deeplearning.ai - 卷积神经网络

卷积神经网络
吴恩达 Andrew Ng

Computer Vision Problems

• Image Classification
• Object Detection
• Neural Style Transfer

Vertical edge detection

• filter (过滤器) (通常是奇数阶)

  ⎛⎝⎜111000−1−1−1⎞⎠⎟$\left(\begin{array}{ccc}1& 0& -1\\ 1& 0& -1\\ 1& 0& -1\end{array}\right)$ 边缘检测

• convolution operation *

• bright pixels on the left and dark pixels on the right

Padding

• (n×n)∗(f×f)=(n−f+1)×(n−f+1)$(n\times n)\ast (f\times f)=(n-f+1)\times (n-f+1)$

  • output will shrink
  • pixels in the corner are used only once, so we loss information near the edge of the image

• 解决上述两个问题的方法 —— Pad

  • with an additional border of one pixel all around the edges
  • pad with zeros by convention
  • so the output will be (n+2p−f+1)×(n+2p−f+1)$(n+2p-f+1)\times (n+2p-f+1)$

• Valid Convolution: No paddings (p = 0)

• Same Convolution: Pad so that output size is the same as the input size

• f 通常是奇数

  • 便于 Same Convolution 的操作
  • 存在中心点 central pixel

Strided Convolution

• 卷积步长 (stride)：每次移动的格子数
• output: (⌊n−fs⌋+1)×(⌊n−fs⌋+1)$(\lfloor \frac{n-f}{s}\rfloor +1)\times (\lfloor \frac{n-f}{s}\rfloor +1)$
• the filter must entirely lies in the image (plus padding region)

Cross-correlation VS. Convolution

• in mathematic, (convolution) before calculation the filter needs a flipping operation (沿副对角线的镜面翻转)
• in ML we usually do not use flipping operation, actually it should be cross-correlation, but by convention we call this convolution
• 卷积满足结合律

Convolution on RGB images

• height, width, channels(depth)

• 图片和过滤器的通道数必须相等

• 

• n×n×nc∗f×f×nc→(n−f+1)×(n−f+1)×n′c$n\times n\times n_c\ast f\times f\times n_c\to (n-f+1)\times (n-f+1)\times n_c^{\prime }$

  nc$n_c$: number of channels; n′c$n_c^{\prime }$: number of filters

• detect n′c$n_c^{\prime }$ features

Example of a layer

• add a bias (偏差) to the output, and then apply a real non-linearity (非线性**函数)
• less prone to over fitting (避免过拟合)
• 上一层的输出作为这一层的输入
• notation
  

A simple convolution network example

• 

• Convolutional Layer (Conv) 卷积层

  Pooling Layer (Pool) 池化层

  Fully Connected Layer (FC) 全连接层

Pooling layer

• reduce the size of representation to speed up computation and make some of the features it detects a bit more robust
• no parameters to learn, just a fixed function, has no weights
• 最后将池化的结果平整化为一个列向量

Max pooling

• break into different regions
• 输出每一个区域的最大值
• 最大池化的超级参数(hyper-parameters)：f=2,s=2$f=2,s=2$ (often)
• usually does not use any padding
• 在某个区域提取到的特征保存在输出里
• if this feature is detected anywhere in this filter, then keep a high number
• 每个信道独立执行最大池化的计算

Average pooling

• 每个区域取平均得到输出
• 最大池化比平均池化更常用

Neural network example

识别数字

• f=2,s=2$f=2,s=2$ 使输入的高和宽减少一半

• 两类卷积的形式

  一个卷积层和一个池化层一起作为一层；或者分为单独的两层

• 一般计算网络层数时，只看具有权重的层

• 池化后的结果和全连接层的单元作笛卡尔连接？？

• not to invent your own settings of hyper parameters, but to look in the literature

• 随着层数的增加，高度和宽度都会减少，信道数会增加

• 
  

Why convolution

• parameter sharing (参数共享) and sparsity of connections (稀疏连接)
• feature detector (特征检测器) 适用于整张图片
• 某一个输出之和一部分输入相关
• good at capturing translation invariance (捕捉平移不变)
• 即使移动几个像素，图片依然具有与原图相似的特征