In the context of optimal transport (OT) methods, subspace detour approach was recently proposed by Muzellec and Cuturi. It consists first finding an plan between measures projected on a wisely chosen then completing it in nearly whole space. The contribution this paper is to extend category methods Gromov–Wasserstein problem, which particular type OT distance involving specific geometry each d...

Abstract The purpose of this article is to study the relationship between numerical invariants certain subspace arrangements coming from reflection groups and arising in representation theory Cherednik algebras. For instance, we observe that knowledge equivariant graded Betti numbers (in sense commutative algebra) any irreducible category ${\mathscr{O}}$ equivalent Kazhdan–Lusztig character obj...

Subspace methods have been extensively used to solve a variety of problems in computer vision including object detection, recognition, and tracking. Typically the subspaces are learned from a training set that contains different configurations or states of a particular object (e.g., variations on shape or appearance). However, in some situations it is not possible to have access to data with mu...

Codes in the projective space over a finite field, referred to as subspace codes, and in particular codes in the Grassmannian, referred to as constant-dimension codes (CDCs), have been proposed for error control in random network coding. In this paper, we first study the covering properties of CDCs. We determine some fundamental geometric properties of the Grassmannian. Using these properties, ...

Subspace-based methods rely on singular value decomposition (SVD) of the sample covariance matrix (SCM) to compute the array signal or noise subspace. For large array, triditional subspace-based algorithms inevitably lead to intensive computational complexity due to both calculating SCM and performing SVD of SCM. To circumvent this problem, a NyströmBased algorithm for array subspace estimation...

A single-channel algorithm is proposed for noise reduction in cochlear implants. The proposed algorithm is based on subspace principles and projects the noisy speech vector onto "signal" and "noise" subspaces. An estimate of the clean signal is made by retaining only the components in the signal subspace. The performance of the subspace reduction algorithm is evaluated using 14 subjects wearing...

Two decades of research shows that Principle Component Analysis is effective and convenient for representation and recognition of human face images. It is a kind of subspace method. Many successful face recognition algorithms follow the subspace method and try to find better subspaces for face recognition. In this paper, we present the projection incorporated subspace method based on PCA. This ...