Peter, the naive approach as mentioned by the paper was to take the 2-norm of the corresponding system matrices and of course lead to bad results. Other than the fact that the geometry of the subspaces were not taken into account, I can't say intuitively why the naive method performed worse. Care to guide me further?

Can anyone explain to me what "subspace angles" are, or point me to where I can read more about it? I only know that its some sort of metric to calculate the difference of two system matrices (well duh), but not much more beyond that. Thanks!

Sunny.

I'm looking forward to the presentation, since I had trouble following parts of the paper.

When they say that the joint statistics between two instants is shift-invariant, what do they mean by that? What are transient actions, and why does the previous assumption not hold for them?

I found this link on subspace angles and ARMA models:
http://www.univ-perp.fr/mtns2000/articles/B124.pdf

Also, geometrically, I have the notion that a subspace angle is the angle created by the intersection of two subspaces. Naturally, it is hard to picture this in your head when dealing with subspaces of more than 3 dimensions.

Is there some information in the L-infinity-norm that is not included in the L2-norm that makes it better?

Edited by author 10-09-2003 03:16 AM
Subspace angles are defined using n-dimensions, so it's kind of confusing... Is it possible to explain the subspace angle in when n is 2 or 3?

I only followed it up to getting the matrix product of the two orthonormal matrices that span two subspaces. The matrix product gives another orthogonal matrix. If the subspaces are planes, is the subspace angle the angle between the intersection of the planes, or the angle between the (original) plane(s) and the orthogonal plane gotten by the product of the two orthonormal matrices?

Singular values are used to calculate the subspace angle.
This is a definition from MathWorld:
Singular values are the square roots of the eigenvalues of A*A, where A* is the adjoint matrix.

For me it's hard to conceptualize if I can't visualize it... and I have no idea what the singular values represent, let alone understanding the meaning of theta.

Mike: I think the shift invariance is due to the markov assumption in their model. Equation 1 has something like x(t+1) = A*x(t) + v(t), which can be time-shifted and still be valid. For example, shifting t by 2 we get x(t+3) = A*x(t+2) + v(t+2). I don't really know what they mean by transient actions, but perhaps they mean movements that are unpredictable, such as a person spontaneously jumping in the air...

This is indeed a rather difficult problem just because of all the small differences between people's gaits. A person's height, weight, and activity could all impact a person's gait. I guess that is why it made sense to use a skeletal model. Even though the system has a few outliers, the system does very well considering the difficulty of the problem.

One question I had was that the paper describes that the Martin distance has an advantage over the Finsler distance. What is this advantage?

When doing the recognition of gaits, this paper uses the k-nearest neighbor algorithm to vote the model from k nearest neighbors. It is an easy way to classify the new sample into one class, because we only need to find the distance between the input sample and training samples. One problem occurs here is how to select k and the size of training set. Since the probability of the k-nearest neighbor assumption can be formulated, if we are given the probability of the occurrence of each model, is there any method we could use this information to find the best k.

Edited by author 10-09-2003 05:17 PM
I believe what they meant by "joint statistics between two instants is shift-invariant" is that the autocorrelation ("joint statistics") between y(t1) and y(t2) is shift-invariant, i.e. wide-sense stationary. in other words, R(t1,t2) = E[y(t1)y(t2)] = E[y(t2+s)y(t2)] = R(s) where s is the time difference.

My take on what the statement "y(t) is from a second-order stationary stochastic process" means that y(t) has a finite autocorrelation (2nd order), and the autocorrelation is dependent on the time difference and the mean is constant (stationary).

A thought regarding the advantage of using Finsler distance is that according to this paper it's gauranteed to be positive "for MIMO systems" while Martin distance is not. Isn't always positive measures a requirement for making the space we're working in a Banach space, and therefore a bunch of other theory applies?

Question 1 from Presentation:
dlyap (matlab function) here's the link:
http://www.mathworks.com/access/helpdesk/h...rol/ref/dlyap.shtml

Question 2:
What are K1 and K2 used for in the matlab code at the end of the paper?

After some investigation, I think that they are the means that are subtracted from each model before the learning step (see the first paragraph of the previous page).

I'm still not sure though.

I want to start a research on gait analysis. What are the fundamental concepts that I must have, i.e. feature extraction etc...

Please give inputs.

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Hi there, I am currently doing research on 'gender classification using gait recognition' I would like to have some sample matlab code to refer to...can anyone tell me where to ask for the sample code for gait recognition?