On 2012-02-29, Gregory Maxwell wrote:
Would an automated “blind" search algorithm possibly
Speaking of that, you probably want to search the list archives for a
thread I started in 2009 titled:
"A stupid optimizer for irregular ambisonic layouts"
In it I provide the source for a simplistic decoder that uses a
generic open source blackbox non-linear optimizer library with a
simple objective to make matrixes.
Before They point it out themselves, I think the fourth installment of
Blah does very much the same. And of course Bruce Wiggins's (I hope)
research was what started this fray out in the first place. So, yes,
this is something that seems to be recommended from more than one
corner, with regard to irregular layouts. But still...
Personally what I find a bit worrisome is that this sort of optimization
retains the blackbox leanings of machine learning as a general
discipline. None of the ambisonic specific, closed form optimization
literature, or the derived specifics of the base optimization problem,
are being utilized. Instead the two (sometimes simultaneous, sometimes
even not that) Gerzonian equations are being fed into one or another
optimization framework, with no regard to what happens then, and without
feeding in all of the age-old mathematical-physical knowhow of how those
systems of equations behave. Like for instance psychoacoustical
sensitivity estimates from the BBC era.
In addition to being a fan of black box algorithms, including all of the
stuff that goes under the rubric of "data mining" (professionally I make
my living as a database guy), I'm also a little bit of a skeptic towards
the stuff. At least as far as the math I know and love suggests I should
be.
For example, when using support vector machines to fit polynomial bases,
how many people actually care to evaluate the Vapnik-Cervonekis bound
intrinsic to the problem, and then bound it in a principled fashion
before commencing to optimize numerically? That after all is the most
principled framework in which to bound overfitting by the machine --
i.e. the very same thing which leads to speaker detent within the
ambisonic framework, even after simple dimensional constraints have
already been dealt with.
And how many actually take a look at the early bispectral model of
Gerzon? Or the third one which name I don't remember right now? Even if
those aren't backed up by psychoacoustics, they are still very, *very*
relevant as (easily, formally, in-principled-fashion) saturable
optimization criteria (in the usual ambisonic L^2 sense no less).
I don't think going with the easy route and just using blackbox
optimizers does the job best, here. Instead, I would think we have to
find a way to inject more and more current, analytically purified,
psychoacoustic knowledge into the system, before we even start to
optimize. Even if numerical optimization still remains the key in
reaching a local optimum in this kind of a very difficult nonlinear
optimization problem.
Once again, Robert Greene, please help me if I'm falling short on the
hard math, somehow.
I like the generic optimization approaches _more_ than more
mathematically elegant closed form solutions because it's easy to play
around with the objective functions— and usually any change to the
objective makes your closed form solutions need to start from scratch.
So to reiterate, numerical optimization is a must, because the most
general problem seems to be analytically intractable. I'm even pretty
sure that certain rig configurations could be shown to be impossible to
solve using analytic means, and even instable around their steepest,
global optimum if that was ever found.
At the same time, though, I think a more well-thought out optimization
criterion, with some intelligent, psychoacoustically minded
regularization built in, and perhaps utilizing not only the L^2 norm but
also the L^1 at the same time, could still cut the mustard. That's only
going to happen if we push more and more of the post-Gerzon
psychoacoustic research into the optimization criterion and then use an
optimization engine capable of dealing with that sort of thing.
That isn't being done now. Even to accelerate convergence, or to give a
global, smooth starting point for the optimization procedure(s), or to
regularize the eventual outcome. Why not? Are we really that lazy (well
I am, but are the researchers in the feel as lazy as me as well?)
https://people.xiph.org/~greg/ambisonics/ambi_opt.c
Under xiph.org? Ooh! Please, more of that. And then more reseach plus
application in how to optimally code/decode even first order using
Vorbis (or some derivative?).
Giving a brief glance at the code, now with several more years of
experience with optimization— and I see that my objective function
appears differentiable. If I were to do this again I'd probably use a
C++ reverse mode automatic differentiation library, so that I could
get a version of the objective with gradients.
Don't. With ambisonic, you will have to deal with both pantophony and
periphony, and the transition between them is decidedly singular. No
stock numerical library can deal with something like that, that I know
of.
My email archives indicate that Aaron Heller made a version with a
bunch of improvements like RME rE optimization, and adding direction
mismatch between rE and rV as part of the objective.
Yes. That's part of the BLaH work, and very, *very* cool. But even
there, the precise tradeoff between directional error in rV and rE seems
to be more of an instintual decision than a one based on hard science.
The resulting decoder is exceptionally good compared to anything
preceding it, true, but I don't think it's necessarily the best, as a
global solution, or especially that it would generalize too easily to
higher orders.
Somewhere I had some version with support for higher orders and 3d but
I don't know where that is right now.
If you had it, I'd bet it'd suck -- if only a bit -- compared to the
optimum 3D code we will eventually find.
There are a lot of things you can do starting from a simple framework
like this.
Finally, no contest there. It's just that little nagging detail beyond
which annoys me...so. :)
--
Sampo Syreeni, aka decoy - de...@iki.fi, http://decoy.iki.fi/front
+358-50-5756111, 025E D175 ABE5 027C 9494 EEB0 E090 8BA9 0509 85C2
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