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number which is a categorical variable which you get down so from a simple neuron we will
parameters connected to one parameter and it can even go down by a successive stages
of parametric connections which goes down and finally is what enters into what we call
and what this does is that we define something as a neural network and then say that this
neural network is able to classify images and as we go down over there now one important
fact which you will have to take care over here is that as we are learning over here
then that would mean that somehow with experience going by that definition somehow with experience
which we are gaining we will be able to do that task much better
so that means necessarily that as we show it more number of samples of features and
which are associated number of categorical variables over there then this whole network
over here which i call as a neural network would be able to really associate any unknown
this learning you will have to go down through the way of gradient checking and optimizations
this so we have the mathematical equation but lets lets get down into what it looks
like so say i have three different variables x one x two and x three and these can be three
the image and say over here is the average entropy of the image ok so we can have three
different features over there for one single image given down now once we have these three
of the image x three is also scalar and now together what we can do is we can associate
with certain vector and then we can sort of sum them up ok so x one will be multiplied
by a weight w one x two will be multiplied by a weight w two x three will be multiplied
then my output over here so the form of y is something which is written down as w naught
will be a n plus one term summation which comes down over here now from there as we
sort of a matrix representation is what is given down over here ok so what w is basically
and that is equal to w naught itself and x is another vector of all the ah scalars which
are arranged in terms of a matrix over there so this is a matrix form of representation
now once i have that one what i can do is i can relate this y to my predicted class
this f n l can have two different forms some common forms are something like this the first
my x s over here i dont have any sort of a control over my x so these can be anything
from minus infinity to plus infinity for the purpose of simplicity we keep down the fact
that let these be real valued numbers and not complex valued numbers that that does
to plus infinity now that i have these also open ranged then what i get down from this
to me that can be anything from minus infinity to plus infinity which would typically make
just put a threshold over there say that if the value is greater than zero make it one
of functions say a sigmoid non linearity so what it would do is that as my y becomes tending
now in the same way as i go with my second non linearity which is called as a tan hyperbolic
so you can put down your values of y is varying from minus infinity to plus infinity and you
can very intuitively see that as the value of y goes down to minus infinity this value
tends to minus one as the value goes to plus infinity this value tends to plus one and
say just give down the argument that if it is greater than zero make it one less than
i have three scalar values over here so what i can do is i can associate it to some different
number of patterns which i want to different number of predictors which i want to do so
being the contrast and x three being the average entropy on the image i want to classify whether
that is a ball in the image yes or no and whether the image is a photograph or image
down subscripted dually now with it with this dual weight subscription what happens technically
which i want to classify and the first subscript is the one which connects down which feature
is being connected to which target neuron over here ok
done for y one and p one in terms of an equation now if i get down another parameter p two
and thats what i was saying that do you have another different thing to predict and that
may be that whether its a natural image or this was a sketched image now for that you
will have a similar set of equation which you get down over here now you can clearly
outputs can be designed over here
now similarly i can extend it to some n number of some some k number of neurons over here
now once you stand on all the row vectors you get down a rectangular matrix over there
equation and then accordingly your predicted neurons will also be stacked into one single
was applied on a scalar and thats why this can be extended on to a matrix valued form
function and that will give you the same sort of a vector output which comes down over here
now essentially what this helps you is that you can relate down some j number of input
neurons to some k number of output neurons in in straight simple terms now from there
once you are able to relate it down next what comes down is that i will have certain sort
of error when i am able to relate it down it means that so using these three features
and some combination of weights which are present over here i will be able to predict
and there is a value which is coming down from this neuron itself ok now the difference
between the true value say in the first case there was a ball but it predicted there wasnt
a ball so there is its an error its a clear case of an error so but here what i would
get done is that the error value is one ok in the other way round where say there wasnt
the ground truth also says that there isnt a ball it means that it is ah its its a correct
case so similarly we will have it for the second predictor as well now if you see all
of these predictors are independent of each other so it means that the errors are also
distance between the predicted vector over here this p that becomes a matrix
now and the actual ground truth which is so between your p hat and your p so this will
learning over here is in a sense that i should be somehow able to get down a network such
essentially happens in that case is we use a method called as error back propagation
so what it would do is say i have a set of observations x one ok so this one over here
is no more related to one particular feature but that one which we are putting down over
here in this relationship is actually which is related down to
truth and i have my predicted value similarly i keep on doing such that i have n number
of images in something which is called as a training set so what happens in a training
set in this kind of a problem which is a supervised learning problem is that you have a set of
images some n number of images and for each image you also know what is the class label
given to it so here we were asking down two questions whether this there is a ball in
image kind of thing
so there are two vectors over here which i there is a two dimensional vector or two parameters
which i want to predict down to class levels so that should also be known to me so there
training set ok now on the other side i am going to predict out all of this with a certain
given form of my weights over there now initially what i would do is i would start with a neural
difference is coming down for each so i get the euclidean distance for each sample so
for x one x two x three similarly it up to x n i get down this difference coming down
you look carefully into this one
so my p hats are what are dependent on all my excess over here ok but these x values
they dont change in the whole data set right the only thing which changes within the network
the whole objective is that i want to get down a particular value of w which is the
only thing variable and adjustable within my neural network such that my cost function
over here is minimum and this has to be minimum when you need to have done the minimum error
over there as you get down your minimum error in this case this has to be zero so your jw
start with a random guess of w within a k th iteration so my k at the start of it will
be k equal to zero ok so at k equal to zero i start with some w over here now with that
w i will be able to get down my these predictions over here p one to p n hat from there i would
is a partial derivative of the cost function with respect to my weight at that particular
of these predictions from there i would get down get down as the j w for w k plus one
and then i would iterate it over such that at some point of time i would reach down this
minimum value of w and then just stop over here ok