  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.
