Robot learning, such as reinforcement learning, generally needs a well-defined state space in order to converge. However, building such a state space is one of the main issues of robot learning because of the interdependence between state and action spaces, which resembles the well-known "chicken and egg" problem. This article proposes a method of action-based state space construction for vision-based mobile robots. Basic ideas to cope with the interdependence are that we define a state as a cluster of input vectors from which the robot can reach the goal state or the state already obtained by a sequence of one kind of action primitive regardless of its length, and that this sequence is defined as one action. To realize these ideas, we need many data (experiences) of the robot and we must cluster the input vectors as hyper ellipsoids so that the whole state space is segmented into a state transition map in terms of action from which the optimal action sequence is obtained. To show the validity of the method, we apply it to a soccer robot that tries to shoot a ball into a goal. The simulation and real experiments are shown.