High-dimensional sparse data emerge in many critical application domains such as cybersecurity, healthcare, anomaly detection, and trend analysis. To quickly extract meaningful insights from massive volumes of these multi-dimensional data, scientists employ unsupervised analysis tools based on tensor decomposition (TD) methods. However, real-world sparse tensors exhibit highly irregular shapes, data distributions, and sparsity, which pose significant challenges for making efficient use of modern parallel architectures. This study breaks the prevailing assumption that compressing sparse tensors into coarse-grained structures (i.e., tensor slices or blocks) or along a particular dimension/mode (i.e., mode-specific) is more efficient than keeping them in a fine-grained, mode-agnostic form. Our novel sparse tensor representation, Adaptive Linearized Tensor Order (ALTO), encodes tensors in a compact format that can be easily streamed from memory and is amenable to both caching and parallel execution. To demonstrate the efficacy of ALTO, we accelerate popular TD methods that compute the Canonical Polyadic Decomposition (CPD) model across a range of real-world sparse tensors. Additionally, we characterize the major execution bottlenecks of TD methods on multiple generations of the latest Intel Xeon Scalable processors, including Sapphire Rapids CPUs, and introduce dynamic adaptation heuristics to automatically select the best algorithm based on the sparse tensor characteristics. Across a diverse set of real-world data sets, ALTO outperforms the state-of-the-art approaches, achieving more than an order-of-magnitude speedup over the best mode-agnostic formats. Compared to the best mode-specific formats, which require multiple tensor copies, ALTO achieves more than 5.1x geometric mean speedup at a fraction (25%) of their storage.

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