This paper proposes a data collaboration analysis framework for distributed data sets. The proposed framework involves centralized machine learning while the original data sets and models remain distributed over a number of institutions. Recently, data has become larger and more distributed with decreasing costs of data collection. Centralizing distributed data sets and analyzing them as one data set can allow for novel insights and attainment of higher prediction performance than that of analyzing distributed data sets individually. However, it is generally difficult to centralize the original data sets because of a large data size or privacy concerns. This paper proposes a data collaboration analysis framework that does not involve sharing the original data sets to circumvent these difficulties. The proposed framework only centralizes intermediate representations constructed individually rather than the original data set. The proposed framework does not use privacy-preserving computations or model centralization. In addition, this paper proposes a practical algorithm within the framework. Numerical experiments reveal that the proposed method achieves higher recognition performance for artificial and real-world problems than individual analysis.