Related papers: Product Manifold Learning
Polynomial factorization in conventional sense is an ill-posed problem due to its discontinuity with respect to coefficient perturbations, making it a challenge for numerical computation using empirical data. As a regularization, this paper…
We address the problem of learning reusable state representations from streaming high-dimensional observations. This is important for areas like Reinforcement Learning (RL), which yields non-stationary data distributions during training. We…
Understanding low-dimensional structures within high-dimensional data is crucial for visualization, interpretation, and denoising in complex datasets. Despite the advancements in manifold learning techniques, key challenges-such as limited…
In the current era of vast data and transparent machine learning, it is essential for techniques to operate at a large scale while providing a clear mathematical comprehension of the internal workings of the method. Although there already…
Disentangled representations seek to recover latent factors of variation underlying observed data, yet their identifiability is still not fully understood. We introduce a unified framework in which disentanglement is achieved through…
Nonnegative matrix factorization is a powerful technique to realize dimension reduction and pattern recognition through single-layer data representation learning. Deep learning, however, with its carefully designed hierarchical structure,…
The success of deep neural networks in image classification and learning can be partly attributed to the features they extract from images. It is often speculated about the properties of a low-dimensional manifold that models extract and…
One develops a fast computational methodology for principal component analysis on manifolds. Instead of estimating intrinsic principal components on an object space with a Riemannian structure, one embeds the object space in a numerical…
Deep generative models for graphs have exhibited promising performance in ever-increasing domains such as design of molecules (i.e, graph of atoms) and structure prediction of proteins (i.e., graph of amino acids). Existing work typically…
Automated per-instance algorithm selection and configuration have shown promising performances for a number of classic optimization problems, including satisfiability, AI planning, and TSP. The techniques often rely on a set of features…
This article introduces a new data-driven approach that leverages a manifold embedding generated by the invertible neural network to improve the robustness, efficiency, and accuracy of the constitutive-law-free simulations with limited…
Dimensionality reduction is the essence of many data processing problems, including filtering, data compression, reduced-order modeling and pattern analysis. While traditionally tackled using linear tools in the fluid dynamics community,…
This paper puts forth a novel bi-linear modeling framework for data recovery via manifold-learning and sparse-approximation arguments and considers its application to dynamic magnetic-resonance imaging (dMRI). Each temporal-domain MR image…
Manifold regularization is a commonly used technique in semi-supervised learning. It enforces the classification rule to be smooth with respect to the data-manifold. Here, we derive sample complexity bounds based on pseudo-dimension for…
Classical metric and non-metric multidimensional scaling (MDS) variants are widely known manifold learning (ML) methods which enable construction of low dimensional representation (projections) of high dimensional data inputs. However,…
Dimensionality reduction algorithms like principal component analysis (PCA) are workhorses of machine learning and neuroscience, but each has well-known limitations. Variants of PCA are simple and interpretable, but not flexible enough to…
We consider the general problem of utilizing both labeled and unlabeled data to improve data representation performance. A new semi-supervised learning framework is proposed by combing manifold regularization and data representation methods…
We propose Pullback Flow Matching (PFM), a novel framework for generative modeling on data manifolds. Unlike existing methods that assume or learn restrictive closed-form manifold mappings for training Riemannian Flow Matching (RFM) models,…
We introduce a methodology for seeking conservation laws within a Hamiltonian dynamical system, which we term ``neural deflation''. Inspired by deflation methods for steady states of dynamical systems, we propose to {iteratively} train a…
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…