Monday, January 29, 2007

inf (glb) and sup

from mathforum

inf means "infimum," or "greatest lower bound." This is
slightly different from minimum in that the greatest lower bound is
defined as:

x is the infimum of the set S [in symbols, x = inf (S)] iff:

a) x is less than or equal to all elements of S
b) there is no other number larger than x which is less than or equal
to all elements of S.

Basically, (a) means that x is a lower bound of S, and (b) means that
x is greater than all other lower bounds of S.

This differs from min (S) in that min (S) has to be a member of S.
Suppose that S = {2, 1.1, 1.01, 1.001, 1.0001, 1.00001, ...}. This
set has no smallest member, no minimum. However, it's trivial to show
that 1 is its infimum; clearly all elements are greater than or equal
to 1, and if we thought that something greater than 1 was a lower
bound, it'd be easy to show some member of S which is less than it.

So that's the difference between inf and min. It's worth noting that
every set has an inf (assuming minus infinity is okay), and that the
two concepts are the same for finite sets.

glb is another way of writing inf (sort for "greatest lower bound")

sup and lub, which are short for "supremum" and "least upper bound."

Saturday, January 20, 2007

Latent Semantic Index (LSI)

1) here is a great explaination to a layman.

or latent semantic analysis

"The term ’semantics’ is applied to the science and study of meaning in language, and the meaning of characters, character strings and words. Not just the language and words themselves, but the true meaning being conveyed in the context in which they are being used.

In 2002 a company called Applied Semantics, an innovator in the use of semantics in text processing, launched a program known as AdSense, which was a form of contextual advertising whereby adverts were placed on website pages which contained text that was relevant to the subject of the adverts.

The matching up of text and adverts was carried out by software in the form of mathematical formulae known as algorithms. It was claimed that these formulae used semantics to analyze the meaning of the text within the web page. In fact, what it initially seemed to do was to match keywords within the page with keywords used in the adverts, though some further interpretation of meaning was evident in the way that some relevant adverts were correctly placed without containing the same keyword character string as used on the web page.


2)from Patterns in Unstructured Data -Discovery, Aggregation, and Visualization