Monte Carlo Dynamic Classifier

Here we introduce the example of model estimation and classification using the MCDC tool, by using motion capture data of CMU Graphics Lab Motion Capture Database. This allows us to illustrate the use of both the Training and Test Components of the MCDC Tool. The motion capture database contains 144 subject data and each subject contains several trials. In this experiment, we used four subject data as listed in the following table.

The data used in this project was obtained from mocap.cs.cmu.edu.
The database was created with funding from NSF EIA-0196217.

Experimental conditions

@(x) x(1, :), ...
@(x) x(2, :)  ...

@(x) zeros(1, size(x, 2)), ...
@(x) zeros(1, size(x, 2)), ...
@(x) zeros(1, size(x, 2))  ...

Source code:  samples/MotionCapturePMCMC2Estimation.m

Commands:

addpath('samples');
MotionCapturePMCMC2Estimation;

PMCMC marginal likelihood estimation of incremental marginal likelihood sequence for each dimension of the observation vectors for Lorenz model versus true incremental marginal likelihood.

The average of mean functions from the estimated model at each MCMC iteration  (y1, y2, y3 in turn)

The above figures could be obtained by using the following function of this toolbox,

Graphs.YEMean(PathForOutput, PathForMatFile);

The log-likelihood estimated at each MCMC iteration

Having trained this model, we can now assess the MCDC Test function using the trained models on each of the left out experimental videos in the leave-one-out cross validation. When considering these results we observe that we expect that the trained model, based on an a prior belief that a linear constant velocity structure is present, should not be optimal for several movements which are more complex with different angular accelerations and non-straight line trajectories. Hence, the trained GP-SSM from subjects 7 and 9 are expected to work more appropriately than the other motions.

In this experiment, we first estimated the parameters of GP-SSMs for each trial data using the PMCMC2 method and created each model. Each trial data/model is assigned to the subject. Then, we examined to classify each trial data to the subject of the model which shows the highest marginal likelihood between all models except for the model of the data examined. It is shown that the MCDCTest function reasonably performs especially for subjects 7 and 9. While the motions of subjects 7 and 9 are relatively stable, the motions of subjects 3 and 5 are dynamically changeable and consequently less likely to be adequately explained by the a prior belief of a linear Gaussian dynamic structure. Improvements in these classifications can be made with non-constant velocity mean functions and non-homogeneous assumptions of the GP covariance kernel.

Source code: samples/MotionCapturePMCMC2Test.m

Commands:

addpath('samples');
MotionCapturePMCMC2test;

Classification accuracy in the model classification experiment