Now, let us have a look at this and type of item does, which we have in case of SUV, in case of SVM.
We will be working with several hypovolemic that the government.
So what is going on is a mathematical function.
This function of government is to the data as input and transform it into a required form.
So.
Here you can see they have this data, which is in the form of the data, which is in two dimensions.
And what now, what Cornell would do is government would transform this data from these two dimensions
to three dimensions where it will add another dimension to it and move earlier.
The problem was that because X and Y were two different dimensions and the data had no linear separation.
So we were not able to separate these and we were not able to create a line between this.
Now, with the presence of the colonel, what happens is the coroner transforms this data from this
dual dimensions to three dimensions.
Now, these three dimensions actually allow us to create a plane between X in Z axis, and this plane
is able to separate both of these clusters.
Now, when we transform this data back to the linear plane, back to the X and Y plane, we can see
that the line, the plane, which we had all actually created, had formed the circle, the plane.
Which is able to classify X and Y and separate X and Y clearly.
Now, what is the coroner the coroner defines the distance measure between new data and the support
vectors that this observation poses to the hyperbole in case of a corner, the corner will be defining
the distance between the new data.
So the government will make sure that the new data, which we are adding to this particular data, the
data which we are actually testing is finite, is evaluated with respect to the government, with respect
to the distance from the plane.
So it is able to define the distance and based on that, it can actually find out which observation,
which are closest to the type of plane and which are not.
The values which are closest to the high poverty, they are known as the support workers and based on
the support vectors, it actually defines how the classification needs to be.
Now, the main task here is how far or how close the lines could be to these support vectors.
That is the hyperbole in which we are creating.
How far or how close can we allow them to get through this support mechanism?
The closer the separation line will be to this support vector, the more accurate the.
Classification will be back.
Another thing is that there are a few more parameters which allow us to define these things.
So let us have a look at that now.
And during the hyper the higher dimensions, the corners will allow the data to be classified in a higher
dimension.
So there are corners which are present for the lower dimensions of their corners, which are present
for the higher dimensions.
So the corner like polynomial corner and a radial corner.
These are two corners which are used for the higher dimension.
So they transform the input space into higher dimension.
If they have a linear kernel, it will not transform the data into higher dimension.
It will just walk on the X and Y axis.
But when we have the polynomial going, it will only.
Wolf, it will allow to have more complex functions and considered more complex functions.
Eileen O'Connor will only create a straight line so a linear kernel will only be able to create a straight
line via the polynomial and radial kernel will be able to capture the complex features, also the complex
shapes of the data.
So that is why for higher dimensional data, we use polynomial and.
Now, here we can see the visualization of the scene, so here when we have a linear kernel, we have
a straight line of separation which is needed.
So here we have just created a straight line and the straight line was able to classify the data accurately.
But when the data is actually in a polynomial form, that is, it has different goals.
So in that case, we can use the polynomial and the situations where the 5N is a lot more complex and
cannot be figured in a single goal.
So in those cases, we will be using these radial basis function.
Here you can see that here we have small clusters of data separator and these are still belonging to
the same classes.
And around these we have the.
Another class, so these are more accurately classified by the radial basis function.
Now, how far these line of separations will be is decided by the hyper barometer.
So that is see value now what they see value, see value is on the regularization parameter.
Now, when the value of C is large.
Then the value of sea is large, the smaller margin hyper plane will be considered since it stresses
on getting all the brownie points classified vertically and a small value of sea will consider a large
margin piper plane.
And even if some points are misclassified by the hyperbole.
So what does the sea value emphasize on the sea value?
Emphasis on the distance from the support vectors.
So.
Here we have these vectors and here we have this hyperbole.
Now, if the value of SI will be large, then we will be trying to have the distance smaller and then
the value of SI will be small.
Then we will try to maximize the distance from this site separating hyperbole.
So let's have a look at the image related to that.
So here you can see when sea value is very small, the distances get very high.
So when the distances get very high, the.
Few of the data point actually fall inside this and these might get misclassified.
Why then did we increase the value of see, what happens is that the margin is kept very small and so
that there is no point which gets misclassified.
So the larger the value of C, the lesser the chance of misclassification.
So here you can see the diagram later.
So here we have created a clear line.
I'm here.
The value as the value of these is that more closely to the data classes, which we have.
So the higher the value of C, the lesser the chances of misclassification, because then the margin
separation will be less than.
And a little bit by the media is the guerma value.
Now, the gamma barometer defines how far the influence of each training observation affects the calculation
of the optimal hyperbole.
That is how far the influence of each training observation affects the calculation of optimal hyperbole.
Now it defines how far the influence of a single training example reaches.
So if they have one training example, then how much influence will it have on the hyper creation?
If that is, each point will be having the area around it, which will be impacted.
So if they have low value of Gamma, then it will then up Datapoint will have a very long impact for
the hypovolemic creation.
That is, it will have a father boundry.
When we have a high value of gamma, it means that we want to have the type of plain-clothes it will
allow the hyper plane to be created closer to it.
Now the gamma barometer is the inverse of the radius of the influence.
So the higher the value of gamma, the lower the radius will be lower the radius of the lensmen.
So.
Ladies, so here we have Gameau values small, so this means that the radius of influence will be high,
so it will try to keep the boundary as far as possible.
That is why the boundaries are straight in line and are farther away from the point.
Why, as the value of gamma increases, the points allow the boundary to be closer to them.
So because the impact of the point is low, so it is allowing the type of hydroplaned to be closer to
it.
Hence we have such boundaries.
Now, let us have a look at the pros of this swim so it works really well with a clear margin of separation.
So in case we have data which has a clear space of margin where the classes are well separated in those
conditions.
SVM will work very well next is it is effective in higher dimensional spaces because we have the corners
available which can actually deal with high dimensions, then it is effective in cases where the number
of dimension is greater than the number of samples.
Why is this so?
Let's say we have 20, 20 data points and we have more number of dimensions.
Number of dimensions would be the number of features that we have now.
If we have more number of features, there will be more number of dimensions available now because while
classifying using SVM, we are not really worried about all the data points which are present, but
only about four years hence.
We don't really need that much amount of data.
And SVM, there is no need to have large amount of data, would have a better performance for having
a better performance, we need a better, cleaner separation than what we are going to have a better
performance, but more a little bit more number of rules of data that would not really mean that we
can have a better classified from the film.
OK, so in this case, if it can work really well, if that is high amount of dimensions, because if
there are a number of dimensions, then it will allow it to find those dimensions where the data can
actually be separated.
Then because the community which we are using is actually being used to convert this data into higher
dimensions.
Now, when we already have higher dimensions, then it is easier task.
Now it uses a subset of training points in the decision function called support vector.
So it is a memory efficient.
Now, again, same point because there is no need of all the points.
All the data points are not needed.
We only need the support vectors.
That design will be more efficient in nature.
And again, it will be better for me and it will not be as complex as other algorithms, which will
take a lot of time to do to actually get trained.
Now, what are the funds now, it does not perform well when we have large data set because it required
training, time is higher.
OK, so it will not perform well when we have large data said, because it will have to compare their
distances and then find out.
So it is better to have a smaller data set.
We can clearly find the line of separation, then use it now.
It also does not perform well when the data has some more noises like this that classes are overlapping.
Now, here you can see when the glasses are separated, it is working fine, but when it gets closer
to the data, it actually is not able to classify it.
So when the glasses wave is overlapping, then it will not be able to find a line, a line of separation,
and then it will not find a line of separation.
Then obviously it will not be able to classify it properly.
Now, SVM does not directly provide a probability estimate, so we cannot find a probability of a point
being in one particular glass because it can StreetLink give which glass it will belong to, but it
will not give a probability because anyhow, it is calculating based on the distance from the from the
line of separation rate.
So it cannot really calculate the probability of it being in one glass.
Now these are calculated using the expensive five fold cross-validation it is included in the related
SVC method of the Vitan Cyclone Lababidi.
So this is about SBM in the next session, we will have a look at the whole walkthrough of SBM on a
tax data so that you will have a clearer picture of how this is implemented.