Principal Component Analysis (PCA) is a widely popular technique for reducing the dimensionality of a dataset. Interestingly, when dimensions of the dataset grow too large, existing state-of-the-art methods for PCA face scalability issue due to the explosion of intermediate data. Moreover, in a geographically distributed environment where most of today's data are originally generated, these methods require unnecessary data transmissions as they apply centralized algorithms for PCA and thus are proven to be inefficient. To solve these problems, we take advantage of the zero-noise-limit Probabilistic PCA model, which provably outputs the correct principal components, and introduce a block-division method for it in order to suppress the explosion of intermediate data efficiently. We employ several optimization ideas such as mean propagation for preserving sparsity, dynamic tuning of the number of blocks to automatically adjust to large dimensions, etc. Additionally, in the geo-distributed environment, we propose a communication efficient solution by reducing idle time, passing only the required parameters, and choosing geographically ideal central datacenter for faster accumulation. We refer to our algorithm as TallnWide. Our empirical evaluation with real datasets shows that TallnWide can successfully handle significantly higher dimensional data (10x) than existing methods, and offer up to 2.9x improvement in running time in the geo-distributed environment compared to the conventional approaches. For reproducibility and extensibility of our work, we make the source code of TallnWide publicly available at https://github.com/tmadnan10/TallnWide. (C) 2021 Elsevier Ltd. All rights reserved.
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