(This is a work in progress. Feedback is welcome) An analytical comparison is made between slow feature analysis (SFA) and the successor representation (SR). While SFA and the 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, multiple variants of the SFA algorithm are explored analytically and then applied to the setting of an MDP, leading to a family of eigenvalue problems involving the SR and other related quantities. These resulting eigenvalue problems are then illustrated in the toy setting of a gridworld, where it is demonstrated that the place- and grid-like fields often associated to the SR can equally be generated using SFA.

本研究针对慢特征分析与后继表示之间的关系进行了详细比较，揭示了它们在数学特性及信息敏感性方面的相似性。研究结果表明，多种慢特征分析算法的变体可以在马尔可夫决策过程（MDP）中应用，并构建出一系列与后继表示相关的特征值问题，进一步展示了慢特征分析能够生成与后继表示相似的空间字段。