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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

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.
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
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
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
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
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
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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