Once an affinity measure has been defined between two nonlinear dynamical systems, we use kNearest Neighbors (kNN) Classification. Also to perform more sophisticated classification, we can use kernel SVMs with the previously defined kernels.



Lip contours  Landmark features  Distance features 

Finsler distance  
Martin distance  
Frobenius distance 
Another method for defining a measure of affinity between two LDS is through a kernel. The Martin Kernel, defined as:
Martin kernel 
comes directly from the associated Martin Distance and is immediately computable from the subspace angles. Chan and Vasconcelos proposed another metric based on the KullbackLeibler Divergence between the probability distributions of the outputs of the dynamical systems:
Vishwanathan et. al. introduced the family of Binet Cauchy kernels for the analysis of dynamical systems. One of these kernels, called the trace kernel between two ARMA model can be evaluated as:
Once an affinity metric has been defined between two linear dynamical systems, we use kNearest Neighbors (kNN) Classification in the case of distances or kFurthest Neighbors (kFN) Classification for kernels. Also to perform more sophisticated classification, we use kernel SVMs with the previously defined kernels.
Groups  First row of the figure shows G4, the first 2 rows make up G8 and all the figures together represent G12.
The following table shows the classification errors of all groups in the name and digit
scenarios for landmark trajectories, L, using the PCAbased identification method, and using
both 1NN classification with 5 different distances and SVM classification with
3 different kernels.

