卷积神经网络
吴恩达 Andrew Ng

Face recognition & Neural style transfer

Face Recognition

What is face recognition?

Verification 验证

• Input image, name/ID
• Output whether the input image is that of the claimed person
• “is this the claimed person?”

Recognition 识别

• Has a database of K persons
• Get an input image
• Output ID if the image is any of the K persons (or “not recognized”)
• “who is this person?”

One Shot Learning

• learn from one example to recognize the person again
• 一个类别只有一个样本供学习
• learn a similarity function, 输入两张照片，判断其相似度

Siamese Network

• 图片输入一个卷积网络，输出一个特征向量，作为该图片的编码

• parameters of neural network define an encoding f(x(i))$f(x^{(i)})$

• DeepFace: Closing the Gap to Human-Level Performance in Face Verification

• FaceNet: A Unified Embedding for Face Recognition and Clustering

  FaceNet learns a neural network that encodes a face image into a vector of 128 numbers.

Triplet Loss

• anchor (原图)，positive image(同一个人)，negative image(不同的人)

• margin 间隔

  • 防止学习到的参数为全零
  • 使得 A和P、A和N 的差距变大

• triplet loss function is defined on triples of images

• L(A,P,N)=max(∥f(A)−f(P)∥2−∥f(A)−f(N)∥2+α,0)$\mathcal{L}(A,P,N)=max(\Vert f(A)-f(P){\Vert }^2-\Vert f(A)-f(N){\Vert }^2+\alpha ,0)$

  J=∑L(A(i),P(i),N(i))$\mathcal{J}=\sum \mathcal{L}(A^{(i)},P^{(i)},N^{(i)})$

• if A, P, N are chosen randomly, d(A,P)+α≤d(A,N)$d(A,P)+\alpha \le d(A,N)$

• 一般情况下不同人的照片差距就比同一人照片的大

Face Verification and Binary Classification

• 两个图片一组，输出0/1，表示不相同/相同

• 预先计算 encoding 的值，下次需要比对时不必再通过卷积网络计算

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Neural Style Transfer

What is neural style transfer?

• 神经风格转换
• **C**ontent, **S**tyle, **G**enerated image

What are deep ConvNets learning?

Visualizing deep layers

• 第一层的隐藏单元通常会找一些简单的特征，比如边缘、颜色、阴影等
• 第二层似乎检测到更复杂的形状和模式
• 第三层明显检测到更复杂的模式
• 第四层检测到的模式和特征更加复杂

Cost Function

• J(G)=αJContent(C,G)+βJStyle(S,G)$J(G)=\alpha J_{Content}(C,G)+\beta J_{Style}(S,G)$
• Initiate G randomly
• Use gradient descent to minimize J(G)

Content Cost Function

• use hidden layer l to compute content cost
• let a[l](C)$a^{[l](C)}$ and a[l](G)$a^{[l](G)}$ be the actication of layer l on the images
• if a[l](C)$a^{[l](C)}$ and a[l](G)$a^{[l](G)}$ are similar, both images have similar content
• JContent(C,G)=∥a[l](C)−a[l](G)∥2$J_{Content}(C,G)=\Vert a^{[l](C)}-a^{[l](G)}{\Vert }^2$

Style Cost Function

• G[l]kk′=∑n[l]Hi=1∑n[l]Wj=1a[l]i,j,ka[l]i,j,k′$G_{k{k}^{{}^{\prime }}}^{[l]}=\sum _{i=1}^{n_H^{[l]}}\sum _{j=1}^{n_W^{[l]}}{a}_{i,j,k}^{[l]}{a}_{i,j,k^{{}^{\prime }}}^{[l]}$

• J[l]Style(S,G)=∑n[l]Ck=1∑n[l]Ck′=1(G[l](S)kk′−G[l](G)kk′)$J_{Style}^{[l]}(S,G)=\sum _{k=1}^{n_C^{[l]}}\sum _{k^{{}^{\prime }}=1}^{n_C^{[l]}}(G_{k{k}^{{}^{\prime }}}^{[l](S)}-G_{k{k}^{{}^{\prime }}}^{[l](G)})$

• JStyle(S,G)=∑lλ[l]J[l]Style(S,G)$J_{Style}(S,G)=\sum _l{\lambda }^{[l]}{J}_{Style}^{[l]}(S,G)$

1D and 3D Generalizations

3D Convolution