# [Convolutional Neural Networks] week4. Special applications: Face recognition & Neural style transfer

This week: two special application of ConvNet.

## I-Face Recognition

### What is face recognition

**Face verification & face recognition**

- verification: input = image and ID → output whether the image and ID are the same.
- recognition: database = K persons, input = image → output = ID of the image among the K person or "not recognized".

→ the verification system's precision needs to be very high in order to be used in face recognition.

### One Shot Learning

"one shot": learn from just *one* example, and able to recognize the person again.

A CNN+softmax is not practical, e.g. when new images are added to database, output_dim will change...

⇒ instead, learn a *similarity* function.

`d(img1, img2)`

= degree of difference between images. + threshold `tau`

### Siamese Network

To learn a disimilarity function: *Siamese Network*.

Use CNN+FC to **encode*** a pic *`x`

* into vector *`f(x)`

*.*

⇒ define disimilarity function d(x1, x2) as distance between encoded vectors.

More formally:

want to learn NN params for the encoding f(x) such that:

when x1 and x2 are same person, dist(f(x1), f(x2)) is small, otherwise large.

### Triplet Loss

triplet: (*anchor, positive, negative)*.

want f(A) similar to f(P) and different from f(N):

i.e. want `d(A, P) - d(A, N) <= 0`

⇒ to avoid NN from learning a trival output (i.e. all encodings are identical, d(A, P)=d(A, N)=0), *add margin *`alpha`

.

want `d(A, P) - d(A, N) + alpha<= 0`

**Loss function definition**:

similar to hinge loss: `L = max(0, d(A,P)-d(A,N) + alpha)`

→ Generate triplets from dataset, and feed to the NN.

note: here we do need >1 pics of the same person (Anchor and Positive).

**Choosing triplets A, P, N**

If A,P,N are *randomly* chosen, the constraint is easily satisfied → NN won't learn much.

→ *choose A,P,N that are "hard" to train on. *Computation efficiency of learning is improved.

(*details presented in the FaceNet paper*)

in practice: better download pretrained model.

### Face Verification and Binary Classification

Triplet loss is one way of doing face verification.

another way that works as well: treat as a binary classification problem.

Given input image x1 and x2 → feed f(x1) and f(x2) to a logistic regression unit.

→ feed the *difference in encodings* and feed to logistic regression.

computation trick: precompute encodings of imgs in database at inference time.

## II-Neural Style Transfer

### What is neural style transfer?

content image `C`

+ style image `S`

→ generated image `G`

### What are deep ConvNets learning?

**visualize hidden units of different layers**

Pick *one unit* in 1st layer → find the *nine image patches that maximize the unit's activation*.

In deeper layers: units can see larger image patches → gather nine argmax image patchs as before.

deeper layers can detect higher level shapes:

layer 3:

layer 4:

### Cost Function

Define a cost function *for the generated image*.

`J(G)`

measure how good is an image, contains two parts:

`J_content(C, G)`

: how similar is G to C`J_style(S, G)`

: how similar is G to S.

**Find generated image G**

(similar to embedding?)

- initialize G randomly
- Use gradient-descent to minimized J(G)

### Content Cost Function

`J_content(C, G)`

*Given a pre-trained CNN*, use *hidden layer l* to compute J_content. The depth of *l* controls the level of details focuses on.

Define J_content(C, G) = difference (e.g. L2-norm) between the activation of layer l of image C and image G.

### Style Cost Function

Use layer `l`

to measure "style".

→ **style** defined as *correlation between activations across channels*.

e.g. `n_C=5`

channels of slices `n_W * n_H`

.

correlation between 2 channel ~= *which high-level features tend to occur / not occur together in an image.*

**style matrix**

notation:

`a_ijk`

= (scalar)activation at hight=`i`

, width=`j`

, channel=`k`

- "Style matrix)
`G[l]`

, (G for "Gram matrix") shape =`n_C * n_C`

, measures*how correlated any two channels are.*(i.e. G[l] measures the degree to which the activations of different feature detectors in layer l vary (or correlate) together with each other.) `G_kk`

' = correlation between kth and k'th channel.

:= sum_over_i_j( a_ijk * a_ijk')

mathematically, this "correlation" is unnormalized cross-covariance (without substracting the mean).

Compute `G`

for both the style image and generated image.

→ J_style(Gen_img, Sty_img) = difference (Frobenius norm) between G(gen) and G(sty)

In practice, take J_style for multiple layers:

### 1D and 3D Generalizations

images: 2D data.

→ *generalize convolution to 1D and 3D data.*

**1D data**

e.g. EKG data (heart voltage).

(note: most 1D data use RNN...)

**3D data**

have height width and depth,

e.g. C.T. data; movie date (frame by frame)

→ generalized from 2D

#### Part 13 of series «Andrew Ng Deep Learning MOOC»：

- [Neural Networks and Deep Learning] week1. Introduction to deep learning
- [Neural Networks and Deep Learning] week2. Neural Networks Basics
- [Neural Networks and Deep Learning] week3. Shallow Neural Network
- [Neural Networks and Deep Learning] week4. Deep Neural Network
- [Improving Deep Neural Networks] week1. Practical aspects of Deep Learning
- [Improving Deep Neural Networks] week2. Optimization algorithms
- [Improving Deep Neural Networks] week3. Hyperparameter tuning, Batch Normalization and Programming Frameworks
- [Structuring Machine Learning Projects] week1. ML Strategy (1)
- [Structuring Machine Learning Projects] week2. ML Strategy (2)
- [Convolutional Neural Networks] week1. Foundations of Convolutional Neural Networks
- [Convolutional Neural Networks] week2. Deep convolutional models: case studies
- [Convolutional Neural Networks] week3. Object detection
- [Convolutional Neural Networks] week4. Special applications: Face recognition & Neural style transfer
- [Sequential Models] week1. Recurrent Neural Networks
- [Sequential Models] week2. Natural Language Processing & Word Embeddings
- [Sequential Models] week3. Sequence models & Attention mechanism

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