Distributed data analysis without revealing the individual data has recently attracted significant attention in several applications. A collaborative data analysis through sharing dimensionality reduced representations of data has been proposed as a non-model sharing-type federated learning. This paper analyzes the accuracy and privacy evaluations of this novel framework. In the accuracy analysis, we provided sufficient conditions for the equivalence of the collaborative data analysis and the centralized analysis with dimensionality reduction. In the privacy analysis, we proved that collaborative users' private datasets are protected with a double privacy layer against insider and external attacking scenarios.