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.

翻译：高维稀疏数据出现在网络安全、医疗健康、异常检测和趋势分析等许多关键应用领域中。为了从海量多维数据中快速提取有意义的洞察，科学家们采用基于张量分解（TD）方法的无监督分析工具。然而，现实世界中的稀疏张量呈现出高度不规则的形状、数据分布和稀疏性，这给高效利用现代并行架构带来了重大挑战。本研究打破了将稀疏张量压缩为粗粒度结构（即张量切片或块）或沿特定维度/模式（即模式特定）比将其保持在细粒度、模式无关形式更高效的普遍假设。我们提出的新型稀疏张量表示方法——自适应线性化张量序（ALTO），将张量编码为紧凑格式，该格式易于从内存中流式传输，并适用于缓存和并行执行。为展示ALTO的有效性，我们加速了计算一系列真实世界稀疏张量上标准多模分解（CPD）模型的流行TD方法。此外，我们刻画了TD方法在多代最新Intel Xeon可扩展处理器（包括Sapphire Rapids CPU）上的主要执行瓶颈，并引入了动态自适应启发式方法，根据稀疏张量特征自动选择最优算法。在多样化的真实数据集上，ALTO优于现有最先进方法，相比最佳模式无关格式实现了超过一个数量级的加速。与需要多个张量副本的最佳模式特定格式相比，ALTO在仅为其25%的存储空间下实现了超过5.1倍的几何平均加速。