ATC: an Advanced Tucker Compression library for multidimensional data

We present ATC, a C++ library for advanced Tucker-based compression of multidimensional numerical data, based on the sequentially truncated higher-order singular value decomposition (ST-HOSVD) and bit plane truncation. Several techniques are proposed to improve compression rate, speed, memory usage and error control. First, a hybrid truncation scheme is described which combines Tucker rank truncation and TTHRESH quantization [Ballester-Ripoll et al., IEEE Trans. Visual. Comput. Graph., 2020]. We derive a novel expression to approximate the error of truncated Tucker decompositions in the case of core and factor perturbations. Furthermore, a Householder-reflector-based approach is proposed to compress the orthogonal Tucker factors. Certain key improvements to the quantization procedure are also discussed. Moreover, particular implementation aspects are described, such as ST-HOSVD procedure using only a single transposition. We also discuss several usability features of ATC, including the presence of multiple interfaces, extensive data type support and integrated downsampling of the decompressed data. Numerical results show that ATC maintains state-of-the-art Tucker compression rates, while providing average speed-ups of 2.6-3.6 and halving memory usage. Furthermore, our compressor provides precise error control, only deviating 1.4% from the requested error on average. Finally, ATC often achieves significantly higher compression than non-Tucker-based compressors in the high-error domain.