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Orthogonal Projections Based on Hyperbolic and Spherical n-Simplex [PDF]
Advances in Mathematical Physics, 2015 Orthogonal projection along a geodesic to the chosen k-plane is introduced using edge and Gram matrix of an n-simplex in hyperbolic or spherical n-space. The distance from a point to k-plane is obtained by the orthogonal projection.
Murat Savas +2 more
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Almost minimal orthogonal projections [PDF]
Israel Journal of Mathematics, 2020 The projection constant $\Pi(E):=\Pi(E, \ell_\infty)$ of a finite-dimensional Banach space $E\subset\ell_\infty$ is by definition the smallest norm of a linear projection of $\ell_\infty$ onto $E$. Fix $n\geq 1$ and denote by $\Pi_n$ the maximal value of
Basso, Giuliano
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SOP: Selective Orthogonal Projection for Composed Image Retrieval [PDF]
SensorsThe proliferation of intelligent sensor networks in urban surveillance and remote sensing has triggered the explosive growth of unstructured visual sensor data.
Su Cheng, Guoyang Liu
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Orthogonal Projection Loss [PDF]
2021 IEEE/CVF International Conference on Computer Vision (ICCV), 2021 Deep neural networks have achieved remarkable performance on a range of classification tasks, with softmax cross-entropy (CE) loss emerging as the de-facto objective function. The CE loss encourages features of a class to have a higher projection score on the true class-vector compared to the negative classes. However, this is a relative constraint and
Ranasinghe, Kanchana +4 more
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Application of Orthogonal Polynomial in Orthogonal Projection of Algebraic Surface
Axioms, 2022 Point orthogonal projection onto an algebraic surface is a very important topic in computer-aided geometric design and other fields. However, implementing this method is currently extremely challenging and difficult because it is difficult to achieve to ...
Xudong Wang, Xiaowu Li, Yuxia Lyu
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An enhanced text classification model by the inverted attention orthogonal projection module
Connection Science, 2023 The orthogonal projection method has made significant progress in text classification, especially in generating discriminative features. This method obtains more pure and suitable for classification features by projecting text features onto the ...
Hong Zhao, Chenpeng Zhang, Aolong Wang
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On the uniqueness of minimal projections in Banach spaces [PDF]
Opuscula Mathematica, 2012 Let \(X\) be a uniformly convex Banach space with a continuous semi-inner product. We investigate the relation of orthogonality in \(X\) and generalized projections acting on \(X\). We prove uniqueness of orthogonal and co-orthogonal projections.
Ewa Szlachtowska, Dominik Mielczarek
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Restricted orthogonal gradient projection for continual learning
AI Open, 2023 Continual learning aims to avoid catastrophic forgetting and effectively leverage learned experiences to master new knowledge. Existing gradient projection approaches impose hard constraints on the optimization space for new tasks to minimize ...
Zeyuan Yang +4 more
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Low-Rank and Sparse Decomposition of Compressive Sensing Observation Signals [PDF]
Jisuanji gongcheng, 2022 Low-rank and sparse decomposition can be used in video surveillance analysis.This composition is more difficult to perform on Compressive Sensing(CS) videos than on videos sampled by the Nyquist theorem.Inspired by the method of projecting Nyquist ...
PAN Jinfeng, YIN Liju, GAO Mingliang, ZOU Guofeng
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Spectral approximation methods for Fredholm integral equations with non-smooth kernels
Mathematical Modelling and Analysis, 2022 In this paper, polynomially based projection and modified projection methods for approximating the solution of Fredholm integral equations with a kernel of Green’s function type are studied.
Chafik Allouch +2 more
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