Correlated Topographic Analysis : Estimating an Ordering of Correlated Components
Correlated Topographic Analysis : Estimating an Ordering of Correlated Components
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相关拓扑分析：估计相关组件的排序
DOI：
10.1007/s10994-013-5351-x
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发表时间：
2013
期刊：
影响因子：
7.5
通讯作者：
Hayaru Shouno and Aapo Hyvärinen
中科院分区：
文献类型：
--
作者：
Hiroaki Sasaki;Michael U. Gutmann;Hayaru Shouno and Aapo Hyvärinen
本文介绍了一种新的方法，我们称之为相关地形分析（CTA），估计非高斯成分和它们的顺序（地形）。该方法的灵感来自最近的独立分量分析（伊卡）的变种，即，利用伊卡不能删除的残留统计依赖的一个中心动机。我们假设附近的地形安排的组件具有线性和能量的相关性，而遥远的组件是统计独立的。我们使用这些依赖关系来固定组件的顺序。我们首先提出的组件的生成模型。然后，我们推导出一个近似的可能性模型的基础上。此外，由于梯度方法往往陷入局部最优，我们提出了一个三步优化方法，显着提高地形估计。使用模拟数据，我们表明，CTA估计排序的组件和概括以前的方法在地形估计。最后，为了证明CTA的广泛适用性，我们学习了三种真实的数据的地形表示：自然图像，模拟复杂细胞的输出和文本数据。
This paper describes a novel method, which we call correlated topographic analysis (CTA), to estimate non-Gaussian components and their ordering (topography). The method is inspired by a central motivation of recent variants of independent component analysis (ICA), namely, to make use of the residual statistical dependency which ICA cannot remove. We assume that components nearby on the topographic arrangement have both linear and energy correlations, while far-away components are statistically independent. We use these dependencies to fix the ordering of the components. We start by proposing the generative model for the components. Then, we derive an approximation of the likelihood based on the model. Furthermore, since gradient methods tend to get stuck in local optima, we propose a three-step optimization method which dramatically improves topographic estimation. Using simulated data, we show that CTA estimates an ordering of the components and generalizes a previous method in terms of topography estimation. Finally, to demonstrate that CTA is widely applicable, we learn topographic representations for three kinds of real data: natural images, outputs of simulated complex cells and text data.