Topographic Analysis of Correlated Components
Topographic Analysis of Correlated Components
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发表时间：
2012-11
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通讯作者：
Hiroaki Sasaki;Michael U Gutmann;Hayaru Shouno;Aapo Hyvärinen
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作者：
Hiroaki Sasaki;Michael U Gutmann;Hayaru Shouno;Aapo Hyvärinen
独立成分分析 (ICA) 是一种估计尽可能在统计上独立的成分的方法。然而，在许多实际应用中，估计的分量不是独立的。 ICA 的最新变体已经利用此类剩余依赖性来估计组件的排序（拓扑）。与 ICA 一样，这些变体中的组件被假定为不相关，这可能是一个相当严格的条件。在本文中，我们解决了这个缺点。我们提出了一种源生成模型，其中组件可以具有线性和高阶相关性，它概括了迄今为止使用的模型。基于该模型，我们推导出一种估计地形表示的方法。在人工数据的数值实验中，新方法被证明比之前提出的 ICA 扩展具有更广泛的适用性。我们学习两种真实数据集的地形表示：初级视觉皮层中模拟复杂细胞的输出和文本数据。
Independent component analysis (ICA) is a method to estimate components which are as statistically independent as possible. However, in many practical applications, the estimated components are not independent. Recent variants of ICA have made use of such residual dependencies to estimate an ordering (topography) of the components. Like in ICA, the components in those variants are assumed to be uncorrelated, which might be a rather strict condition. In this paper, we address this shortcoming. We propose a generative model for the source where the components can have linear and higher order correlations, which generalizes models in use so far. Based on the model, we derive a method to estimate topographic representations. In numerical experiments on articial data, the new method is shown to be more widely applicable than previously proposed extensions of ICA. We learn topographic representations for two kinds of real data sets: for outputs of simulated complex cells in the primary visual cortex and for text data.