Visualizing global manifold based on distributed local data abstractions

Mining distributed data for global knowledge is getting more attention recently. The problem is especially challenging when data sharing is prohibited due to local constraints like limited bandwidth and data privacy. In this paper, we investigate how to derive the embedded manifold (as a 2-D map) for a horizontally partitioned data set, where data cannot be shared among the partitions directly. We propose a model-based approach which computes hierarchical local data abstractions, aggregates the abstractions, and finally learns a global generative model - generative topographic mapping (GTM) based on the aggregated data abstraction. We applied the proposed method to two benchmarking data sets and demonstrated that the accuracy of the derived manifold can effectively be controlled by adjusting the data granularity level of the adopted local abstraction.