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，选择凸散度作为独立性的性能标准。这个测度是广义对数的来源。得到的算法命名为f-ICA。作为特例，f-ICA包含最小互信息ICA。f-ICA可以实现为(a)动量法（增加先前的增量）和(b)前瞻法（增加估计的未来增量）。这两种方法的速度都比最小互信息方法快几倍，而代价是增加一些内存。因此，这个项目的第一部分是成功的，给出了加速的ICA算法和与广义对数相关的统计度量的新特性。除了理论上的复杂性外，本项目还成功获得了以下实验结果：(i)在任何ICA算法中，排列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的组件。研究者提出了一种注入先验知识作为正则化项的方法。通过这种方法，最重要的组件总是作为第一个出现。创建了一个软件系统，它超出了实验室一级，即更一般的用户一级。（iii）利用上述软件系统，成功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），(b)视觉区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.