  An appearance-based robot self-localization problem is considered in the
machine learning framework. The appearance space is composed of all possible
images, which can be captured by a robot's visual system under all robot
localizations. Using recent manifold learning and deep learning techniques, we
propose a new geometrically motivated solution based on training data
consisting of a finite set of images captured in known locations of the robot.
The solution includes estimation of the robot localization mapping from the
appearance space to the robot localization space, as well as estimation of the
inverse mapping for modeling visual image features. The latter allows solving
the robot localization problem as the Kalman filtering problem.
