Related papers: Dynamic Principal Components in the Time Domain

This paper studies the problem of dimension reduction, tailored to improving time series forecasting with high-dimensional predictors. We propose a novel Supervised Deep Dynamic Principal component analysis (SDDP) framework that…

This paper develops a distributed model predictive control (DMPC) strategy for a class of discrete-time linear systems with consideration of globally coupled constraints. The DMPC under study is based on the dual problem concerning all…

The dynamic mode decomposition (DMD) is a data-driven method used for identifying the dynamics of complex nonlinear systems. It extracts important characteristics of the underlying dynamics using measured time-domain data produced either by…

We propose a novel approach to design a robust Model Predictive Controller (MPC) for constrained uncertain linear systems. The uncertain system is modeled as linear parameter varying with additive disturbance. Set bounds for the system…

Dissipative particle dynamics (DPD) belongs to a class of models and computational algorithms developed to address mesoscale problems in complex fluids and soft matter in general. It is based on the notion of particles that represent…

Time series domain adaptation aims to transfer the complex temporal dependence from the labeled source domain to the unlabeled target domain. Recent advances leverage the stable causal mechanism over observed variables to model the…

A new look on the principal component analysis has been presented. Firstly, a geometric interpretation of determination coefficient was shown. In turn, the ability to represent the analyzed data and their interdependencies in the form of…

A method of quantizing parametrized systems is developed that is based on a kind of ``gauge invariant'' quantities---the so-called perennials (a perennial must also be an ``integral of motion''). The problem of time in its particular form…

We consider principal component analysis for contaminated data-set in the high dimensional regime, where the dimensionality of each observation is comparable or even more than the number of observations. We propose a deterministic…

In this article, we introduce a procedure for selecting variables in principal components analysis. The procedure was developed to identify a small subset of the original variables that best explain the principal components through…

Determinantal point processes (DPPs) are probability models over subsets of a ground set that favor diverse selections while suppressing redundancy. That is, they tend to assign higher likelihood to collections whose elements complement one…

We propose a new data-driven method to select the optimal number of relevant components in Principal Component Analysis (PCA). This new method applies to correlation matrices whose time autocorrelation function decays more slowly than an…

Time series generation models are crucial for applications like data augmentation and privacy preservation. Most existing time series generation models are typically designed to generate data from one specified domain. While leveraging data…

We introduce a set of local procedures that are capable of controlling distributed systems that exhibit complex dynamical behavior. These local controllers need only perturb local parameters and use local information about the state of the…

We introduce data to predictive control, D2PC, a framework to facilitate the design of robust and predictive controllers from data. The proposed framework is designed for discrete-time stochastic linear systems with output measurements and…

This paper addresses the problem of consistently estimating a continuous-time (CT) diffusively coupled network (DCN) to identify physical components in a physical network. We develop a three-step frequency-domain identification method for…

We present a nonparametric way to retrieve a system of differential equations in embedding space from a single time series. These equations can be treated with dynamical systems theory and allow for long term predictions. We demonstrate the…

Domain adaptation (DA) is a statistical learning problem that arises when the distribution of the source data used to train a model differs from that of the target data used to evaluate the model. While many DA algorithms have demonstrated…

Thermodynamic conventions suffer from describing dynamical distinctions, especially when the structural and energetic changes induced by localized rare events are insignificant. By using the ensemble theory in the trajectory space, we…

Principal Component Analysis (PCA) and its nonlinear extension Kernel PCA (KPCA) are widely used across science and industry for data analysis and dimensionality reduction. Modern deep learning tools have achieved great empirical success,…