Multilinear Principal Component Analysis (MPCA) is an important tool for analyzing tensor data. It performs dimension reduction similar to PCA for multivariate data. However, standard MPCA is sensitive to outliers. It...
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作者：
Wu, ChaoDepartment of Mathematics
Statistics and Computer Science University of Illinois at Chicago ChicagoIL60607 United States
In this paper, we study the singularity formation phenomenon of the 1D model of Electron Magnetohydrodynamics (EMHD) given by (1.1). We will construct a solution whose C3-norm blows up in finite time. Then, we will sh...
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In this paper,we introduce a novel Multi-scale and Auto-tuned Semi-supervised Deep Subspace Clustering(MAS-DSC)algorithm,aimed at addressing the challenges of deep subspace clustering in high-dimensional real-world da...
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In this paper,we introduce a novel Multi-scale and Auto-tuned Semi-supervised Deep Subspace Clustering(MAS-DSC)algorithm,aimed at addressing the challenges of deep subspace clustering in high-dimensional real-world data,particularly in the field of medical *** deep subspace clustering algorithms,which are mostly unsupervised,are limited in their ability to effectively utilize the inherent prior knowledge in medical *** MAS-DSC algorithm incorporates a semi-supervised learning framework that uses a small amount of labeled data to guide the clustering process,thereby enhancing the discriminative power of the feature ***,the multi-scale feature extraction mechanism is designed to adapt to the complexity of medical imaging data,resulting in more accurate clustering *** address the difficulty of hyperparameter selection in deep subspace clustering,this paper employs a Bayesian optimization algorithm for adaptive tuning of hyperparameters related to subspace clustering,prior knowledge constraints,and model loss *** experiments on standard clustering datasets,including ORL,Coil20,and Coil100,validate the effectiveness of the MAS-DSC *** results show that with its multi-scale network structure and Bayesian hyperparameter optimization,MAS-DSC achieves excellent clustering results on these ***,tests on a brain tumor dataset demonstrate the robustness of the algorithm and its ability to leverage prior knowledge for efficient feature extraction and enhanced clustering performance within a semi-supervised learning framework.
Contrastive learning (CL) has emerged as a powerful framework for learning representations of images and text in a self-supervised manner while enhancing model robustness against adversarial attacks. More recently, re...
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Now a days in EFL procedure of education the ability of reading became as significant belief and personal-efficacy reading as a basic understanding for students. By monitoring the acknowledged participates under the b...
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Many underwater robotic applications relying on vision sensors require proper camera calibration, i.e. knowing the incoming light ray for each pixel in the image. While for the ideal pinhole camera model all viewing r...
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We propose a Regularized Adaptive Momentum Dual Averaging (RAMDA) algorithm for training structured neural networks. Similar to existing regularized adaptive methods, the subproblem for computing the update direction ...
ISBN:
(纸本)9798331314385
We propose a Regularized Adaptive Momentum Dual Averaging (RAMDA) algorithm for training structured neural networks. Similar to existing regularized adaptive methods, the subproblem for computing the update direction of RAMDA involves a nonsmooth regularizer and a diagonal preconditioner, and therefore does not possess a closed-form solution in general. We thus also carefully devise an implementable inexactness condition that retains convergence guarantees similar to the exact versions, and propose a companion efficient solver for the subproblems of both RAMDA and existing methods to make them practically feasible. We leverage the theory of manifold identification in variational analysis to show that, even in the presence of such inexactness, the iterates of RAMDA attain the ideal structure induced by the regularizer at the stationary point of asymptotic convergence. This structure is locally optimal near the point of convergence, so RAMDA is guaranteed to obtain the best structure possible among all methods converging to the same point, making it the first regularized adaptive method outputting models that possess outstanding predictive performance while being (locally) optimally structured. Extensive numerical experiments in large-scale modern computer vision, language modeling, and speech tasks show that the proposed RAMDA is efficient and consistently outperforms state of the art for training structured neural network. Implementation of our algorithm is available at https://***/ismoptgroup/RAMDA/.
We study graph spanners for point-set in the high-dimensional Euclidean space. On the one hand, we prove that spanners with stretch $\lt \sqrt{2}$ and subquadratic size are not possible, even if we add Steiner points....
We study graph spanners for point-set in the high-dimensional Euclidean space. On the one hand, we prove that spanners with stretch $\lt \sqrt{2}$ and subquadratic size are not possible, even if we add Steiner points. On the other hand, if we add extra nodes to the graph (non-metric Steiner points), then we can obtain $(1+\epsilon)$-approximate spanners of subquadratic size. We show how to construct a spanner of size $n^{2-\Omega\left(\epsilon^{3}\right)}$, as well as a directed version of the spanner of size $n^{2-\Omega\left(\epsilon^{2}\right)}$. We use our directed spanner to obtain an algorithm for computing $(1+\epsilon)$-approximation to Earth-Mover Distance (optimal transport) between two sets of size n in time $n^{2-\Omega\left(\epsilon^{2}\right)}$.
The management of radioactive sources is a critical process that ensures the safe and responsible handling of radioactive materials throughout their lifecycle. These sources require careful management from production ...
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Given news articles about an entity, such as a public figure or organization, timeline summarization (TLS) involves generating a timeline that summarizes the key events about the entity. However, the TLS task is too u...
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