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So it turns out one of the common applications of PCA is actually this text data representations as well. When you apply PCA to this sort of data, the resulting algorithm, it often just goes by a different name, just latent semantic indexing. For the sake of completeness, I should say that in LSI, you usually skip the preprocessing step.

For various reasons, in LSI, you usually don't normalize the mean of the data to one, and you usually don't normalize the variance of the features to one. These are relatively minor differences, it turns out, so it does something very similar to PCA.

Normalizing the variance to one for text data would actually be a bad idea because all the words are – because that would have the affect of dramatically scaling up the weight of rarely occurring words. So for example, the word aardvark hardly ever appears in any document. So to normalize the variance of the second feature to one, you end up – you're scaling up the weight of the word aardvark dramatically. I don't understand why [inaudible].

So let's see. [Inaudible] the language, something that we want to do quite often is, give it two documents, XI and XJ, to measure how similar they are. So for example, I may give you a document and ask you to find me more documents like this one. We're reading some article about some user event of today and want to find out what other news articles there are. So I give you a document and ask you to look at all the other documents you have in this large set of documents and find the documents similar to this.

So this is typical text application, so to measure the similarity between two documents in XI and XJ, [inaudible] each of these documents is represented as one of these high-dimensional vectors. One common way to do this is to view each of your documents as some sort of very high-dimensional vector. So these are vectors in the very high-dimensional space where the dimension of the vector is equal to the number of words in your dictionary.

So maybe each of these documents lives in some 50,000-dimension space, if you have 50,000 words in your dictionary. So one nature of the similarity between these two documents that's often used is what's the angle between these two documents. In particular, if the angle between these two vectors is small, then the two documents, we'll consider them to be similar. If the angle between these two vectors is large, then we consider the documents to be dissimilar.

So more formally, one commonly used heuristic, the national language of processing, is to say that the similarity between the two documents is a co-sine of the angle theta between them. For similar values, anyway, the co-sine is a decreasing function of theta. So the smaller the angle between them, the larger the similarity. The co-sine between two vectors is, of course, just [inaudible] divided by – okay? That's just the linear algebra or the standard geometry definition of the co-sine between two vectors.

Here's the intuition behind what LSI is doing. The hope, as usual, is that there may be some interesting axis of variations in the data, and there maybe some other axis that are just noise. So by projecting all of your data on lower-dimensional subspace, the hope is that by running PCA on your text data this way, you can remove some of the noise in the data and get better measures of the similarity between pairs of documents.

Questions & Answers

anyone know any internet site where one can find nanotechnology papers?
Damian Reply
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
many many of nanotubes
what is the k.e before it land
what is the function of carbon nanotubes?
I'm interested in nanotube
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Machine learning. OpenStax CNX. Oct 14, 2013 Download for free at http://cnx.org/content/col11500/1.4
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