Face recognition&Neural style transfer
Face recognition
Verification&Recognition
- Verification：验证1对1的关系是否正确
- Recognition：从数据库中识别出一个目标，是1对K的关系
One-shot学习
Learn from one example to recognize the person again
similarity函数
输入两张图片img1,img2，输出两张图片差异的程度，若差异足够小\(d(img1,img2)<t\)，则认为两张图片相同
Siamese network
训练网络使同一个人的embeddings:\(f(x^{(i)})，f(x^{(j)})\)相差尽量小
Triplet Loss
三元损失函数基于A,P,N三张图片，A测试图片，P正确图片，N错误图片
\[d(A,P) - d(A,N) + \alpha \leq0\] \[L(A,P,N) = max(||f(A) - f(P)||^2 - ||f(A) - f(N)||^2 +\alpha , 0)\] \[J = \sum_{i=1}^mL(A^{(i)},P^{(i)},N^{(i)})\]Neural style transfer
cost function
对于图片C要转换到风格S,生成图片G,定义成本函数为
\[J(G) = \alpha J_{Content}(C,G) + \beta J_{Style}(S,G)\]产生图片G的步骤
- 随机初始化G:100 x 100 x3
- 用梯度下降最小化J(G)：\(G := G - \frac \alpha{\alpha G}J(G)\)
Content cost Function
取神经网络中间的隐藏层l计算内容损失Content cost
\[J_{Contnent}(C,G) = \frac1n||a^{[l](C)} - a^{[l](G)}||^2\]Style cost Function
取神经网络隐藏层l,定义style为不同通道之间的相关性
GRAM matrix:
\[G^{[l](S)}_{kk'} = \sum_{i=1}^{n_H^{[l]}}\sum_{j=1}^{n_W^{[l]}}a_{i,j,k}^{[l](S)}a_{i,j,k'}^{[l](S)}\] \[G^{[l](G)}_{kk'} = \sum_{i=1}^{n_H^{[l]}}\sum_{j=1}^{n_W^{[l]}}a_{i,j,k}^{[l](G)}a_{i,j,k'}^{[l](G)}\] \[J_{style}^{[l]}(S,G) = \frac1{(2*n_H^{[l]}*n_W^{[l]}*n_C^{[l]})^2}\sum_k\sum_{k'}(G^{[l](S)}_{kk'} - G^{[l](G)}_{kk'} )^2\] \[J_{style}(S,G) = \sum_l\lambda^{[l]}J^{[l]}_{style}(S,G)\]1D&3D Convolutions
1 x 14 conv 1 x 5 —-> 1 x 10
14 x 14 x14 x1 conv 5 x 5 x 5 x1 —->10 x 10 x 10 x 1
