Euclidean embedding algorithms transform data defined in an arbitrary metric space to the Euclidean space, which is critical to many visualization techniques. At big-data scale, these algorithms need to be scalable to massive dataparallel infrastructures. Designing such scalable algorithms and understanding the factors affecting the algorithms are important research problems for visually analyzing big data. We propose a framework that extends the existing Euclidean embedding algorithms to scalable ones. Specifically, it decomposes an existing algorithm into naturally parallel components and non-parallelizable components. Then, data parallel implementations such as MapReduce and data reduction techniques are applied to the two categories of components, respectively. We show that this can be possibly done for a collection of embedding algorithms. Extensive experiments are conducted to understand the important factors in these scalable algorithms: scalability, time cost, and the effect of data reduction to result quality. The result on sample algorithms: FastMap-MR and LMDS-MR shows that with the proposed approach the derived algorithms can preserve result quality well, while achieving desirable scalability.
Alavi, Z. S.,
& Chen, K.
(2015). Scalable Euclidean Embedding for Big Data. .