This paper proposes a new map building framework for mobile robot named Localization-Free Mapping by Dimensionality Reduction (LFMDR). In this framework, the robot map building is interpreted as a problem of reconstructing the 2-D coordinates of ob jects so that they maximally preserve the local proximity of the ob jects in the space of robot's observation history. Not only traditional linear PCA but also recent manifold learning techniques can be used for solving this problem. In contrast to the SLAM framework, LFMDR framework does not require localization procedures nor explicit measurement and motion models. In the latter part of this paper, we will demonstrate "visibility-only" and "bearing-only" localization-free mappings which are derived by applying LFMDR framework to the visibility and bearing measurements respectively.