1.       No need to construct the latent space

2.       No need to learn the latent to ambient and/or ambient to latent mapping

3.       The learning of the correlation coefficients only need very few parameters. GPLVM, GPDM, Spectrial LVM need to tune lots of parameters

4.       The training for obtaining the correlation coefficients are much faster than GPLVM and GPDM.

5.       In laten variable models, we need to assume the parametric form of the probability distribution of the ambient variables given the  latent variables. But in our method we do not need that assumption and thus is more general

6.       As long as there are structural relationships among the state variables, the PLS is able to discover it. 

Some disadvantage of GPLVM and GPDM

I just tried using kernel pLS to extract the nonlinearies in the 3D human motion data, and then used the extracted coefficients matrix for prediction in the RBPF tracking framework. However I found that the tracking error is very high. The reason, I am thinking, could be:

1. The kernel gram matrix bias towards the testing points that are similar to the training points. That is only if the training samples are similar to the testing points, the learned coefficients matrix is useful.

In order to verify the idea, I need to

 1) Do predictions using the coefficients learned from kernel pLS, without integrating into the tracking framework. Try to analyze the predictions errors obtained from different training data points.

 2) Try to use training motion cycles that are 'similar' to the testing motions. That only works if we have the testing motions available.

Some unresolbed questions:

1)Do I need to make the data zero-mean or not? I tried on two data sets, and I found that non-centralized kernel PLS is better, though still worse than PLS.

2) how to determine Kernel parameter? now the sigmma (RBF kernel parameter in the kernel PLS) is determined by cross validatation.  

1. Compare with PCA in terms of latent space mapping

2. What is the advantage of our method? Using examples to illustrate 'smart sampling'

3. Partition the sample space in upper and lower body to see the performance.

4. Try a more sophisticated dynamical model, at least a second order markov model. "Your dynamical model is very simple, just a 1st order markov model. Why don't you use something more complicated, or at least a second order markov model?"

5. Using kernel to capture nonlinearties in the motion space. "Why are you using a linear relationship between left and right side of the body? "

 6. Analyze the error cases. "I also concern about the error cases shown in the vidoes. They should have been analyzed and discussed. "