected tangent space-based approximation of manifold-valued data

Autor: Diepeveen, Willem, Chew, Joyce, Needell, Deanna

When generalizing schemes for real-valued data approximation or decomposition to data living in Riemannian manifolds, tangent space-based schemes are very attractive for the simple reason that these spaces are linear. An open challenge is to do this

Externí odkaz: http://arxiv.org/abs/2306.00507

Locally Optimal Eigenvectors of Regular Simplex Tensors

Autor: Wang, Lei

Identifying locally optimal solutions is an important issue given an optimization model. In this paper, we focus on a special class of symmetric tensors termed regular simplex tensors, which is a newly-emerging concept, and investigate its local opti

Externí odkaz: http://arxiv.org/abs/2303.00274

New Riemannian preconditioned algorithms for tensor completion via polyadic decomposition

Autor: Dong, Shuyu, Gao, Bin, Guan, Yu, Glineur, François

Publikováno v: SIAM Journal on Matrix Analysis and Applications, 43-2 (2022), 840-866

We propose new Riemannian preconditioned algorithms for low-rank tensor completion via the polyadic decomposition of a tensor. These algorithms exploit a non-Euclidean metric on the product space of the factor matrices of the low-rank tensor in the p

Externí odkaz: http://arxiv.org/abs/2101.11108

Structure from Local Optima: Learning Subspace Juntas via Higher Order PCA

Autor: Vempala, Santosh S., Xiao, Ying

We present a generalization of the well-known problem of learning k-juntas in R^n, and a novel tensor algorithm for unraveling the structure of high-dimensional distributions. Our algorithm can be viewed as a higher-order extension of Principal Compo

Externí odkaz: http://arxiv.org/abs/1108.3329

An AO-ADMM Approach to Constraining PARAFAC2 on All Modes

Autor: Marie Roald, Carla Schenker, Vince D. Calhoun, Tülay Adali, Rasmus Bro, Jeremy E. Cohen, Evrim Acar

Publikováno v: Roald, M, Schenker, C, Calhoun, V D, Adali, T, Bro, R, Cohen, J E & Acar, E 2022, ' An AO-ADMM Approach to Constraining PARAFAC2 on All Modes ', SIAM Journal on Mathematics of Data Science, vol. 4, no. 3, pp. 1191-1222 . https://doi.org/10.1137/21M1450033
SIAM Journal on Mathematics of Data Science
SIAM Journal on Mathematics of Data Science, 2022, 4 (3), pp.1191-1222. ⟨10.1137/21M1450033⟩

Analyzing multi-way measurements with variations across one mode of the dataset is a challenge in various fields including data mining, neuroscience and chemometrics. For example, measurements may evolve over time or have unaligned time profiles. The

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fc8f5991199a510114bf305b004f2b9b
https://curis.ku.dk/portal/da/publications/an-aoadmm-approach-to-constraining-parafac2-on-all-modes(dd651ebc-6bf8-47dc-bbd0-6ef6c9d69de1).html