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Let's just delve a little deeper into those examples to convey more intuition about what LSI is doing. So look further in the definition of the co-sine similarity measure. So the numerator or the similarity between the two documents was this inner product, which is therefore sum over K, XIK, XJK. So this inner product would be equal to zero if the two documents have no words in common. So this is really – sum over K – indicator of whether documents, I and J, both contain the word, K, because I guess XIK indicates whether document I contains the word K, and XJK indicates whether document J contains the word, K.

So the product would be one only if the word K appears in both documents. Therefore, the similarity between these two documents would be zero if the two documents have no words in common. For example, suppose your document, XI, has the word study and the word XJ, has the word learn. Then these two documents may be considered entirely dissimilar.

[Inaudible] effective study strategies. Sometimes you read a news article about that. So you ask, what other documents are similar to this? If there are a bunch of other documents about good methods to learn, than there are words in common. So similarity [inaudible]is zero.

So here's a cartoon of what we hope [inaudible] PCA will do, which is suppose that on the horizontal axis, I plot the word learn, and on the vertical access, I plot the word study. So the values take on either the value of zero or one. So if a document contains the words learn but not study, then it'll plot that document there. If a document contains neither the word study nor learn, then it'll plot that at zero, zero.

So here's a cartoon behind what PCA is doing, which is we identify lower dimensional subspace. That would be sum – eigen vector, we get out of PCAs. Now, supposed we have a document about learning. We have a document about studying. The document about learning points to the right. Document about studying points up. So the inner product, or the co-sine angle between these two documents would be – excuse me. The inner product between these two documents will be zero. So these two documents are entirely unrelated, which is not what we want.

Documents about study, documents about learning, they are related. But we take these two documents, and we project them onto this subspace. Then these two documents now become much closer together, and the algorithm will recognize that when you say the inner product between these two documents, you actually end up with a positive number. So LSI enables our algorithm to recognize that these two documents have some positive similarity between them.

So that's just intuition about what PCA may be doing to text data. The same thing goes to other examples and the words study and learn. So you have – you find a document about politicians and a document with the names of prominent politicians. That will also bring the documents closer together, or just any related topics, they end up [inaudible] points closer together and just lower dimensional space.

Questions & Answers

what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
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
Daniel
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
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
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.
Tarell
what is the actual application of fullerenes nowadays?
Damian
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.
Tarell
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.
Virgil
is Bucky paper clear?
CYNTHIA
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.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Berger describes sociologists as concerned with
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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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