This paper introduces a novel mapping and localization framework for mobile robots named ”co-embedding”, partly inspired by human cognitive mapping process. In this method, the spatial relationship among objects (i.e., map) and robot's trajectory are reconstructed in a bottom-up way by embedding the high-dimensional observation data into a low-dimensional space with a set of locally linear transformations. Our method is much different from the traditional SLAM approach in that it does not require motion and sensor models in advance. Compared with other mapping and localization methods based on dimensionality reduction, ours has some remarkable features such as the capability of dealing with largely missing data, and semi-supervised learning formulation to utilize prior spatial information. We evaluated the effectiveness of the proposed method by simulation and experiment.