Sparse symmetric tensors are an important class of tensors, and their decompositions serve as powerful tools for revealing low-rank structures. This paper introduces SymProp, a novel approach for scaling sparse symmetric Tucker decomposition by propagating symmetry through intermediate computations. SymProp optimizes two key computational kernels: Sparse Symmetric Tensor Times Same Matrix chain ($\mathrm{S}^{3}$TTMc) for Higher-Order Orthogonal Iteration (HOOI) and Sparse Symmetric Tensor Times Same Matrix chain Times Core ($\mathrm{S}^{3}$TTMcTC) for Higher-Order QR Iteration (HOQRI). Our method employs a metaprogramming-based index iteration approach to efficiently handle the upper triangular parts of intermediate dense symmetric tensors. SymProp achieves up to$50.9 \times$speedup over SPLATT and up to$360.8 \times$over Compressed Sparse Symmetric (CSS) format on the$\mathbf{S}^{3}$TTMc operation. Moreover, our$S^{3}$TTMc and$S^{3}$TTMcTC implementations support tensor orders four levels higher than state-of-the-art methods. Our HOQRI demonstrates superior scalability and up to a$33.6 \times$speedup over optimized HOOI. By enabling more scalable Tucker decompositions for higher orders, decomposition ranks, and dimension sizes, SymProp opens new possibilities for analyzing complex hypergraph structures in fields such as network science, data mining, and machine learning.

Hypergraphs are a popular paradigm to represent complex real-world networks exhibiting multi-way relationships of varying sizes. Mining centrality in hyper-graphs via symmetric adjacency tensors has only recently become computationally feasible for large and complex datasets. To enable scalable computation of these and related hypergraph analytics, here we focus on the Sparse Symmetric Tensor Times Same Vector (S3TTVC) operation. We introduce the Compound Compressed Sparse Symmetric (CCSS) format, an extension of the compact CSS format for hypergraphs of varying hyperedge sizes and present a shared-memory parallel algorithm to compute S3TTVC. We experimentally show S3TTVc computation using the CCSS format achieves better performance than the naive baseline, and is subsequently more performant for hypergraph$H$-eigenvector centrality.

Tensor-based methods are receiving renewed attention in recent years due to their prevalence in diverse real-world applications. There is considerable literature on tensor representations and algorithms for tensor decompositions, both for dense and sparse tensors. Many applications in hypergraph analytics, machine learning, psychometry, and signal processing result in tensors that are both sparse and symmetric, making them an important class for further study. Similar to the critical Tensor Times Matrix chain operation (TTMc) in general sparse tensors, theSparseSymmetricTensorTimesSameMatrixchain (S$^{3}$TTMc) operation is compute and memory intensive due to high tensor order and the associated factorial explosion in the number of non-zeros. We present the novel Compressed Sparse Symmetric (CSS) format for sparse symmetric tensors, along with an efficient parallel algorithm for the S$^{3}$TTMcoperation. We theoretically establish that S$^{3}$TTMcon CSS achieves a better memory versus run-time trade-off compared to state-of-the-art implementations, and visualize the variation of the performance gap over the parameter space. We demonstrate experimental findings that confirm these results and achieve up to$2.72 \times$speedup on synthetic and real datasets. The scaling of the algorithm on different test architectures is also showcased to highlight the effect of machine characteristics on algorithm performance.

MOTIVATION: Reconstruction of genome-scale networks from gene expression data is an actively studied problem. A wide range of methods that differ between the types of interactions they uncover with varying trade-offs between sensitivity and specificity have been proposed. To leverage benefits of multiple such methods, ensemble network methods that combine predictions from resulting networks have been developed, promising results better than or as good as the individual networks. Perhaps owing to the difficulty in obtaining accurate training examples, these ensemble methods hitherto are unsupervised. RESULTS: In this article, we introduce EnGRaiN, the first supervised ensemble learning method to construct gene networks. The supervision for training is provided by small training datasets of true edge connections (positives) and edges known to be absent (negatives) among gene pairs. We demonstrate the effectiveness of EnGRaiN using simulated datasets as well as a curated collection of Arabidopsis thaliana datasets we created from microarray datasets available from public repositories. EnGRaiN shows better results not only in terms of receiver operating characteristic and PR characteristics for both real and simulated datasets compared with unsupervised methods for ensemble network construction, but also generates networks that can be mined for elucidating complex biological interactions. AVAILABILITY AND IMPLEMENTATION: EnGRaiN software and the datasets used in the study are publicly available at the github repository: https://github.com/AluruLab/EnGRaiN. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.