26 papers · ranked by Valyu relevance
Hongfu Guo, Wencheng Zou, Zeyu Zhang, Shuishan Zhang + 2 more
MANIFOLD REGULARIZATION CLASSIFICATION MODEL BASED ON IMPROVED DIFFUSION MAP Hongfu Guo Leceister Institution Dalian University of Technology hg203@student.le.ac.uk Shuishan Zhang Dalian Leceister Institution Dalian University of Technology sz252@student.le.ac.uk Wencheng Zou Dalian Leceister Institution Dalian…
Madiha Javeed, Mohammad Shorfuzzaman, Nawal Alsufyani, Samia Allaoua Chelloug + 3 more
'Samia Allaoua Chelloug' 'Ahmad Jalal' 'Jeongmin Park' 'Yilun Shang'] Human locomotion is an imperative topic to be conversed among researchers. Predicting the human motion using multiple techniques and algorithms has always been a motivating subject matter. For this, different methods have shown the ability of…
Charles Jin, Martin Rinard
We apply concepts from manifold regularization to develop new regularization techniques for training locally stable deep neural networks. Our regularizers are based on a sparsification of the graph Laplacian which holds with high probability when the data is sparse in high dimensions, as is common in deep learning.…
Muhammad Zafran Muhammad Zaly Shah, Anazida Zainal, Fuad A. Ghaleb, Abdulrahman Al-Qarafi + 2 more
Data streaming applications such as the Internet of Things (IoT) require processing or predicting from sequential data from various sensors. However, most of the data are unlabeled, making applying fully supervised learning algorithms impossible. The online manifold regularization approach allows sequential learning…
Martin Storath, Andreas Weinmann
In this paper, we consider the variational regularization of manifold-valued data in the inverse problems setting. In particular, we consider TV and TGV regularization for manifoldvalued data with indirect measurement operators. We provide results on the well-posedness and present algorithms for a numerical realization…
Nam D. Nguyen, Jiawei Huang, Daifeng Wang
The biological processes from genotype to phenotype are complex involving multi-scale mechanisms. Increasing multi-modal data enables deeper understanding of underlying complex mechanisms in various phenotypes. However, integrating and interpreting such large-scale multi-modal data remains challenging, especially given…
Martin Höller, Andreas Weinmann
Many methods for processing scalar and vector valued images, volumes and other data in the context of inverse problems are based on variational formulations. Such formulations require appropriate regularization functionals that model expected properties of the object to reconstruct. Prominent examples of regularization…
René Ciak, Melanie Melching, Otmar Scherzer
We present an approach for variational regularization of inverse and imaging problems for recovering functions with values in a set of vectors. We introduce regularization functionals, which are derivative-free double integrals of such functions. These regularization functionals are motivated from double integrals…
Hang Li, Enrique Del Castillo
The theory of optimal design of experiments has been traditionally developed on an Euclidean space. In this paper, new theoretical results and an algorithm for finding the optimal design of an experiment located on a Riemannian manifold are provided. It is shown that analogously to the results in Euclidean spaces…
Ding Li, Scott Dick
Graph-based algorithms are known to be effective approaches to semi-supervised learning. However, there has been relatively little work on extending these algorithms to the multi-label classification case. We derive an extension of the Manifold Regularization algorithm to multi-label classification, which is…
Youyu Liu, Baozhu Zou, Jiao Xu, Siyang Yang + 2 more
'Anastasios Doulamis'] A point cloud obtained by stereo matching algorithm or three-dimensional (3D) scanner generally contains much complex noise, which will affect the accuracy of subsequent surface reconstruction or visualization processing. To eliminate the complex noise, a new regularization algorithm for…
Weifeng Liu, Yang Li, Xu Lin, Dacheng Tao + 2 more
'Kewei Chen'] Co-training is a major multi-view learning paradigm that alternately trains two classifiers on two distinct views and maximizes the mutual agreement on the two-view unlabeled data. Traditional co-training algorithms usually train a learner on each view separately and then force the learners to be…
Liangchen Liu, Juncai He, Richard Tzong‐Han Tsai
In this paper, we study linear regression applied to data structured on a manifold. We assume that the data manifold is smooth and is embedded in a Euclidean space, and our objective is to reveal the impact of the data manifold's extrinsic geometry on the regression. Specifically, we analyze the impact of the…
Zheng Zhai, Hengchao Chen, Zhigang Yao
Ridge estimation is an important manifold learning technique. The goal of this paper is to examine the effects of nonlinear transformations on the ridge sets. The main result proves the inclusion relationship between ridges: R(f ◦ p) ⊆ R(p), provided that the transformation f is strictly increasing and concave on the…
Na Yu, Jin-Xing Liu, Ying-Lian Gao, Chun-Hou Zheng + 2 more
The development of single-cell RNA-sequencing (scRNA-seq) technology has enabled the measurement of gene expression in individual cells. This provides an unprecedented opportunity to explore the biological mechanisms at the cellular level. However, existing scRNA-seq analysis methods are susceptible to noise and…
Serena Hughes, Timothy Hamilton, Tom Kolokotrones, Eric J. Deeds
Manifold learning builds on the “manifold hypothesis,” which posits that data in high-dimensional datasets are drawn from lower-dimensional manifolds. Current tools generate global embeddings of data, rather than the local maps used to define manifolds mathematically. These tools also cannot assess whether the manifold…
Dhruv Kohli, Johannes S. Nieuwenhuis, Alexander Cloninger, Gal Mishne + 1 more
With the ubiquity of high-dimensional datasets in various biological fields, identifying low-dimensional topological manifolds within such datasets may reveal principles connecting latent variables to measurable instances in the world. The reliable discovery of such manifold structure in high-dimensional datasets can…
Dhruv Kohli, Johannes S. Nieuwenhuis, Katja Zegwaard, Alexander Cloninger + 2 more
With the ubiquity of high-dimensional datasets in various biological fields, identifying low-dimensional topological manifolds within such datasets may reveal principles connecting latent variables to measurable instances in the world. The reliable discovery of such manifold structure in high-dimensional datasets can…
Uri Cohen, SueYeon Chung, Daniel D. Lee, Haim Sompolinsky
Stimuli are represented in the brain by the collective population responses of sensory neurons, and an object presented under varying conditions gives rise to a collection of neural population responses called an object manifold. Changes in the object representation along a hierarchical sensory system are associated…
Johannes Schwab, Stephan Antholzer, Markus Haltmeier
Deep learning and (deep) neural networks are emerging tools to address inverse problems and image reconstruction tasks. Despite outstanding performance, the mathematical analysis for solving inverse problems by neural networks is mostly missing. In this paper, we introduce and rigorously analyze families of deep…
Alexander Smith, Spencer Runde, Alex Chew, Atharva Kelkar + 3 more
Molecular dynamics (MD) simulations are used in diverse scientific and engineering fields such as drug discovery, materials design, separations, biological systems, and reaction engineering. These simulations generate highly complex datasets that capture the 3D spatial positions, dynamics, and interactions of thousands…
Charles Eads
This report describes and illustrates a set of automatable multicomponent exponential relaxation analysis protocols that are model-agnostic and suited to extracting information under circumstances when little prior knowledge about the underlying system is used. Methods are illustrated and mathematical and physical…
Authors not listed
Electrochemical impedance spectroscopy (EIS) coupled with distribution of relaxation times (DRT) analysis is a robust framework for characterizing electrochemical systems. However, DRT deconvolution is often plagued by spurious peaks, hindering accurate process identification and quantitative parameter estimation. To…
Stefano Battaglia, Lina Fransén, Ignacio Fdez. Galván, Roland Lindh
In this work we present a new approach to fix the intruder state problem (ISP) in CASPT2 based on σp regularization. The resulting \$σ^p\$-CASPT2 method is compared to previous techniques, namely the real and imaginary level shifts, on a theoretical basis and by performing a series of systematic calculations. The…
Justin Eilertsen, Wylie Stroberg, Santiago Schnell
The determination of a substrate or enzyme activity by coupling of one enzymatic reaction with another easily detectable (indicator) reaction is a common practice in the biochemical sciences. Usually, the kinetics of enzyme reactions is simplified with singular perturbation analysis to derive rate or time course…
Denis Tikhonov
Here, we present a new approach for obtaining radial distribution functions (RDF) from the electron diffraction data using a regularized weighted sine least-squares spectral analysis (rwsLSSA). It allows for explicitly transferring the measured experimental uncertainties in the reduced molecular scattering function to…