Belief Rényi Divergence of Divergence and its Application in Time Series Classification

• Published in: IEEE transactions on knowledge and data engineering Vol. 36; no. 8; pp. 3670 - 3681
• Main Authors: Zhang, Lang, Xiao, Fuyuan
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.08.2024; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Basic converters; belief divergence of divergence; belief Rényi divergence; classification; Classification algorithms; Complexity; Complexity theory; D-S evidence theory; Divergence; Evidence theory; Feature extraction; Machine learning; Measurement uncertainty; Time measurement; Time series; Time series analysis; uncertainty
• ISSN: 1041-4347; 1558-2191
• DOI: 10.1109/TKDE.2024.3369719

Time series data contains the amount of information to reflect the development process and state of a subject. Especially, the complexity is a valuable factor to illustrate the feature of the time series. However, it is still an open issue to measure the complexity of sophisticated time series due to its uncertainty. In this study, based on the belief R<inline-formula><tex-math notation="LaTeX">\acute{e}</tex-math> <mml:math><mml:mover accent="true"><mml:mi>e</mml:mi><mml:mo>´</mml:mo></mml:mover></mml:math><inline-graphic xlink:href="xiao-ieq3-3369719.gif"/> </inline-formula>nyi divergence, a novel time series complexity measurement algorithm, called belief R<inline-formula><tex-math notation="LaTeX">\acute{e}</tex-math> <mml:math><mml:mover accent="true"><mml:mi>e</mml:mi><mml:mo>´</mml:mo></mml:mover></mml:math><inline-graphic xlink:href="xiao-ieq4-3369719.gif"/> </inline-formula>nyi divergence of divergence (BR<inline-formula><tex-math notation="LaTeX">\acute{e}</tex-math> <mml:math><mml:mover accent="true"><mml:mi>e</mml:mi><mml:mo>´</mml:mo></mml:mover></mml:math><inline-graphic xlink:href="xiao-ieq5-3369719.gif"/> </inline-formula>DOD), is proposed. Specifically, the BR<inline-formula><tex-math notation="LaTeX">\acute{e}</tex-math> <mml:math><mml:mover accent="true"><mml:mi>e</mml:mi><mml:mo>´</mml:mo></mml:mover></mml:math><inline-graphic xlink:href="xiao-ieq6-3369719.gif"/> </inline-formula>DOD algorithm takes the boundaries of time series value into account. What is more, according to the Dempster-Shafer (D-S) evidence theory, the time series is converted to the basic probability assignments (BPAs) and it measures the divergence of a divergence sequence. Then, the secondary divergence of the time series is figured out to represent the complexity of the time series. In addition, the BR<inline-formula><tex-math notation="LaTeX">\acute{e}</tex-math> <mml:math><mml:mover accent="true"><mml:mi>e</mml:mi><mml:mo>´</mml:mo></mml:mover></mml:math><inline-graphic xlink:href="xiao-ieq7-3369719.gif"/> </inline-formula>DOD algorithm is applied to sets of cardiac inter-beat interval time series, which shows the superiority of the proposed method over classical machine learning methods and recent well-known works.