相关论文: Multiscale Trend Analysis

Data mining, particularly the analysis of multivariate time series data, plays a crucial role in extracting insights from complex systems and supporting informed decision-making across diverse domains. However, assessing the similarity of…

Many real-world time series exhibit multiple seasonality with different lengths. The removal of seasonal components is crucial in numerous applications of time series, including forecasting and anomaly detection. However, many…

We propose a novel approach to the problem of clustering hierarchically aggregated time-series data, which has remained an understudied problem though it has several commercial applications. We first group time series at each aggregated…

We propose criteria that define a trend for time series with inherent multi-scale features. We call this trend the {\it tendency} of a time series. The tendency is defined empirically by a set of criteria and captures the large-scale…

This paper introduces new methodology based on the field of Topological Data Analysis for detecting anomalies in multivariate time series, that aims to detect global changes in the dependency structure between channels. The proposed…

This work is devoted to a comprehensive analysis of topological data analysis fortime series classification. Previous works have significant shortcomings, such aslack of large-scale benchmarking or missing state-of-the-art methods. In this…

Time series forecasting presents significant challenges in real-world applications across various domains. Building upon the decomposition of the time series, we enhance the architecture of machine learning models for better multivariate…

Multivariate time series classification is a task with increasing importance due to the proliferation of new problems in various fields (economy, health, energy, transport, crops, etc.) where a large number of information sources are…

Time Series Alignment is a critical task in signal processing with numerous real-world applications. In practice, signals often exhibit temporal shifts and scaling, making classification on raw data prone to errors. This paper introduces a…

The decomposition of time series into components is an important task that helps to understand time series and can enable better forecasting. Nowadays, with high sampling rates leading to high-frequency data (such as daily, hourly, or…

Multivariate time series analysis is a vital but challenging task, with multidisciplinary applicability, tackling the characterization of multiple interconnected variables over time and their dependencies. Traditional methodologies often…

This paper presents a multiscale approach to efficiently compute approximate optimal transport plans between point sets. It is particularly well-suited for point sets that are in high-dimensions, but are close to being intrinsically…

A new method is proposed which allows a reconstruction of time series based on higher order multiscale statistics given by a hierarchical process. This method is able to model the time series not only on a specific scale but for a range of…

Multivariate time series forecasting is widely used in various fields. Reasonable prediction results can assist people in planning and decision-making, generate benefits and avoid risks. Normally, there are two characteristics of time…

Sequentially obtained dataset usually exhibits different behavior at different data resolutions/scales. Instead of inferring from data at each scale individually, it is often more informative to interpret the data as an ensemble of time…

This paper addresses a common problem with hierarchical time series. Time series analysis demands the series for a model to be the sum of multiple series at corresponding sub-levels. Hierarchical Time Series presents a two-fold problem.…

The study of topology is strictly speaking, a topic in pure mathematics. However in only a few years, Topological Data Analysis (TDA), which refers to methods of utilizing topological features in data (such as connected components, tunnels,…

Piecewise Aggregate Approximation (PAA) is a competitive basic dimension reduction method for high-dimensional time series mining. When deployed, however, the limitations are obvious that some important information will be missed,…

Hierarchical forecasting is a key problem in many practical multivariate forecasting applications - the goal is to simultaneously predict a large number of correlated time series that are arranged in a pre-specified aggregation hierarchy.…

Time series often appear in an additive hierarchical structure. In such cases, time series on higher levels are the sums of their subordinate time series. This hierarchical structure places a natural constraint on forecasts. However,…