A Novel Statistical Method Based on Dynamic Models for Classification
This work addresses the challenge of effectively reducing dimension and exploring dynamic features for classifying functional data, which is incremental as it builds on existing methods by incorporating dynamic modeling, with potential clinical value in diagnosing cardiovascular diseases through ECG analysis.
The authors tackled the problem of classifying dynamic or functional data by proposing a method that models the data using second-order ordinary differential equations (ODEs) and uses the estimated parameters as features for classifiers. They demonstrated that this ODE-based approach outperforms neural networks using Fourier expansion coefficients in classifying normal and abnormal QRS complexes in ECG data, showing improved performance in this specific application.
Realizations of stochastic process are often observed temporal data or functional data. There are growing interests in classification of dynamic or functional data. The basic feature of functional data is that the functional data have infinite dimensions and are highly correlated. An essential issue for classifying dynamic and functional data is how to effectively reduce their dimension and explore dynamic feature. However, few statistical methods for dynamic data classification have directly used rich dynamic features of the data. We propose to use second order ordinary differential equation (ODE) to model dynamic process and principal differential analysis to estimate constant or time-varying parameters in the ODE. We examine differential dynamic properties of the dynamic system across different conditions including stability and transient-response, which determine how the dynamic systems maintain their functions and performance under a broad range of random internal and external perturbations. We use the parameters in the ODE as features for classifiers. As a proof of principle, the proposed methods are applied to classifying normal and abnormal QRS complexes in the electrocardiogram (ECG) data analysis, which is of great clinical values in diagnosis of cardiovascular diseases. We show that the ODE-based classification methods in QRS complex classification outperform the currently widely used neural networks with Fourier expansion coefficients of the functional data as their features. We expect that the dynamic model-based classification methods may open a new avenue for functional data classification.