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Extended Predictable Feature Analysis (PFAx) [Richthofer and Wiskott, 2017]is an extension of PFA [Richthofer and Wiskott, 2015] that allows generating agoal-directed control signal of an agent whose dynamics has previously beenlearned during a training phase in an unsupervised manner. PFAx hardly requiresassumptions or prior knowledge of the agent's sensor or control mechanics, orof the environment. It selects features from a high-dimensional input byintrinsic predictability and organizes them into a reasonably low-dimensionalmodel.  While PFA obtains a well predictable model, PFAx yields a model ideallysuited for manipulations with predictable outcome. This allows forgoal-directed manipulation of an agent and thus for local navigation, i.e. forreaching states where intermediate actions can be chosen by a permanent descentof distance to the goal. The approach is limited when it comes to globalnavigation, e.g. involving obstacles or multiple rooms.  In this article, we extend theoretical results from [Sprekeler and Wiskott,2008], enabling PFAx to perform stable global navigation. So far, the mostwidely exploited characteristic of Slow Feature Analysis (SFA) was thatslowness yields invariances. We focus on another fundamental characteristics ofslow signals: They tend to yield monotonicity and one significant property ofmonotonicity is that local optimization is sufficient to find a global optimum.  We present an SFA-based algorithm that structures an environment such thatnavigation tasks hierarchically decompose into subgoals. Each of these can beefficiently achieved by PFAx, yielding an overall global solution of the task.The algorithm needs to explore and process an environment only once and canthen perform all sorts of navigation tasks efficiently. We support thisalgorithm by mathematical theory and apply it to different problems.

Global Navigation Using Predictable and Slow Feature Analysis in Multiroom Environments, Path Planning and Other Control Tasks