Accelerated Independent Component Analysis Using Generalized Logarithm

使用广义对数加速独立分量分析

• 批准号: 13680465
• 负责人: MATSUYAMA Yasuo
• 金额: $ 2.24万
• 依托单位: Waseda University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2001
• 资助国家: 日本
• 起止时间: 2001 至 2002
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13680465/
• 关键词: independent component analysis; convex divergence; momentum; functional magnetic resonance imaging; brain functional map; fast algorithm; f-ICA; fMRI; 脳機能解析

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.

独立分量分析 (ICA) 是一种估计生成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。该度量是广义对数的来源。所获得的算法被命名为f-ICA。 f-ICA 包含作为特殊情况的最小互信息 ICA。 f-ICA 可以实现为（a）添加先前增量的动量方法，以及（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几倍，但代价是增加一些额外的内存。因此，该项目的第一部分通过提供加速 ICA 算法和与广义对数相关的统计度量的新特性而取得了成功。除了理论的复杂性之外，该项目还成功获得了以下实验结果：（i）任何ICA算法，排列不确定性都是不可避免的。用户有义务在算法收敛后检查每个独立分量。研究人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，最重要的组件总是出现在第一个。（ii）创建了一个软件系统，该系统超出了实验室级别，即更一般的用户级别。（iii）通过使用上述软件系统，人类成功获取大脑功能图； (a) 运动图像识别的主要区域（背枕皮质），以及 (b) 视觉区域的 V1 和 V2 区域的分离。

项目成果

Y.Matsuyama, N.Katsumata, R.Kawamura: "Optimization transfer using convex divergence : f-ICA and alpha-EM algorithm with examples"Proc. Int. Symp. on Information Theory and Its Applications. 2. 667-670 (2002)

Y.Matsuyama、N.Katsumata、R.Kawamura：“使用凸散度的优化传输：f-ICA 和 alpha-EM 算法示例”Proc。

Y.Matsuyama, S.Imahara, N.Katsumata: "Optimization transfer for computational learning : A hierarchy from f-ICA and alpha-EM to their off springs"Proc. Int. Joint Conf. on Neural Networks. 3. 1883-1888 (2002)

Y.Matsuyama、S.Imahara、N.Katsumata：“计算学习的优化迁移：从 f-ICA 和 alpha-EM 到其后代的层次结构”Proc。

Y.Matsuyama, N.Katsumata, S.Imahara: "Independent component analysis using convex divergence"Proc. Int. Conf. on Neural Networks. 3. 1173-1178 (2001)

Y.Matsuyama、N.Katsumata、S.Imahara：“使用凸散度的独立成分分析”Proc。

Y.Matsuyama et al.: "Independent component analysis using convex divergence"Proc. Int. Conf. on Neural Information Processing. 3. 1173-1178 (2001)

Y.Matsuyama 等人：“使用凸散度的独立成分分析”Proc。

Y. Matsuyama, N. Katsumata and R. Kawamura: "Optimization transfer using convex divergence: f-ICA and alpha-EM with examples"Proc. Int. Symp. on Information Theory and Its Applications. Vol. 2. 667-670 (2002)

Y. Matsuyama、N. Katsumata 和 R. Kawamura：“使用凸散度的优化传递：f-ICA 和 alpha-EM 示例”Proc。