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MachineLearning-Lecture08

Instructor (Andrew Ng) :Okay. Good morning. Welcome back. If you haven’t given me the homework yet, you can just give it to me at the end of class. That’s fine. Let’s see. And also just a quick reminder – I’ve actually seen project proposals start to trickle in already, which is great. As a reminder, project proposals are due this Friday, and if any of you want to meet and chat more about project ideas, I also have office hours immediately after lecture today. Are there any questions about any of that before I get started today? Great.

Okay. Welcome back. What I want to do today is wrap up our discussion on support vector machines and in particular we’ll also talk about the idea of kernels and then talk about [inaudible] and then I’ll talk about the SMO algorithm, which is an algorithm for solving the optimization problem that we posed last time.

To recap, we wrote down the following context optimization problem. All this is assuming that the data is linearly separable, which is an assumption that I’ll fix later, and so with this optimization problem, given a training set, this will find the optimal margin classifier for the data set that maximizes this geometric margin from your training examples.

And so in the previous lecture, we also derived the dual of this problem, which was to maximize this. And this is the dual of our primal [inaudible] optimization problem. Here, I’m using these angle brackets to denote inner product, so this is just XI transpose XJ for vectors XI and XJ. We also worked out the ways W would be given by sum over I alpha I YI XI.

Therefore, when you need to make a prediction of classification time, you need to compute the value of the hypothesis applied to an [inaudible], which is G of W transpose X plus B where G is that threshold function that outputs plus one and minus one. And so this is G of sum over I alpha I. So that can also be written in terms of inner products between input vectors X.

So what I want to do is now talk about the idea of kernels, which will make use of this property because it turns out you can take the only dependers of the algorithm on X is through these inner products. In fact, you can write the entire algorithm without ever explicitly referring to an X vector [inaudible] between input feature vectors. And the idea of a high kernel is as following – let’s say that you have an input attribute. Let’s just say for now it’s a real number. Maybe this is the living area of a house that you’re trying to make a prediction on, like whether it will be sold in the next six months.

Quite often, we’ll take this feature X and we’ll map it to a richer set of features. So for example, we will take X and map it to these four polynomial features, and let me acutely call this mapping Phi. So we’ll let Phi of X denote the mapping from your original features to some higher dimensional set of features.

So if you do this and you want to use the features Phi of X, then all you need to do is go back to the learning algorithm and everywhere you see XI, XJ, we’ll replace it with the inner product between Phi of XI and Phi of XJ. So this corresponds to running a support vector machine with the features given by Phi of X rather than with your original one-dimensional input feature X.

Questions & Answers

can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
ninjadapaul
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
ninjadapaul
I don't understand what the A with approx sign and the boxed x mean
ninjadapaul
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
ninjadapaul
oops. ignore that.
ninjadapaul
so you not have an equal sign anywhere in the original equation?
ninjadapaul
Commplementary angles
Idrissa Reply
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
kkk nice
Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
Embra Reply
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
Nancy Reply
rolling four fair dice and getting an even number an all four dice
ramon Reply
Kristine 2*2*2=8
Bridget Reply
Differences Between Laspeyres and Paasche Indices
Emedobi Reply
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
Mary Reply
is it 3×y ?
Joan Reply
J, combine like terms 7x-4y
Bridget Reply
im not good at math so would this help me
Rachael Reply
yes
Asali
I'm not good at math so would you help me
Samantha
what is the problem that i will help you to self with?
Asali
how do you translate this in Algebraic Expressions
linda Reply
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris 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
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
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
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
can nanotechnology change the direction of the face of the world
Prasenjit Reply
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.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele 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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