Related papers: Learning Manifolds from Non-stationary Streaming D…

Active area of research in AI is the theory of manifold learning and finding lower-dimensional manifold representation on how we can learn geometry from data for providing better quality curated datasets. There are however various issues…

We investigate recurrent neural networks with asymmetric interactions and demonstrate that the inclusion of self-couplings or sparse excitatory inter-module connections leads to the emergence of a densely connected manifold of dynamically…

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,…

In this paper, we propose a computationally tractable and theoretically supported non-linear low-dimensional generative model to represent real-world data in the presence of noise and sparse outliers. The non-linear low-dimensional manifold…

We adapt previous research on category theory and topological unsupervised learning to develop a functorial perspective on manifold learning, also known as nonlinear dimensionality reduction. We first characterize manifold learning…

We address the challenge of representation learning from a continuous stream of video as input, in a self-supervised manner. This differs from the standard approaches to video learning where videos are chopped and shuffled during training…

We consider the estimation of an i.i.d. (possibly non-Gaussian) vector $\xbf \in \R^n$ from measurements $\ybf \in \R^m$ obtained by a general cascade model consisting of a known linear transform followed by a probabilistic componentwise…

In a recent paper, the authors proposed a general methodology for probabilistic learning on manifolds. The method was used to generate numerical samples that are statistically consistent with an existing dataset construed as a realization…

This paper presents a methodology for creating streaming, distributed inference algorithms for Bayesian nonparametric (BNP) models. In the proposed framework, processing nodes receive a sequence of data minibatches, compute a variational…

Flow matching has emerged as a powerful generative modeling approach with flexible choices of source distribution. While Gaussian distributions are commonly used, the potential for better alternatives in high-dimensional data generation…

Uniform Manifold Approximation and Projection (UMAP) is a widely used manifold learning technique for dimensionality reduction. This paper studies UMAP, supervised UMAP, and several competing dimensionality reduction methods, including…

This survey is written in summer, 2016. The purpose of this survey is to briefly introduce nonlinear dimensionality reduction (NLDR) in data reduction. The first two NLDR were respectively published in Science in 2000 in which they solve…

We formulate a reduced-order strategy for efficiently forecasting complex high-dimensional dynamical systems entirely based on data streams. The first step of our method involves reconstructing the dynamics in a reduced-order subspace of…

Graph diffusion models have made significant progress in learning structured graph data and have demonstrated strong potential for predictive tasks. Existing approaches typically embed node, edge, and graph-level features into a unified…

Natural data observed in $\mathbb{R}^n$ is often constrained to an $m$-dimensional manifold $\mathcal{M}$, where $m < n$. This work focuses on the task of building theoretically principled generative models for such data. Current generative…

In a number of disciplines, the data (e.g., graphs, manifolds) to be analyzed are non-Euclidean in nature. Geometric deep learning corresponds to techniques that generalize deep neural network models to such non-Euclidean spaces. Several…

Dripping water from a faucet is a typical example exhibiting rich nonlinear phenomena. For such a system, the time stamps at which water drops separate from the faucet can be directly observed in real experiments, and the time series of…

Unsupervised fault detection in multivariate time series plays a vital role in ensuring the stable operation of complex systems. Traditional methods often assume that normal data follow a single Gaussian distribution and identify anomalies…

Deep metric learning maps visually similar images onto nearby locations and visually dissimilar images apart from each other in an embedding manifold. The learning process is mainly based on the supplied image negative and positive training…

Manifolds discovered by machine learning models provide a compact representation of the underlying data. Geodesics on these manifolds define locally length-minimising curves and provide a notion of distance, which are key for reduced-order…