Accelerated Independent Component Analysis Using Generalized Logarithm

独立分量分析(ICA)是一种估计产生观测信号的未知独立分量的方法。在本研究中，选择凸离散度作为独立性的表现标准。这个度量是广义对数的来源。所得到的算法称为f-ICA。作为特例，f-ICA包含最小互信息ICA。F-ICA可以被实现为(A)添加先前增量的动量方法，和(B)添加估计的未来增量的前瞻方法。这两种方法的速度都比最小互信息方法快好几倍，但只需增加几个内存。因此，通过给出加速ICA算法和与广义对数相关的统计度量的新性质，本项目的第一部分是成功的。除了理论上的复杂性，本项目还成功地获得了以下实验结果：(I)在任何ICA算法中，置换不确定性都是不可避免的。在算法收敛后，用户有义务检查每个独立分量。调查员提出了一种将先验知识作为正则化项注入的方法。通过这种方法，最重要的部分总是出现在第一个。(Ii)创建了一个软件系统，它超出了实验室级别，即更一般的用户级别。(Iii)通过使用上述软件系统，成功地获得了人脑的功能图：(A)运动图像识别的主要区域(枕背皮质)，以及(B)视觉区域的V1和V2区域的分离。

Independent Component Analysis (ICA) is a method to estimate unknown independent components which generate observed signals. In this research, the convex divergence was selected as the performance criterion for the independence. This measure is the source of the generalized logarithm. The obtained algorithm is named the f-ICA. The f-ICA contains the minimum mutual information ICA as a special case. The f-ICA can be realized as (a) the momentum method which adds the previous increment, and (b) the look-ahead method which adds the estimated future increment. Both methods show several times faster speed than the minimum mutual information method at the cost of a few additional memory. Thus, the first part of this project was successful by giving the accelerated ICA algorithm and novel properties of statistical measures related to the generalized logarithm.In addition to the theoretical sophistication, the following experimental results are successfully obtained in this project:(i) In any ICA algorithms, permutation indeterminacy is unavoidable. Users are obliged to check every independent component after the convergence of the algorithm. The investigator presented a way to inject prior knowledge as a regularization term. By this method, the most important component always appears as the first one.(ii) A software system was created, which is beyond a laboratory level, i.e., a more general user level.(iii) By using the above software system, human brain's functional maps are successfully obtained; (a) the main area of moving image recognition (dorsal occipital cortex), and (b) a separation of V1 and V2 regions of visual areas.