# 1.14 Machine learning lecture 15  (Page 3/15)

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.

find the 15th term of the geometric sequince whose first is 18 and last term of 387
The given of f(x=x-2. then what is the value of this f(3) 5f(x+1)
hmm well what is the answer
Abhi
how do they get the third part x = (32)5/4
can someone help me with some logarithmic and exponential equations.
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
so you not have an equal sign anywhere in the original equation?
hmm
Abhi
is it a question of log
Abhi
🤔.
Abhi
Commplementary angles
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
hii
Uday
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
a perfect square v²+2v+_
kkk nice
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
rolling four fair dice and getting an even number an all four dice
Kristine 2*2*2=8
Differences Between Laspeyres and Paasche Indices
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
how do you translate this in Algebraic Expressions
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
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.
what is nano technology
what is system testing?
preparation of nanomaterial
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
what is system testing
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
how did you get the value of 2000N.What calculations are needed to arrive at it
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