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Search · four archives
16 papers · ranked by Valyu relevance
Patrick R. Johnstone, Jonathan Eckstein
Projective splitting is a family of methods for solving inclusions involving sums of maximal monotone operators. First introduced by Eckstein and Svaiter in 2008, these methods have enjoyed significant innovation in recent years, becoming one of the most flexible operator splitting frameworks available. While weak…
Patrick R. Johnstone, Jonathan Eckstein
This work describes a new variant of projective splitting for solving maximal monotone inclusions and complicated convex optimization problems. In the new version, cocoercive operators can be processed with a single forward step per iteration. In the convex optimization context, cocoercivity is equivalent to Lipschitz…
Patrick R. Johnstone, Jonathan Eckstein
This work is concerned with the classical problem of finding a zero of a sum of maximal monotone operators. For the projective splitting framework recently proposed by Combettes and Eckstein, we show how to replace the fundamental subproblem calculation using a backward step with one based on two forward steps. The…
Patrick R. Johnstone, Jonathan Eckstein
A recent innovation in projective splitting algorithms for monotone operator inclusions has been the development of a procedure using two forward steps instead of the customary proximal steps for operators that are Lipschitz continuous. This paper shows that the Lipschitz assumption is unnecessary when the forward…
M. Marques Alves, J. E. Navarro Caballero, R. T. Marcavillaca
We propose and study a strongly convergent inexact inertial projective splitting (PS) algorithm for finding zeros of composite monotone inclusion problems involving the sum of finitely many maximal monotone operators. Strong convergence of the iterates is ensured by projections onto the intersection of appropriately…
Pontus Giselsson
We propose and analyze a versatile and general algorithm called nonlinear forwardbackward splitting (NOFOB). The algorithm consists of two steps; first an evaluation of a nonlinear forward-backward map followed by a relaxed projection onto the separating hyperplane it constructs. The key of the method is the…
Pennipat Nabheerong, Warissara Kiththiworaphongkich, Watcharaporn Cholamjiak
'Watcharaporn Cholamjiak'] To detect breast cancer in mammography screening practice, we modify the inertial relaxed CQ algorithm with Mann's iteration for solving split feasibility problems in real Hilbert spaces to apply in an extreme learning machine as an optimizer. Weak convergence of the proposed algorithm is…
Claire Simpson, Evgeniy Tabatsky, Zainab Rahil, Devon J. Eddins + 11 more
Unsupervised clustering is a powerful machine-learning technique widely used to analyze high-dimensional biological data. It plays a crucial role in uncovering patterns, structure, and inherent relationships within complex datasets without relying on predefined labels. In the context of biology, high-dimensional data…
Francisco J. Aragón-Artacho, Radu I. Boţ, David Torregrosa-Belén
In this work, we study resolvent splitting algorithms for solving composite monotone inclusion problems. The objective of these general problems is finding a zero in the sum of maximally monotone operators composed with linear operators. Our main contribution is establishing the first primal-dual splitting algorithm…
Samantha N. Petti, Sean R. Eddy
Statistical inference and machine learning methods are benchmarked on test data independent of the data used to train the method. Biological sequence families are highly non-independent because they are related by evolution, so the strategy for splitting data into separate training and test sets is a nontrivial choice…
Daniel F. Scharler, Johannes Siegele, Hans-Peter Schröcker
We investigate factorizability of a quadratic split quaternion polynomial. In addition to inequality conditions for existence of such factorization, we provide lucid geometric interpretations in the projective space over the split quaternions.
Kaitlin M. Stouffer, Menno P. Witter, Daniel J. Tward, Michael I. Miller
Reconstructing dense 3D anatomical coordinates from 2D projective measurements has become a central problem in digital pathology for both animal models and human studies. We describe a new family of diffeomorphic mapping technologies called Projective LDDMM which generate diffeomorphic mappings of dense human MRI…
YuanBin Wang, XingWei Wang, Bin Zhang, Ying Wang
A well-known method proposed by Quan to compute projective invariants of 3D points uses six points in three 2D images. The method is nonlinear and complicated. It usually produces three possible solutions. It is noted previously that the problem can be solved directly and linearly using six points in five images. This…
Michela Mancini, John A. Christian, Pooya Sareh
Intersecting two conics is a classical problem that is frequently encountered in many different areas of science, engineering, and art. For example, under perspective projection (e.g., in camera images), any degree-two curve (a conic) or surface (a quadric) projects to a conic. This is important since polynomials of…
Denis Kleverov, Ekaterina Aladyeva, Alexey Serdyukov, Maxim N. Artyomov
Non-negative matrix factorization (NMF) is one of the most powerful linear algebra tools, which has found application in various areas of data analysis, including computational biology. Despite numerous optimization methods devised for NMF, our comprehension of the inherent topological structure within factorizable…
Kaitlin Stouffer, Menno Witter, Claire Chen, Eileen Xu + 5 more
Since Braak’s initial histological observations, it has been recognized that Alzheimer’s disease (AD) neurofibrillary tangles (NFTs) appear in the medial temporal lobe (MTL) of the brain very early in the disease course. MRI-based shape diffeomorphometry markers have demonstrated pre-clinical AD changes in the MTL but…