线性子空间学习的Hebbian/Anti-Hebbian神经网络：流数据多维尺度的推导
A Hebbian/Anti-Hebbian Neural Network for Linear Subspace Learning: A Derivation from Multidimensional Scaling of Streaming Data
摘要：
早期感觉处理的神经网络模型通常减少流输入数据的维度。这样的网络学习主子空间，在主成分分析（PCA）的意义上，通过调整突触权重根据活动相关的学习规则。当从原则成本函数导出时，这些规则是非局部的，因此在生物学上是不可信的。与此同时，生物学上合理的本地规则已被假定，而不是来自一个原则性的成本函数。在这里，为了弥合这一差距，我们通过最小化原则成本函数，推导出一个在流数据上进行子空间学习的生物学上合理的网络。在偏离以前的工作，其中成本量化的表示，或重建，错误，我们采用了多维尺度（MDS）的成本函数流数据。由此产生的算法只依赖于生物学上合理的赫布和反赫布的本地学习规则。在随机设置中，突触权重收敛到将输入数据投影到主子空间上的稳态。如果数据由非平稳分布生成，则网络可以跟踪主子空间。因此，我们的结果使一个算法理论的神经计算的一步。
英文摘要：
Neural network models of early sensory processing typically reduce the dimensionality of streaming input data. Such networks learn the principal subspace, in the sense of principal component analysis (PCA), by adjusting synaptic weights according to activity-dependent learning rules. When derived from a principled cost function these rules are nonlocal and hence biologically implausible. At the same time, biologically plausible local rules have been postulated rather than derived from a principled cost function. Here, to bridge this gap, we derive a biologically plausible network for subspace learning on streaming data by minimizing a principled cost function. In a departure from previous work, where cost was quantified by the representation, or reconstruction, error, we adopt a multidimensional scaling (MDS) cost function for streaming data. The resulting algorithm relies only on biologically plausible Hebbian and anti-Hebbian local learning rules. In a stochastic setting, synaptic weights converge to a stationary state which projects the input data onto the principal subspace. If the data are generated by a nonstationary distribution, the network can track the principal subspace. Thus, our result makes a step towards an algorithmic theory of neural computation.
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