Learning Visual Spatial Pooling by Strong PCA Dimension Reduction
Learning Visual Spatial Pooling by Strong PCA Dimension Reduction
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DOI：
10.1162/neco_a_00843
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发表时间：
2016-07-01
影响因子：
2.9
通讯作者：
Hyvarinen, Aapo
中科院分区：
文献类型：
--
作者：
Hosoya, Haruo;Hyvarinen, Aapo
在视觉建模中，视觉细胞的不变性通常用池化机制来解释，其中对某些刺激参数具有相似选择性的神经元的输出被整合，以获得对其他参数的一定程度的不变性。例如，相位不变 V1 复杂细胞池的经典能量模型对偏好相似方向但不同相位的简单细胞进行建模。先前的研究，例如独立子空间分析，已经表明 V1 复杂单元的相位不变特性可以从自然输入的空间统计中学习。然而，以前的方法假设神经输出具有平方非线性来捕获能量相关性；从神经生物学的角度来看，这种非线性可以说是不自然的，但由于它与形式主义的紧密结合而很难改变。此外，他们使用了一些复杂的目标函数，需要昂贵的计算来进行优化。在这项研究中，我们表明可以使用基于主成分分析的强降维以更简单的方式学习视觉空间池。这种方法学会忽略输入的大部分详细空间结构，从而估计线性池矩阵。使用这个框架，我们证明了以这种方式学习的模型 V1 简单单元的池化，即使具有平方以外的非线性，也可以重现 V1 复杂单元的标准调谐特性。为了进一步理解，我们分析了池化模型的几种变体，并认为合理的池化通常可以从任何类型的保留几个第一主成分并抑制其余主成分的线性变换中获得。特别是，我们展示了经典的维纳滤波理论如何导致这样一种变体。
In visual modeling, invariance properties of visual cells are often explained by a pooling mechanism, in which outputs of neurons with similar selectivities to some stimulus parameters are integrated so as to gain some extent of invariance to other parameters. For example, the classical energy model of phase-invariant V1 complex cells pools model simple cells preferring similar orientation but different phases. Prior studies, such as independent subspace analysis, have shown that phase-invariance properties of V1 complex cells can be learned from spatial statistics of natural inputs. However, those previous approaches assumed a squaring nonlinearity on the neural outputs to capture energy correlation; such nonlinearity is arguably unnatural from a neurobiological viewpoint but hard to change due to its tight integration into their formalisms. Moreover, they used somewhat complicated objective functions requiring expensive computations for optimization. In this study, we show that visual spatial pooling can be learned in a much simpler way using strong dimension reduction based on principal component analysis. This approach learns to ignore a large part of detailed spatial structure of the input and thereby estimates a linear pooling matrix. Using this framework, we demonstrate that pooling of model V1 simple cells learned in this way, even with nonlinearities other than squaring, can reproduce standard tuning properties of V1 complex cells. For further understanding, we analyze several variants of the pooling model and argue that a reasonable pooling can generally be obtained from any kind of linear transformation that retains several of the first principal components and suppresses the remaining ones. In particular, we show how the classic Wiener filtering theory leads to one such variant.