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Enabling Homomorphic Analytical Operations on Compressed Scientific Data with Multi-stage Decompression

Xuan Wu, Sheng Di, Tripti Agarwal, Kai Zhao, Xin Liang, Franck Cappello

Abstract

Error-controlled lossy compressors have been widely used in scientific applications to reduce the unprecedented size of scientific data while keeping data distortion within a user-specified threshold. While they significantly mitigate the pressure for data storage and transmission, they prolong the time to access the data because decompression is required to transform the binary compressed data into meaningful floating-point numbers. This incurs noticeable overhead for common analytical operations on scientific data that extract or derive useful information, because the time cost of the operations could be much lower than that of decompression. In this work, we design an error-controlled lossy compression and analytical framework that features multi-stage decompression and homomorphic analytical operation algorithms on intermediate decompressed data for reduced data access latency. Our contributions are threefold. (1) We abstract a generic compression pipeline with partial decompression to multiple intermediate data representations and implement four instances based on state-of-the-art high-throughput scientific data compressors. (2) We carefully design homomorphic algorithms to enable direct operations on intermediate decompressed data for three types of analytical operations on scientific data. (3) We evaluate our approach using five real-world scientific datasets. Experimental evaluations demonstrate that our method achieves significant speedups when performing analytical operations on compressed scientific data across all three targeted analytical operation types.

Enabling Homomorphic Analytical Operations on Compressed Scientific Data with Multi-stage Decompression

Abstract

Error-controlled lossy compressors have been widely used in scientific applications to reduce the unprecedented size of scientific data while keeping data distortion within a user-specified threshold. While they significantly mitigate the pressure for data storage and transmission, they prolong the time to access the data because decompression is required to transform the binary compressed data into meaningful floating-point numbers. This incurs noticeable overhead for common analytical operations on scientific data that extract or derive useful information, because the time cost of the operations could be much lower than that of decompression. In this work, we design an error-controlled lossy compression and analytical framework that features multi-stage decompression and homomorphic analytical operation algorithms on intermediate decompressed data for reduced data access latency. Our contributions are threefold. (1) We abstract a generic compression pipeline with partial decompression to multiple intermediate data representations and implement four instances based on state-of-the-art high-throughput scientific data compressors. (2) We carefully design homomorphic algorithms to enable direct operations on intermediate decompressed data for three types of analytical operations on scientific data. (3) We evaluate our approach using five real-world scientific datasets. Experimental evaluations demonstrate that our method achieves significant speedups when performing analytical operations on compressed scientific data across all three targeted analytical operation types.

Paper Structure

This paper contains 42 sections, 14 equations, 11 figures, 5 tables, 4 algorithms.

Table of Contents

  1. introduction
  2. related work
  3. Error-controlled Lossy Compressors
  4. Homomorphic Compression
  5. Problem Formulation and Overview
  6. Objective
  7. Target Operations on Scientific Data
  8. Statistical computation
  9. Numerical differentiation
  10. Multivariate derivation
  11. Design Overview
  12. Error-controlled Compression with Partial Decompression
  13. Homomorphic analytical operation
  14. Statistical Computation
  15. Mean
  16. ...and 27 more sections

Figures (11)

  • Figure 1: Overview of HSZ compression and homomorphic analytical operation pipelines. $D_m$ (metadata), $D_p$ (decorrelated data), $D_q$ (quantized data), $D_f$ (fully decompressed data) represent intermediate data representations in different decompression stages.
  • Figure 2: Compression ratios of homomorphic compressors and baselines.
  • Figure 3: Decompression throughput of 1D compressors.
  • Figure 5: Throughput of computing mean (1D).
  • Figure 7: Throughput of computing standard deviation (1D).
  • ...and 6 more figures