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Network embedding is an effective technique to learn the low-dimensional representations of nodes in networks. Real-world networks are usually with multiplex or having multi-view representations from different relations. Recently, there has…

Machine Learning · Computer Science 2022-03-08 Qifan Wang , Yi Fang , Anirudh Ravula , Ruining He , Bin Shen , Jingang Wang , Xiaojun Quan , Dongfang Liu

Deep learning is the mainstream technique for many machine learning tasks, including image recognition, machine translation, speech recognition, and so on. It has outperformed conventional methods in various fields and achieved great…

Machine Learning · Computer Science 2018-06-01 Na Lei , Zhongxuan Luo , Shing-Tung Yau , David Xianfeng Gu

The success of machine learning algorithms generally depends on data representation, and we hypothesize that this is because different representations can entangle and hide more or less the different explanatory factors of variation behind…

Machine Learning · Computer Science 2014-04-24 Yoshua Bengio , Aaron Courville , Pascal Vincent

We propose a kernel-spectral embedding algorithm for learning low-dimensional nonlinear structures from high-dimensional and noisy observations, where the datasets are assumed to be sampled from an intrinsically low-dimensional manifold and…

Machine Learning · Statistics 2023-07-07 Xiucai Ding , Rong Ma

Data augmentation is a widely used technique and an essential ingredient in the recent advance in self-supervised representation learning. By preserving the similarity between augmented data, the resulting data representation can improve…

Machine Learning · Statistics 2025-01-16 Shulei Wang

We present a novel framework for learning cost-efficient latent representations in problems with high-dimensional state spaces through nonlinear dimension reduction. By enriching linear state approximations with low-order polynomial terms…

Numerical Analysis · Mathematics 2026-05-27 Rudy Geelen , Laura Balzano , Karen Willcox

We adapt a manifold sampling algorithm for the nonsmooth, nonconvex formulations of learning that arise when imposing robustness to outliers present in the training data. We demonstrate the approach on objectives based on trimmed loss.…

Optimization and Control · Mathematics 2018-07-10 Matt Menickelly , Stefan M. Wild

Dimensionality reduction is often used as an initial step in data exploration, either as preprocessing for classification or regression or for visualization. Most dimensionality reduction techniques to date are unsupervised; they do not…

Machine Learning · Statistics 2020-06-17 Jake S. Rhodes , Adele Cutler , Guy Wolf , Kevin R. Moon

Representation learning is currently a very hot topic in modern machine learning, mostly due to the great success of the deep learning methods. In particular low-dimensional representation which discriminates classes can not only enhance…

Machine Learning · Computer Science 2015-04-13 Wojciech Marian Czarnecki , Rafał Józefowicz , Jacek Tabor

The manifold hypothesis presumes that high-dimensional data lies on or near a low-dimensional manifold. While the utility of encoding geometric structure has been demonstrated empirically, rigorous analysis of its impact on the learnability…

Machine Learning · Computer Science 2024-06-04 Bobak T. Kiani , Jason Wang , Melanie Weber

In this paper, we propose a semi-supervised dictionary learning method that uses both the information in labelled and unlabelled data and jointly trains a linear classifier embedded on the sparse codes. The manifold structure of the data in…

Machine Learning · Computer Science 2018-12-12 Khanh-Hung Tran , Fred-Maurice Ngole-Mboula , Jean-Luc Starck

Representation learning is typically applied to only one mode of a data matrix, either its rows or columns. Yet in many applications, there is an underlying geometry to both the rows and the columns. We propose utilizing this coupled…

Machine Learning · Statistics 2018-10-17 Gal Mishne , Eric C. Chi , Ronald R. Coifman

Supervised deep learning is most commonly applied to difficult problems defined on large and often extensively curated datasets. Here we demonstrate the ability of deep representation learning to address problems of classification and…

Machine Learning · Computer Science 2022-11-30 Benjamin L. Badger

Learning mappings of data on manifolds is an important topic in contemporary machine learning, with applications in astrophysics, geophysics, statistical physics, medical diagnosis, biochemistry, 3D object analysis. This paper studies the…

Numerical Analysis · Mathematics 2020-07-21 Guido Montúfar , Yu Guang Wang

Probabilistic Manifold Decomposition (PMD)\cite{doi:10.1137/25M1738863}, developed in our earlier work, provides a nonlinear model reduction by embedding high-dimensional dynamics onto low-dimensional probabilistic manifolds. The PMD has…

Numerical Analysis · Mathematics 2026-01-13 Jiaming Guo , Dunhui Xiao

We propose a new method for embedding graphs while preserving directed edge information. Learning such continuous-space vector representations (or embeddings) of nodes in a graph is an important first step for using network information…

Machine Learning · Computer Science 2017-09-15 Sami Abu-El-Haija , Bryan Perozzi , Rami Al-Rfou

Deep learning has had tremendous success at learning low-dimensional representations of high-dimensional data. This success would be impossible if there was no hidden low-dimensional structure in data of interest; this existence is posited…

Many of the existing methods for learning joint embedding of images and text use only supervised information from paired images and its textual attributes. Taking advantage of the recent success of unsupervised learning in deep neural…

Computer Vision and Pattern Recognition · Computer Science 2017-03-21 Yao-Hung Hubert Tsai , Liang-Kang Huang , Ruslan Salakhutdinov

Manifold learning flows are a class of generative modelling techniques that assume a low-dimensional manifold description of the data. The embedding of such a manifold into the high-dimensional space of the data is achieved via learnable…

Machine Learning · Statistics 2025-03-07 Kyriakos Flouris , Ender Konukoglu

Graph representation learning is a fast-growing field where one of the main objectives is to generate meaningful representations of graphs in lower-dimensional spaces. The learned embeddings have been successfully applied to perform various…

Machine Learning · Computer Science 2021-12-21 Md. Khaledur Rahman , Ariful Azad