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.

独立的组件分析（ICA）是一种估计产生观察到的信号的未知独立组件的方法。在这项研究中，凸差被选为独立性的绩效标准。该度量是广义对数的来源。获得的算法称为F-KIA。 F-ICA包含最小共同信息ICA作为特殊情况。 F-A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look-aead方法。两种方法显示的速度比最小共同信息方法的速度快几倍，而成本是额外的内存。因此，该项目的第一部分通过给出与广义对数有关的统计措施的加速ICA算法和新的特性，在理论复杂性的增加中，在此项目中成功获得了以下实验结果：（i）在任何ICA算法，置换不确定性不可行。在算法收敛之后，用户必须检查每个独立组件。研究人员提出了一种将先验知识作为正规化项注入的方法。通过这种方法，最重要的组件始终显示为第一个。（ii）创建了软件系统，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，成功获得了人脑的功能图； （a）运动图像识别的主要区域（背枕皮层），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。