Related papers: Multiscale Trend Analysis

Spectra of ordered eigenvalues of finite Random Matrices are interpreted as a time series. Dataadaptive techniques from signal analysis are applied to decompose the spectrum in clearly differentiated trend and fluctuation modes, avoiding…

All networks can be analyzed at multiple scales. A higher scale of a network is made up of macro-nodes: subgraphs that have been grouped into individual nodes. Recasting a network at higher scales can have useful effects, such as decreasing…

In this paper, a nonlinear system of fractional ordinary differential equations with multiple scales in time is investigated. We are interested in the effective long-term computation of the solution. The main challenge is how to obtain the…

In this paper we employ methods from Statistical Mechanics to model temporal correlations in time series. We put forward a methodology based on the Maximum Entropy principle to generate ensembles of time series constrained to preserve part…

The analysis of temporal networks has a wide area of applications in a world of technological advances. An important aspect of temporal network analysis is the discovery of community structures. Real data networks are often very large and…

Unsupervised learning of time series data, also known as temporal clustering, is a challenging problem in machine learning. Here we propose a novel algorithm, Deep Temporal Clustering (DTC), to naturally integrate dimensionality reduction…

In this work, we propose a multi-stage training strategy for the development of deep learning algorithms applied to problems with multiscale features. Each stage of the pro-posed strategy shares an (almost) identical network structure and…

Interactive segmentation has gained significant attention for its application in human-computer interaction and data annotation. To address the target scale variation issue in interactive segmentation, a novel multi-scale token adaptation…

This paper considers the approximation of the continuous time filtering equation for the case of a multiple timescale (slow-intermediate, and fast scales) that may have correlation between the slow-intermediate process and the observation…

Time series data is prevalent in a wide variety of real-world applications and it calls for trustworthy and explainable models for people to understand and fully trust decisions made by AI solutions. We consider the problem of building…

Deep learning methods are powerful tools in classifying multivariate time series data. Despite their high performance, these methods are hard to interpret, which diminishes their applications in high-risk domains such as healthcare. In this…

We propose a novel algorithm for supervised dimensionality reduction named Manifold Partition Discriminant Analysis (MPDA). It aims to find a linear embedding space where the within-class similarity is achieved along the direction that is…

This paper focuses on causal structure estimation from time series data in which measurements are obtained at a coarser timescale than the causal timescale of the underlying system. Previous work has shown that such subsampling can lead to…

Singular spectrum analysis (SSA), starting from the second half of the XX century, has been a rapidly developing method of time series analysis. Since it can be called principal component analysis for time series, SSA will definitely be a…

This paper proposes a higher-order multiscale computational method for nonlinear thermo-electric coupling problems of composite structures, which possess temperature-dependent material properties and nonlinear Joule heating. The innovative…

Subset selection in multiple linear regression aims to choose a subset of candidate explanatory variables that tradeoff fitting error (explanatory power) and model complexity (number of variables selected). We build mathematical programming…

We introduce and analyze a variant of multivariate singular spectrum analysis (mSSA), a popular time series method to impute and forecast a multivariate time series. Under a spatio-temporal factor model we introduce, given $N$ time series…

I introduce Forecastable Component Analysis (ForeCA), a novel dimension reduction technique for temporally dependent signals. Based on a new forecastability measure, ForeCA finds an optimal transformation to separate a multivariate time…

As time-series applications grow larger, there is increasing demand for symbolic representations that are compact, accurate, and scalable across many signals and computing resources. Current ABBA-based symbolic approximation methods produce…

In this paper, we study temporal splitting algorithms for multiscale problems. The exact fine-grid spatial problems typically require some reduction in degrees of freedom. Multiscale algorithms are designed to represent the fine-scale…