Related papers: Spatiotemporal pattern extraction by spectral anal…

We propose a novel hierarchical spatiotemporal vector quantization framework for unsupervised skeleton-based temporal action segmentation. We first introduce a hierarchical approach, which includes two consecutive levels of vector…

Two-dimensional embeddings obtained from dimensionality reduction techniques such as MDS, t-SNE, or UMAP, are widely used to visualize high-dimensional data and support researchers in visually identifying clusters, outliers, and other…

This paper extends Yosida's mean ergodic theorem in order to compute projections onto non-unitary eigenspaces for spectral operators of scalar-type on locally convex linear topological spaces. For spectral operators with dominating point…

Singular spectrum analysis (SSA) is a nonparametric and adaptive spectral decomposition of a time series. The singular value decomposition of the trajectory matrix and the anti-diagonal averaging leads to a time-series decomposition. In…

We present view-synthesis autoencoders (VSA) in this paper, which is a self-supervised learning framework designed for vision transformers. Different from traditional 2D pretraining methods, VSA can be pre-trained with multi-view data. In…

Solving time-dependent parametric partial differential equations (PDEs) remains a fundamental challenge for neural solvers, particularly when generalizing across a wide range of physical parameters and dynamics. When data is uncertain or…

We propose a convolutional recurrent neural network, with Winner-Take-All dropout for high dimensional unsupervised feature learning in multi-dimensional time series. We apply the proposedmethod for object recognition with temporal context…

Dynamic Mode Decomposition (DMD) is a data-driven technique to identify a low dimensional linear time invariant dynamics underlying high-dimensional data. For systems in which such underlying low-dimensional dynamics is time-varying, a…

Geostationary hyperspectral satellites generate terabytes of data daily, creating critical challenges for storage, transmission, and distribution to the scientific community. We present a variational autoencoder (VAE) approach that achieves…

Compositional observations are an increasingly prevalent data source in spatial statistics. Analysis of such data is typically done on log-ratio transformations or via Dirichlet regression. However, these approaches often make unnecessarily…

A generator of spatio-temporal pseudo-random Gaussian fields that satisfy the "proportionality of scales" property (Tsyroulnikov, 2001) is presented. The generator is based on a third-order in time stochastic differential equation with a…

We introduce an analytical approach that allows predictions and mechanistic insights into the dynamics of nonlinear oscillator networks with heterogeneous time delays. We demonstrate that time delays shape the spectrum of a matrix…

The focus is on the statistical analysis of matrix-valued time series, where data is collected over a network of sensors, typically at spatial locations, over time. Each sensor records a vector of features at each time point, creating a…

Support Vector Machines (SVMs) are well-established Machine Learning (ML) algorithms. They rely on the fact that i) linear learning can be formalized as a well-posed optimization problem; ii) non-linear learning can be brought into linear…

A recent line of work in the machine learning community addresses the problem of predicting high-dimensional spatiotemporal phenomena by leveraging specific tools from the differential equations theory. Following this direction, we propose…

Stationary subspace analysis (SSA) is a blind source separation framework that decomposes linearly mixed multivariate data into stationary and nonstationary components. We extend SSA to spatially indexed data by introducing spatial…

The ability to extract generative parameters from high-dimensional fields of data in an unsupervised manner is a highly desirable yet unrealized goal in computational physics. This work explores the use of variational autoencoders (VAEs)…

Time series of individual subjects have become a common data type in psychological research. These data allow one to estimate models of within-subject dynamics, and thereby avoid the notorious problem of making within-subjects inferences…

Manifold-learning techniques are routinely used in mining complex spatiotemporal data to extract useful, parsimonious data representations/parametrizations; these are, in turn, useful in nonlinear model identification tasks. We focus here…

In this paper, we study vector valued de Branges spaces associated with a de Branges operator, defined as a pair of Fredholm operator valued analytic functions on a domain symmetric with respect to the unit circle. Using a suitable direct…