State-of-the-art hypergraph partitioners utilize a multilevel paradigm to construct progressively coarser hypergraphs across multiple layers, guiding cut refinements at each level of the hierarchy. Traditionally, these partitioners employ heuristic methods for coarsening and do not consider the structural features of hypergraphs. In this work, we introduce a multilevel spectral framework, SHyPar, for partitioning large-scale hypergraphs by leveraging hyperedge effective resistances and flow-based community detection techniques. Inspired by the latest theoretical spectral clustering frameworks, such as HyperEF and HyperSF, SHyPar aims to decompose large hypergraphs into multiple subgraphs with few inter-partition hyperedges (cut size). A key component of SHyPar is a flow-based local clustering scheme for hypergraph coarsening, which incorporates a max-flow-based algorithm to produce clusters with substantially improved conductance. Additionally, SHyPar utilizes an effective resistance-based rating function for merging nodes that are strongly connected (coupled). Compared with existing state-of-the-art hypergraph partitioning methods, our extensive experimental results on real-world VLSI designs demonstrate that SHyPar can more effectively partition hypergraphs, achieving state-of-the-art solution quality.

This paper introduces a scalable algorithmic framework (HyperEF) for spectral coarsening (decomposition) of large-scale hypergraphs by exploiting hyperedge effective resistances. Motivated by the latest theoretical framework for low-resistance-diameter decomposition of simple graphs, HyperEF aims at decomposing large hypergraphs into multiple node clusters with only a few inter-cluster hyperedges. The key component in HyperEF is a nearly-linear time algorithm for estimating hyperedge effective resistances, which allows incorporating the latest diffusion-based non-linear quadratic operators defined on hypergraphs. To achieve good runtime scalability, HyperEF searches within the Krylov subspace (or approximate eigensubspace) for identifying the nearly-optimal vectors for approximating the hyperedge effective resistances. In addition, a node weight propagation scheme for multilevel spectral hypergraph decomposition has been introduced for achieving even greater node coarsening ratios. When compared with state-of-the-art hypergraph partitioning (clustering) methods, extensive experiment results on real-world VLSI designs show that HyperEF can more effectively coarsen (decompose) hypergraphs without losing key structural (spectral) properties of the original hypergraphs, while achieving over $70\times$ runtime speedups over hMetis and $20\times$ speedups over HyperSF.

Graph Neural Networks (GNNs) are currently a hot topic in artificial intelligence, with a huge amount of applications in many domains, ranging from bioinformatics to computer vision, from social network analysis to natural language processing [1]. First introduced in [2], and then far and wide extended with a large number of variants, GNNs can learn embedding representations of generic graphs, by exploiting aggregation functions based on propagation and pooling layers. These building blocks are frequently stacked into a deep network, and the resulting embeddings can be exploited in any high-level task. This kind of architecture has rapidly become the state-of-the-art, or at least a strong competitor, in many application domains dealing with structured data. Historically, in natural language processing (NLP) as well as in other domains, Tree Kernels (TKs) have long been one of the most widely employed technique to handle structured data in the form of trees [3]. A TK is basically a similarity function that captures the degree of similarity of two trees by looking at common fragments within their substructures.

In the process of knowledge discovery and representation in large datasets using formal concept analysis, complexity plays a major role in identifying all the formal concepts and constructing the concept lattice(digraph of the concepts). For identifying the formal concepts and constructing the digraph from the identified concepts in very large datasets, various distributed algorithms are available in the literature. However, the existing distributed algorithms are not very well suitable for concept generation because it is an iterative process. The existing algorithms are implemented using distributed frameworks like MapReduce and Open MP, these frameworks are not appropriate for iterative applications. Hence, in this paper we proposed efficient distributed algorithms for both formal concept generation and concept lattice digraph construction in large formal contexts using Apache Spark. Various performance metrics are considered for the evaluation of the proposed work, the results of the evaluation proves that the proposed algorithms are efficient for concept generation and lattice graph construction in comparison with the existing algorithms.