Re: AW: DM: RE: Data Forms for Mining (Limit on variables)

• Organization: Montclair State University

osborn wrote:
 >
 >  > I am new to this. What is "VC-dimension"?
 >
 > Vapnik-Chervonenkis Dimension. Eg, see "The Nature of Statistical
 > Learning Theory" by VN Vapnik, or "Statistical Learning Theory"
 > by Vapnik. Fairly heavy read...
 >
 > " The VC dimension of a set of indicator functions Q(z,a), a in L,
 > is equal to the largest number h of vectors z1..zl that can be
 > separated into two different classes in all the 2^h possible ways
 > using this set of functions. " The notion here is being able to

I don't get this. The two phrases "the largest number h of vectors
that can be separated into two different classes" and "in
all the 2^h possible ways" is not registering in my brain. How
can a collection be separated into 2 classes in N ways? If it
means what I think I can't see much use for it, or at least
I think there should be more useful "dimensions". For example,
the integers {1,2,3,4,5,6} can be split into Odd/Even, or
"A/not_A (where A means greater than 4), etc.

(These seem to be meaningful in some intrinsic way, to me.)

But it is trivial to create lots of dichotomous divisions.
I can think of a whole set of X/not-X dichotomy
simply by going thru the collection and for each defining a
trivial condition. For example, the set above can be divided
into two sets like this

1) 1 or not_1
2) 2 or not_2
...


6) 6 or not_6

Suppose these are vectors. What is the VC dimension?



--
Regards, Mark
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