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This paper proposes a mesh-free computational framework and machine learning theory for solving elliptic PDEs on unknown manifolds, identified with point clouds, based on diffusion maps (DM) and deep learning. The PDE solver is formulated…

Numerical Analysis · Mathematics 2024-02-28 Senwei Liang , Shixiao W. Jiang , John Harlim , Haizhao Yang

The current state-of-the-art for image annotation and image retrieval tasks is obtained through deep neural networks, which combine an image representation and a text representation into a shared embedding space. In this paper we evaluate…

Computer Vision and Pattern Recognition · Computer Science 2017-08-10 Armand Vilalta , Dario Garcia-Gasulla , Ferran Parés , Eduard Ayguadé , Jesus Labarta , Ulises Cortés , Toyotaro Suzumura

Edge detection, a basic task in the field of computer vision, is an important preprocessing operation for the recognition and understanding of a visual scene. In conventional models, the edge image generated is ambiguous, and the edge lines…

Computer Vision and Pattern Recognition · Computer Science 2022-03-18 Dawei Dai , Chunjie Wang , Shuyin Xia , Yingge Liu , Guoyin Wang

Majority of the current dimensionality reduction or retrieval techniques rely on embedding the learned feature representations onto a computable metric space. Once the learned features are mapped, a distance metric aids the bridging of gaps…

Computer Vision and Pattern Recognition · Computer Science 2018-10-17 Muhammad Kamran Janjua , Shah Nawaz , Alessandro Calefati , Ignazio Gallo

Interpretation and diagnosis of machine learning models have gained renewed interest in recent years with breakthroughs in new approaches. We present Manifold, a framework that utilizes visual analysis techniques to support interpretation,…

Machine Learning · Computer Science 2019-01-18 Jiawei Zhang , Yang Wang , Piero Molino , Lezhi Li , David S. Ebert

To address the dual challenges of the curse of dimensionality and the difficulty in separating intra-cluster and inter-cluster structures in high-dimensional manifold embedding, we proposes an Adaptive Multi-Scale Manifold Embedding (AMSME)…

Machine Learning · Computer Science 2025-03-20 Tianhao Ni , Bingjie Li , Zhigang Yao

As a pivotal branch of machine learning, manifold learning uncovers the intrinsic low-dimensional structure within complex nonlinear manifolds in high-dimensional space for visualization, classification, clustering, and gaining key…

Machine Learning · Computer Science 2025-09-16 Dehua Peng , Zhipeng Gui , Wenzhang Wei , Fa Li , Jie Gui , Huayi Wu , Jianya Gong

A wide range of imaging techniques and data formats available for medical images make accurate retrieval from image databases challenging. Efficient retrieval systems are crucial in advancing medical research, enabling large-scale studies…

Computer Vision and Pattern Recognition · Computer Science 2023-11-23 Farnaz Khun Jush , Tuan Truong , Steffen Vogler , Matthias Lenga

Learning-based single image super-resolution (SISR) methods are continuously showing superior effectiveness and efficiency over traditional model-based methods, largely due to the end-to-end training. However, different from model-based…

Image and Video Processing · Electrical Eng. & Systems 2020-03-24 Kai Zhang , Luc Van Gool , Radu Timofte

Multiple imputation (MI) is a popular approach for dealing with missing data arising from non-response in sample surveys. Multiple imputation by chained equations (MICE) is one of the most widely used MI algorithms for multivariate data,…

Machine Learning · Computer Science 2022-03-22 Zhenhua Wang , Olanrewaju Akande , Jason Poulos , Fan Li

While deep neural networks (NN) significantly advance image compressed sensing (CS) by improving reconstruction quality, the necessity of training current CS NNs from scratch constrains their effectiveness and hampers rapid deployment.…

Computer Vision and Pattern Recognition · Computer Science 2025-02-04 Bin Chen , Zhenyu Zhang , Weiqi Li , Chen Zhao , Jiwen Yu , Shijie Zhao , Jie Chen , Jian Zhang

Non-linear dimensionality reduction can be performed by \textit{manifold learning} approaches, such as Stochastic Neighbour Embedding (SNE), Locally Linear Embedding (LLE) and Isometric Feature Mapping (ISOMAP). These methods aim to produce…

Machine Learning · Statistics 2021-12-09 Theodoulos Rodosthenous , Vahid Shahrezaei , Marina Evangelou

This paper proposed a new explicit nonlinear dimensionality reduction using neural networks for image retrieval tasks. We first proposed a Quasi-curvature Locally Linear Embedding (QLLE) for training set. QLLE guarantees the linear…

Computer Vision and Pattern Recognition · Computer Science 2017-03-14 Shenglan Liu , Jun Wu , Lin Feng , Feilong Wang

Many efforts have been devoted to designing sampling, mining, and weighting strategies in high-level deep metric learning (DML) loss objectives. However, little attention has been paid to low-level but essential data transformation. In this…

Computer Vision and Pattern Recognition · Computer Science 2021-05-24 Zhiyuan Chen , Guang Yao , Wennan Ma , Lin Xu

Class Incremental Learning (CIL) aims to sequentially learn new classes while avoiding catastrophic forgetting of previous knowledge. We propose to use Masked Autoencoders (MAEs) as efficient learners for CIL. MAEs were originally designed…

Computer Vision and Pattern Recognition · Computer Science 2023-08-25 Jiang-Tian Zhai , Xialei Liu , Andrew D. Bagdanov , Ke Li , Ming-Ming Cheng

Image retrieval can be formulated as a ranking problem where the goal is to order database images by decreasing similarity to the query. Recent deep models for image retrieval have outperformed traditional methods by leveraging…

Computer Vision and Pattern Recognition · Computer Science 2019-06-19 Jerome Revaud , Jon Almazan , Rafael Sampaio de Rezende , Cesar Roberto de Souza

An approach to incorporate deep learning within an iterative image reconstruction framework to reconstruct images from severely incomplete measurement data is presented. Specifically, we utilize a convolutional neural network (CNN) as a…

Computer Vision and Pattern Recognition · Computer Science 2017-09-05 Brendan Kelly , Thomas P. Matthews , Mark A. Anastasio

Many important problems in science and engineering require solving the so-called parametric partial differential equations (PDEs), i.e., PDEs with different physical parameters, boundary conditions, shapes of computational domains, etc.…

Numerical Analysis · Mathematics 2024-02-06 Zhanhong Ye , Xiang Huang , Hongsheng Liu , Bin Dong

Locally Linear Embedding (LLE) is a nonlinear spectral dimensionality reduction and manifold learning method. It has two main steps which are linear reconstruction and linear embedding of points in the input space and embedding space,…

Machine Learning · Statistics 2021-04-06 Benyamin Ghojogh , Ali Ghodsi , Fakhri Karray , Mark Crowley

We present an extension to masked autoencoders (MAE) which improves on the representations learnt by the model by explicitly encouraging the learning of higher scene-level features. We do this by: (i) the introduction of a perceptual…

Computer Vision and Pattern Recognition · Computer Science 2023-03-29 Samyakh Tukra , Frederick Hoffman , Ken Chatfield