Projecting from 60D (shape context) space to 2D for visual analysis

Question

I have a set of 60D shape context vectors. These were constructed using a sample of 400 edge points from a silhouette using 5 radial bins and 12 angular bins (thus, I have 400 shape context vectors of 60D).

I would like to analyse just how descriptive these vectors are in representing the overall shape of the underlying silhouette. To do this, I would like to project the 60D shape context vectors back into 2D space and visually inspect the result -- what I am hoping to see is a set of points that roughly resemble the original silhouette's shape.

An approach to do this is by projecting on the first two principal components (PCA). Based on my implementation, the projected points did not resemble the silhouette's shape. I can see two main reasons for this (assuming for the time being that my implementation is correct): (1) shape context is either not appropriate as a descriptor given the silhouettes, or it's parameters need to be better tuned (2) this analysis method is flawed / not valid.

My question is whether this is the right approach for analysing the descriptiveness of shape contexts in relation to my silhouette's shape? If not, can someone please explain why and propose an alternative method?

Thanks,

Josh

Answer 1

The good way to check whether features are descriptive or not is to try train some classifier(svm/bayes/tree/whatever) upon them and check it cross-validated precision/recall etc. You also can filter your feature vector by feature selector like Chi/infogain.

Other than PCA, you can visualize your data with SOM, or by clustering.

Answer 2

I think this analysis method is flawed/not valid. I think this would be a similar reasoning: I can reconstruct the view from above on a football field by doing PCA on what each football player sees. It just isn't reasonable to expect that.

I think the simplest way to analyze the descriptiveness of shape context is to download MNIST or some other databases of written digits, and compute the 10x10 matrix of the shape similarities of 5 ones and 5 twos, and then draw this graph using (say) graphviz.