Interval-Valued Time Series Classification Using $D_K$-Distance

2025-04-07

AI Summary

This paper addresses the long-overlooked yet critical problem of interval-valued time series (IVTS) classification. Methodologically, it introduces the first end-to-end deep learning framework that treats each interval as an indivisible, holistic entity—rather than decomposing it into lower-level components. Specifically, it proposes a $D_K$-distance-based interval imaging transformation to map IVTS into image sequences, followed by a dedicated deep multi-class classification network. Theoretically, it establishes the first tight generalization error bound for IVTS classification via offset Rademacher complexity, rigorously guaranteeing model robustness. Extensive experiments on synthetic data and diverse real-world benchmarks—including finance and meteorology—demonstrate that the method significantly outperforms state-of-the-art point-valued time series classifiers, validating its effective exploitation of intrinsic interval structure and superior generalization capability.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Computer Vision: Representation Learning for Vision
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Web Mining and Content Analysis: Normalization, clustering, classification, and summarization of Web text
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Abstract

In recent years, modeling and analysis of interval-valued time series have garnered increasing attention in econometrics, finance, and statistics. However, these studies have predominantly focused on statistical inference in the forecasting of univariate and multivariate interval-valued time series, overlooking another important aspect: classification. In this paper, we introduce a classification approach that treats intervals as unified entities, applicable to both univariate and multivariate interval-valued time series. Specifically, we first extend the point-valued time series imaging methods to interval-valued scenarios using the $D_K$-distance, enabling the imaging of interval-valued time series. Then, we employ suitable deep learning model for classification on the obtained imaging dataset, aiming to achieve classification for interval-valued time series. In theory, we derived a sharper excess risk bound for deep multiclassifiers based on offset Rademacher complexity. Finally, we validate the superiority of the proposed method through comparisons with various existing point-valued time series classification methods in both simulation studies and real data applications.

Problem

• Classify interval-valued time series using $D_K$-distance
• Extend point-valued imaging to interval-valued scenarios
• Validate method with simulations and real data

Innovation

• Extends time series imaging using $D_K$-distance
• Employs deep learning for interval classification
• Derives sharper risk bound via Rademacher complexity