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Hello.

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Welcome back.

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In machine learning training examples are often denoted by the letter M.

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We often break our training examples into two sets the training set and the test set training set is

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often denoted by m subscript train and a test set is denoted by m subscript test.

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We denote the number of features by n.

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You can think of number of features as the number of inputs in our previous examples.

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Our neural network had two features in the last example.

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The features were hours of rest and hours of work out in our body builders.

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Example I mean when we work in with image recognition the number of features becomes the number of pixels

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in the image because we will have to find each pixel into the neural network.

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So let's say we want to design a neural network for a binary classification problem.

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Let's say we want to a neural network to take a sixty four by sixty four pixel image and tell us if

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the image has a cat or not to store an image in our computer.

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The computer stores three separate matrices corresponding to the red the green and the blue channels

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of the image 64 pixels by 64 pixels each.

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This means we would have three multiplied by sixty four by sixty four because each image size is sixty

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four by sixty four pixels we multiply by three because we have three channels red green and blue to

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turn these pixel intensity values into feature vectors.

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What we would need to do is en route the m the pixel we need to row the pixel values into a vector like

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this.

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We simply need to take the red matrix which is a 2D array and convert it to affect or meaning a 1 D

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array.

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We do that by list in D.

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The pixel values vertically we take the first rule we write the first value and then we write the second

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value below the first value and then we write the third value below the second value.

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Once we are done with the first rule we continue by listing the values of the second row in the same

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vector.

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We put a second rule of values under the First Rule values.

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We continue doing this until we've added all the rows of the red channel.

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Once that is done we move on to the green channel and then we list all the pixel values of the green

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channel under the red channel.

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Once that is done we do it for the blue channel by listing everything under the green one.

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Once this is done then we will have twelve thousand two hundred and twenty eight features like we can

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see over here.

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That is why this vector.

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Yes that's from 0 and ends at twelve thousand two hundred and twenty eight which is the same as this

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which is the same as sixty four multiplied by sixty four multiplied by three.

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We've taken this and essentially converted it to effector the training examples are put together in

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a matrix denoted here as couple to X capital X then becomes our input matrix representing all training

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examples and features each column in input matrix copy to x represent a single training example the

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first row of the input matrix capital x represents the first feature of the training examples I should

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remind you that whenever I see features you should simply think of inputs input matrix X shall be processed

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by the neural network column by column remember again the columns represent each training example capital

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X belongs to real numbers and the dimension of capital X is the number of features by the number of

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examples the training labels shall be kept in a vector Capital Y where Y 1 is the answer to the question

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is x 1 cuts or not a cut and Y 2 is the answer to the question is x 2 it cuts or not to cut and so on

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and so forth why y it is the value that we predicted whereas Y is the value we expected we can see it

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a y hat is the probability of Y given that we know X and this is how you write it P Y vertical line

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X like that oh no network often has two parameters W and b we shall talk about something else known

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as hyper parameters later on in this course W is known as the way to matrix and B is known as the bias

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we compute my heart by performing at DOT PRODUCT operation between the transpose of the weight matrix

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and the input matrix and the bios.

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And then we apply activation function to the resort.

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Now let's look at a while logistic regression loss function the loss function is simply the function

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for calculating error.

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The simplified lost function we saw in our previous lessons looked at is similar to this predicted value

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minus expected value.

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We square the difference and then multiply by half a more accurate loss function for logistic regression.

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As this one over here minus brackets open why log why not.

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Plus brackets open 1 minus Y bracket close and then lock 1 brackets open 1 minus Y hot.

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You can post the video and take a look at it.

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So this a more accurate lost function for our logistic regression.

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Remember the lost function is applied to just a single training example D cost function is the cost

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of all the parameters.

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In other words the cost function is the average of all the lost functions.

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This is what the cost function looks like.

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We are adding up all the lost functions and then divide into result by the number of training examples.

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This is the cost function which we'll use to train our neural network when we go to code.

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So um this brings us to the end of this lesson and I shall see you in the next lesson.