Compared to a competing supervised algorithm based on a Hidden Markov Model, our unsupervised method demonstrates similar results in the STN detection task and superior results in the DLOR detection task.
This in turn allows for the extraction of the hidden manifold underlying the features and avoids overfitting, facilitating few-sample FS.
Our approach combines three components that are often considered separately: (i) manifold learning for building operators representing the geometry of the variables, (ii) Riemannian geometry of symmetric positive-definite matrices for multiscale composition of operators corresponding to different time samples, and (iii) spectral analysis of the composite operators for extracting different dynamic modes.
We address a three-tier numerical framework based on manifold learning for the forecasting of high-dimensional time series.
At the finer (sample) level, we devise a new metric between samples based on manifold learning that facilitates quantitative structural analysis.
Our approach combines manifold learning, which is a class of nonlinear data-driven dimension reduction methods, with the well-known Riemannian geometry of symmetric and positive-definite (SPD) matrices.
A low-dimensional dynamical system is observed in an experiment as a high-dimensional signal; for example, a video of a chaotic pendulums system.
In this paper, we present new results on the Riemannian geometry of symmetric positive semi-definite (SPSD) matrices.
While several electrocardiogram-derived respiratory (EDR) algorithms have been proposed to extract breathing activity from a single-channel ECG signal, conclusively identifying a superior technique is challenging.
We show analytically that our method is guaranteed to provide a set of orthogonal functions that are as jointly smooth as possible, ordered by increasing Dirichlet energy from the smoothest to the least smooth.
We model the difference between two domains by a diffeomorphism and use the polar factorization theorem to claim that OT is indeed optimal for DA in a well-defined sense, up to a volume preserving map.
Specifically, we show that our proposed method facilitates accurate localization of a moving agent from imaging data it collects.
We propose a metric-learning framework for computing distance-preserving maps that generate low-dimensional embeddings for a certain class of manifolds.
This paper explores a fully unsupervised deep learning approach for computing distance-preserving maps that generate low-dimensional embeddings for a certain class of manifolds.
Often the data is such that the observations do not reside on a regular grid, and the given order of the features is arbitrary and does not convey a notion of locality.
We show that without prior knowledge on the different modalities and on the measured system, our method gives rise to a data-driven representation that is well correlated with the underlying sleep process and is robust to noise and sensor-specific effects.
In this paper, we address the problem of multiple view data fusion in the presence of noise and interferences.
In the wake of recent advances in experimental methods in neuroscience, the ability to record in-vivo neuronal activity from awake animals has become feasible.