We introduce robust principal component analysis from a data matrix in which the entries of
its columns have been corrupted by permutations, termed Unlabeled Principal Component …

We introduce robust principal component analysis from a data matrix in which the entries of
its columns have been corrupted by permutations, termed Unlabeled Principal Component …

ABSTRACT A new Riemannian rank adaptive method (RRAM) is proposed for the low‐rank
tensor completion problem (LRTCP). This problem is formulated as a least‐squares …

The identifiability problem arises naturally in a number of contexts in mathematics and
computer science. Specific instances include local or global rigidity of graphs and unique …

In data science, a number of applications have been emerging involving data recovery from
permutations. Here, we study this problem theoretically for data organized in a rank-deficient …

Many interesting functions arising in applications map into Riemannian manifolds. We
present an algorithm, using the manifold exponential and logarithm, for approximating such …

We lay the geometric foundations for the study of the characteristic polynomial of tensors.
For symmetric tensors of order $ d\geq 3$ and dimension $2 $ and symmetric tensors of …

Completion problems, of recovering a point from a set of observed coordinates, are
abundant in applications to image reconstruction, phylogenetics, and data science. We …

We show that a generic tensor $ T\in\mathbb {F}^{n\times n\times\dots\times n} $ of order $ k
$ and CP rank $ d $ can be uniquely recovered from $ n\log n+ dn\log\log n+ o (n\log\log n) …

Dans cet article, nous proposons une approche pour fournir des bornes d'identifiabilité
générique de modèles tensoriels couplés pour l'estimation de loi de probabilité discrète …