93dd44areorganize datasets and algs, add seismicJeremy Magland 1# Benchmarking Compression Algorithms for Scientific Data Arrays
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3*Jeremy Magland, Center for Computational Mathematics, Flatiron Institute*
5*Last updated: January 2025*
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9## Abstract
3043dd2update paperJeremy Magland 11*Benchcompress* is a benchmarking framework designed to evaluate the performance of various compression algorithms on scientific data arrays, with a special focus on electrophysiology traces. The framework automates the benchmarking process, measuring compression ratio, encoding throughput, and decoding throughput for each algorithm-dataset pair. Results are verified through decompression and comparison with the original data, ensuring accuracy. The benchmark results are stored and visualized through an interactive web interface, allowing users to filter, sort, and explore the data. This paper presents the design, implementation, and preliminary results of Benchcompress, highlighting its utility in identifying optimal compression techniques for scientific datasets.
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13## Introduction
b124abdupdate paperJeremy Magland 15Scientific research often generates large volumes of data that must be stored, shared, and analyzed efficiently. In fields ranging from electrophysiology to climate modeling, these datasets can be enormous, making data compression essential for reducing file sizes, accelerating data transfer, and facilitating both short- and long-term storage. However, the specialized nature of numeric data arrays poses unique challenges that many general-purpose compression algorithms—often optimized for text, images, or video—do not address effectively.
3043dd2update paperJeremy Magland 17Many researchers remain wary of introducing any form of lossy compression to raw data collected from laboratory devices. Rather than experimenting with a wide range of lossy methods and analyzing their impact on scientific results, we adopt a more transparent strategy for lossy compression: apply well-defined, carefully documented transformations, such as quantization, filtering, or normalization, before evaluating the data with strictly lossless compression. For instance, floating-point data often contains bits beyond the precision actually needed, so it frequently compresses poorly unless a preliminary quantization step is used. By estimating the measurement resolution of the acquisition process, we can convert floating-point values to a suitably scaled integer representation, effectively removing these superfluous bits. This approach typically imposes negligible loss in subsequent analyses while significantly improving compressibility. Similarly, filtering (to focus on a specific band of frequencies) and normalization may further enhance compression while remaining straightforward to analyze.
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3043dd2update paperJeremy Magland 19Unlike these preprocessing transformations, some techniques are strictly reversible and should therefore be considered part of the lossless method, rather than part of the preprocessing. For example, delta encoding significantly reduces sample magnitudes in data drawn from continuous signals, improving compression ratios in most lossless compressors. Delta encoding plus a lossless method should then be viewed as a compound lossless technique. For datasets exhibiting even smoother behavior, a more powerful variant, which we will call linear Markov prediction, extends delta encoding to higher-order autoregressive models, often resulting in superior compression.
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3043dd2update paperJeremy Magland 21When assessing compression performance, it is important to consider not only final compression ratios but also how quickly data can be encoded and decoded. Unlike typical web delivery scenarios where data are compressed once and then decompressed repeatedly, scientific workflows may require efficient encoding because data are often compressed at the point of acquisition and then decompressed only once prior to archival. Moreover, scientific requirements vary widely, from long-term preservation to on-demand, cloud-based visualization. In some cases, significant data loss may be acceptable for a high-level overview, whereas in others, minimal alteration of raw measurements is paramount.
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23To help researchers navigate these questions, we introduce Benchcompress, a benchmarking framework designed to systematically evaluate and compare compression algorithms for numeric data arrays. By automating the testing and providing tools for analysis, Benchcompress simplifies the process of identifying which methods work best for particular datasets. In the sections that follow, we describe the system in detail, outline both standard and specialized compression strategies, and present preliminary results from our benchmarks.
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9450f68update paperJeremy Magland 27Traditional compression algorithms like LZW (Lempel-Ziv-Welch), LZ77, BWT (Burrows-Wheeler Transform), and Huffman coding were originally designed for text data where patterns manifest as repeated sequences of characters or words. While these methods can compress numeric data from scientific instruments, they may not be optimal for this use case. Text compression excels at identifying exact matches of recurring patterns, whereas scientific measurements often exhibit more complex relationships between values.
29For example, in text compression, finding repeated instances of common words or phrases leads to efficient encoding. In contrast, scientific data arrays often contain continuous variations where measurement noise and uncertainties mean exact repetition is rare. Even when numeric values are similar, their byte-level representations may share some common bits while differing in others. This characteristic of scientific data suggests that methods explicitly accounting for numerical relationships between values may achieve better compression ratios than general-purpose algorithms.
31## Independent identically distributed samples
33Moving from text to numeric data, we begin with the fundamental case of independently and identically distributed (i.i.d.) discrete data. For such data, where each sample is drawn from a discrete probability distribution (e.g., Bernoulli sampling or quantized Gaussian noise), the theoretical compressed size in bits per sample is determined by the Shannon entropy formula:
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36H(X) = -\sum_{i} p(x_i) \log_2 p(x_i).
37$$
39Here, $p(x_i)$ represents the probability of occurrence of the $i$-th symbol $x_i$ in the discrete distribution. So for example, if we have a Bernoulli distribution with $p=0.5$, the entropy is
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42H_{\text{Bernoulli, p=0.5}} = -0.5 \log_2 0.5 - 0.5 \log_2 0.5 = 1
43$$
0092283paper pageJeremy Magland 45bits per sample. This means that the optimal compression ratio for such a dataset is 8, assuming the samples are stored as 8-bit integers. On the other hand, if $p\neq 0.5$, the entropy becomes lower and we can achieve compression at a rate of less than 1 bit per sample (e.g., for $p=0.1$, the entropy is around 0.47 bits per sample, so the compression ratio would be around 17).
9450f68update paperJeremy Magland 49In practice, achieving this theoretical compression ratio requires sophisticated encoding techniques. Arithmetic coding [@witten1987arithmetic] is one such method, but it is challenging to implement and can be computationally inefficient. A more modern and efficient alternative is asymmetric numeral systems (ANS) [@duda2013asymmetric], which closely approaches the theoretical limit and is incorporated into state-of-the-art compressors such as ZStandard [@zstd]. However, these large, general-use packages are primarily optimized for structured data types, such as text, rather than for numeric scientific data. In our benchmarks, we evaluate ANS using a simple, no-frills, implementation using a Python package we developed for this purpose called `simple_ans`. As anticipated, we show that ANS demonstrates superior performance when compressing i.i.d. samples from a discrete distribution.
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3043dd2update paperJeremy Magland 53The efficiency of pure entropy coders (such as ANS) diminishes when handling more structured data, such as continuous signals (e.g., voltage traces in electrophysiology). Applying delta encoding partially mitigates this limitation by leveraging the continuity properties of the data through differencing. This reversible preprocessing step enhances ANS performance because the deltas are typically smaller than the original samples, leading to lower entropy when assuming independence between samples.
55## Linear Markov prediction
57Even with delta encoding for real or realistic datasets, ANS still can fall short of the compression achieved by methods like ZStandard. To improve its performance by further exploiting temporal correlations in the data, we consider a generalization of delta encoding which we call linear Markov predictive modeling. The Markov prediction scheme employs a linear autoregressive model where each sample is predicted as a linear combination of $M$ previous samples. For a given integer time series $x[t]$, the prediction $\hat{x}[t]$ is computed as:
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59$$
60\hat{x}[t] = \text{round}\left(\sum_{i=1}^M c_i x[t-i] + b\right)
61$$
63where the coefficients $c_i$ and bias term $b$ are determined through least squares regression on a subset of the data. The rounding operation ensures integer predictions. Rather than compressing the original signal directly, the algorithm compresses the integer residual error sequence $r[t] = x[t] - \hat{x}[t]$. This approach proves effective because the residuals typically have smaller magnitude compared with the original signal or with the deltas. The compression process stores three components: the floating-point model coefficients, a small set of initial integer values required to begin prediction, and the compressed integer residual sequence. During reconstruction, the original signal is recovered by computing predictions and adding back the residuals:
65$$
66x[t] = \text{round}\left(\sum_{i=1}^M c_i x[t-i] + b\right) + r[t]
67$$
69This predictive preprocessing step improves compression performance compared to applying ANS (or other algorithms) directly to either the raw signal or delta-encoded data.
73Describe the various compression methods.
77Describe the datasets we use for benchmarking.
79## Implementation
81[To be added]
83## Results
85[Preliminary results to be added]
87## Discussion
89[Discussion to be added]
91## Conclusion
93[Conclusion to be added]
95## References