ICA与PCA的区别在于：ICA要求找到最大独立的方向，各个成分是独立的；PCA要求找到最大方差的方向，各个成分是正交的。

 常用的ICA算法有一下几种，如图中所示：

常用的ICA工具包如下图所示：

 

X=AS ，u=WX

Infomax（Information Maximum）介绍：

• Proposed by Linsker in 1992
• Popularized by Bell & Sejnowski in 1995
• First applied to fMRI data in 1998
• Promising performance on a number of BSS

Properties
• Intuitively meaningful contrast function (mutual information)
• Typically provides a simple learning rule
• Choice of nonlinearity is required
• Used on majority of fMRI applications

x = input, y = g(w, x) = output, u=wx

Infomax算法中存在一个学习率，使得W不断更新，最后输入x和输出y之间的互信息最大。

Negentropy/Kurtosis
• Assumes non-Gaussian sources
• Motivated by central limit theorem, the mixtures will be (more) Gaussian
• The independent components are calculated by maximizing the KL divergence between the output
pdfs and a Gaussian pdf.
• Negentropy is always non-negative and is zero only if the variable is Gaussian.
 

GroupICA介绍：

Group ICA can be broken up into 6 stages.
• Preprocessing
Same Preprocessing that you normally do in SPM. Realignment, motion correction, co-registration, etc.
• Data Reduction
 Implemented using PCA.
• ICA Separation
Implemented using any ICA algorithm( Infomax, Optimal ICA, FastICA).
• Back Reconstruction
Individual Subject Components are back reconstructed using the results from PCA.
• Component calibration

including 1) scaling and 2) sign change Using the functional data the components, time courses and spatial maps, are converted from arbitrary units to percent signal change.
• Group Statistics
Using the subject's back reconstructed components statistics are calculated.

GroupICA公式解析如下：

  For Subject i（the first reduction）

(L×V=L×K K×V )

V: the number of voxels;

K: the number of fMRI time points;

L: the time dimension after first reduction

 For M subjects:X is the group fMRI data after second reduction (N×V)

转载本文请联系原作者获取授权，同时请注明本文来自张高燕科学网博客。
链接地址：https://blog.sciencenet.cn/blog-479412-391808.html

上一篇：方差分析（ANOVA）
下一篇：两幅图像的相关系数