【计算神经科学冒险者们】2.3 神经编码：特征选择(Neural Encoding：Feature Selection)
Today's Task：How to find the components of this model
1 选取特征Feature
1.1 How to proceed?
Our problem is one of dimensionality!
For instance, in the case of the movie we showed the retina, we can define a movie in terms of the intensity of three colors in every pixel in one megapixel image.
1.2 Dimensionality reduction
Start with a very high dimensional description(e.g. an image or a time-varying waveform) and pick out a small set of relevant dimensions.
s(t)----dicretize------>s(k)
采样系统对于不同的刺激的响应，我们可以识别是什么输入触发响应。
1.3 What is the right stimulus to use?
We want to sample the responses of the system to a variety of stimuli so we can characterize what it is about the input that triggers responses.
One common and useful method is to use Gaussian white noise.
1.4 Determining multiple features from white noise
这里只要了解spike-trigger 平均值这个概念，就是把数据整合起来，得到一条类似于高斯函数的曲线，峰值对应的横坐标表示的值。
1.5 Reverse correlation: the spike-triggered average 反相关系数：尖峰平均值
横坐标上表示的是一个响应spike，我们提取从开始刺激到产生响应的时间，取它们的平均值，得到一条噪声较少的曲线。
每列值都是一个图像，这里包括时间维度和空间维度。
1.6 Linear filtering
Stimulus feature f is a vector in a high-dimensional stimulus space
线性过滤器，相当于卷积，也相当于投影。我们有一个刺激s（方向与t3相同），投影到f上s·f（？？？）
2 Determining the nonlinear input/output function
The input/output function is:
This can be found from data using Bayes' rule:
P（s1）是一个高斯曲线
Nonlinear input/output function
2.1 Linear/nonlinear models
3 High-dimensional feature selection
Less basc coding models
有多个过滤，选择多个特征。core detector neuron 每个对不同的频率的过滤。
Determining multiple feature from white noise
How could we find features？
3.1 Principal component analysis
PCA's job is to find low dimengtional structure of a cloud of points.
compression.
PCA: eigenfaces
common stracture, may be restructive by little number of photos
PCA: spike sorting
PCA gives us a method to:
1. Find a representation of our data which has lower dimensionality, giving us a computationallyeasier problem to work with.
2. Find the vectors along which the variation of our data is maximal in our feature space.
4 Finding interesting features in the retina
right group——on
left group——off
这节听得很蒙蔽啊，还是找本教科书看看吧
