Cost Function

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From the course by deeplearning.ai

Convolutional Neural Networks

15565 ratings

deeplearning.ai

Convolutional Neural Networks

15565 ratings

Course 4 of 5 in the Specialization Deep Learning

This course will teach you how to build convolutional neural networks and apply it to image data. Thanks to deep learning, computer vision is working far better than just two years ago, and this is enabling numerous exciting applications ranging from safe autonomous driving, to accurate face recognition, to automatic reading of radiology images. You will: - Understand how to build a convolutional neural network, including recent variations such as residual networks. - Know how to apply convolutional networks to visual detection and recognition tasks. - Know to use neural style transfer to generate art. - Be able to apply these algorithms to a variety of image, video, and other 2D or 3D data. This is the fourth course of the Deep Learning Specialization.

From the lesson

Special applications: Face recognition & Neural style transfer

Discover how CNNs can be applied to multiple fields, including art generation and face recognition. Implement your own algorithm to generate art and recognize faces!

What is neural style transfer?2:02

What are deep ConvNets learning?7:57

Cost Function3:59

Content Cost Function3:37

Style Cost Function13:17

1D and 3D Generalizations9:08

Meet the Instructors

Andrew Ng
CEO/Founder Landing AI; Co-founder, Coursera; Adjunct Professor, Stanford University; formerly Chief Scientist,Baidu and founding lead of Google Brain
Head Teaching Assistant - Kian Katanforoosh
Lecturer of Computer Science at Stanford University, deeplearning.ai, Ecole CentraleSupelec
Teaching Assistant - Younes Bensouda Mourri
Mathematical & Computational Sciences, Stanford University, deeplearning.ai

To build a Neural Style Transfer system,

let's define a cost function for the generated image.

What you see later is that by minimizing this cost function,

you can generate the image that you want.

Remember what the problem formulation is.

You're given a content image C,

given a style image S and you goal is to generate a new image

G. In order to implement neural style transfer,

what you're going to do is define a cost function J of G that measures how good is

a particular generated image and we'll use gradient to

descent to minimize J of G in order to generate this image.

How good is a particular image?

Well, we're going to define two parts to this cost function.

The first part is called the content cost.

This is a function of the content image and of the generated image and

what it does is it measures how similar is the contents of the generated image

to the content of the content image C. And then going to

add that to a style cost function which is now a function of

S,G and what this does is it measures how similar is

the style of the image G to the style of the image S. Finally,

we'll weight these with two hyper parameters alpha and beta to

specify the relative weighting between the content costs and the style cost.

It seems redundant to use two different hyper parameters to specify

the relative cost of the weighting.

One hyper parameter seems like it would be enough but

the original authors of the Neural Style Transfer Algorithm,

use two different hyper parameters.

I'm just going to follow their convention here.

The Neural Style Transfer Algorithm I'm

going to present in the next few videos is due to Leon Gatys,

Alexander Ecker and Matthias.

Their papers is not too hard to read so after watching these few videos if you wish,

I certainly encourage you to take a look at their paper as well if you want.

The way the algorithm would run is as follows,

having to find the cost function J of G in

order to actually generate a new image what you do is the following.

You would initialize the generated image

G randomly so it might be 100 by 100 by 3 or 500 by 500 by

3 or whatever dimension you want it to be.

Then we'll define the cost function J of G on the previous slide.

What you can do is use gradient descent to minimize this so you can update G as

G minus the derivative respect to the cost function of J of G. In this process,

you're actually updating the pixel values of this image G which is

a 100 by 100 by 3 maybe rgb channel image.

Here's an example, let's say you start with this content image and this style image.

This is a another probably Picasso image.

Then when you initialize G randomly,

you're initial randomly generated image is

just this white noise image with each pixel value chosen at random.

As you run gradient descent,

you minimize the cost function J of G slowly through the pixel value so then you get

slowly an image that looks more and more like

your content image rendered in the style of your style image.

In this video, you saw the overall outline of

the Neural Style Transfer Algorithm where you define

a cost function for the generated image G and minimize it.

Next, we need to see how to define

the content cost function as well as the style cost function.

Let's take a look at that starting in the next video.

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