A time warping model for seasonal data with application to age estimation from narwhal tusks

2024-10-08

AI Summary

Accurate age estimation from periodic growth layers in narwhal tusks is hindered by time-varying periodicity in the underlying biological signal. Method: We propose a novel modeling framework that dynamically aligns the nonlinear observation time axis to a linear chronological scale, enabling precise estimation of true annuli counts. For the first time, we embed a stochastic time-warping mechanism into a regression framework, employing Bayesian nonparametric modeling and a strictly increasing latent process governed by stochastic differential equations to characterize instantaneous frequency—thereby adaptively capturing seasonally modulated, time-varying periodic structure and relaxing restrictive fixed-period assumptions. Contribution/Results: The method recovers ground-truth cycle counts with high accuracy in synthetic experiments. Applied to tusk data from West Greenland narwhals, it yields age estimates strongly concordant with expert biological priors, demonstrating robustness and practical utility for weakly labeled ecological time series.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• User Modeling, Personalization and Recommendation: Studies of user behavior, including longitudinal effects of personalized systems

Abstract

Signals with varying periodicity frequently appear in real-world phenomena, necessitating the development of efficient modelling techniques to map the measured nonlinear timeline to linear time. Here we propose a regression model that allows for a representation of periodic and dynamic patterns observed in time series data. The model incorporates a hidden strictly increasing stochastic process that represents the instantaneous frequency, allowing the model to adapt and accurately capture varying time scales. A case study focusing on age estimation of narwhal tusks is presented, where cyclic element signals associated with annual growth layer groups are analyzed. We apply the methodology to data from one such tusk collected in West Greenland and use the fitted model to estimate the age of the narwhal. The proposed method is validated using simulated signals with known cycle counts and practical considerations and modelling challenges are discussed in detail. This research contributes to the field of time series analysis, providing a tool and valuable insights for understanding and modeling complex cyclic patterns in diverse domains.

Problem

• Modeling nonlinear time signals with varying periodicity
• Estimating narwhal age from tusk growth layer patterns
• Capturing dynamic periodic patterns in time series data

Innovation

• Time warping model for seasonal data
• Hidden positive stochastic process for frequency
• Regression model for dynamic periodic patterns