Pat Gunn (dachte) wrote,
Pat Gunn
dachte

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Questions on SVD

I woke up this morning with a few questions on SVDs

  • In dimensionality-reduction, does SVD find the most efficient decomposition possible?
  • In defining efficiency in decomposition, one intuitive measure seems to be that most of the variance is captured in the first vector, and with that satisfied, further criteria are that each successive vector captures as much variance as possible. Is this a reasonable measure? Is it used?
  • Would non-optimality by this measure be more likely for HOSVDs?
  • Are traditional ways of dealing with a sparse matrix applicable to tensors for HOSVDs? Given that higher-dimensional real-world datasets are more often sparse, this may be more of a concern...
As I understand, the vectors are measured by their independence from each other, which I think might be reasonambly close to my notion of optimalitty for dimensionality reduction. I'm not sure if one is a subset of the other - that's something to chew on. The independence measure admits a non-unique result for some matrices - this defines a notion of degeneracy. I unfortunately lack the mental tools to reason well about tensors, so I'll need to do some reading to have ideas about the later questions.

Slashdot recently reported the beginnings of interoperability between Second Life and open servers speaking the same protocol - that opens a number of interesting issues like preservation of the IP regime that SL has on its grid. SL as of present allows people to set the following permissions on things, which take effect as soon as the object is given to someone else: copy, transfer, modify. Certain difficulties are attached with allowing objects to move between servers - largely, if objects are transferred en toto to another server, that server is not guaranteed to preserve/respect those restrictions. Much of an object has already been shown copyable just from the information flow that's needed to allow another client to render an object (promoting outrage among IP-believers and bans from Linden Labs, which has a strong pro-IP stance). I would prefer that permissions go away entirely and side strongly with those who wrote the copybots - intellectual property is, to me, a concept that needs to be abolished. It'll be interesting to see what LL will do though, given how much they've described themselves as being pioneers in IP in digital worlds and the impression they've given content creators that permissions set on items would remain coherent and part of a promoted regime (the latter part is important because we could easily imagine them disallowing object transfers for things with more restrictive settings while at the same time noting such permissions as depreciated and "old news", making a cultural push against them - the effects of this would destroy markets very effectively, just like manipulating price expectations in real markets do).

It says good things about humanity that as of this look, 819 people need their daily-ish dose of amusing nonsense. Merovingan's lj would probably be a good thing to read for people who for some reason never were going to sleep again. If I remember correctly, I first found him when reading up on a few other prominent Wikipedia admins. (which reminds me - is Eric Möller still involved at the highest levels of Wikipedia? .. answer: sigh, yes he is.)

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