揭示慢特征分析与后继表示的数学等价性及其空间表征特性
What is the relation between Slow Feature Analysis and the Successor Representation?
- 通过解析推导建立SFA与SR在马尔可夫决策过程中的形式等价关系
- 在独热编码MDP中，二者均生成网格状表征，其解为对应的特征向量
- SFA矩阵列呈现类位置细胞表征，但不同于已有基于SFA的位置模型
慢特征分析（SFA）是一种从时间序列数据中提取表征的无监督方法。后继表示（SR）是一种基于转移统计的马尔可夫决策过程（MDP）状态表示方法。尽管SFA与SR源自机器学习不同领域，但在数学性质和对信息的敏感度方面具有重要共性。本文从数学与信息敏感性两个维度探讨二者的关联。特别地，在独热编码的MDP设置下，通过解析分析证明了二者在网格状表征作为解/特征向量方面的形式等价性。此外，研究表明SFA矩阵的列包含类位置表征，其形式上不同于已有的基于SFA的位置细胞模型。
原文摘要 · Abstract (English)
Slow feature analysis (SFA) is an unsupervised method for extracting representations from time series data. The successor representation (SR) is a method for representing states in a Markov decision process (MDP) based on transition statistics. While SFA and SR stem from distinct areas of machine learning, they share important properties, both in terms of their mathematics and the types of information they are sensitive to. This work studies their connection along these two axes. In particular, both SFA and SR are explored analytically, and in the setting of a one-hot encoded MDP, a formal equivalence is demonstrated in terms of the grid-like representations that occur as solutions/eigenvectors. Moreover, it is shown that the columns of the matrices involved in SFA contain place-like representations, which are formally distinct from place-cell models that have already been defined using SFA.
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