arXiv:2607. 22843v1 Announce Type: cross Abstract: Self-Organizing Maps (SOMs) have long been used as exploratory tools for high-dimensional data: they organize objects into a two-dimensional topology that reveals clusters, gradients, sparse regions, dense regions, and boundaries.
arXiv:2509. 03373v2 Announce Type: replace Abstract: Dimensionality reduction methods such as t-SNE and UMAP are popular methods for visualizing data with a potential (latent) clustered structure.
arXiv:2510. 11147v2 Announce Type: replace-cross Abstract: This paper introduces torchsom, an open-source Python library that provides a reference implementation of the Self-Organizing Map (SOM) in PyTorch.
arXiv:2507. 07156v2 Announce Type: replace-cross Abstract: Supervised machine learning pipelines trained on features derived from persistent homology have been experimentally observed to ignore much of the information contained in a persistence diagram.
arXiv:2510. 04100v2 Announce Type: replace-cross Abstract: Topological mapping offers a compact and robust representation for navigation, but progress in the field is hindered by the lack of standardized evaluation metrics, datasets, and protocols.
arXiv:2608. 15388v1 Announce Type: new Abstract: Topological deep learning (TDL) methods rely on lifting raw data into higher-order discrete domains such as simplicial complexes, cell complexes, and hypergraphs.
The article reviews the problem of learning graph structures from data, noting that research has traditionally split into two paths: inferring the topology of a single graph from observations on it, and learning a generative distribution from multiple observed graphs to sample new ones. It proposes a unified framework that treats both as inverse problems of a common graph generation process, reviews key methods, and discusses their interrelations, strengths, and limitations. The review highlights opportunities for cross‑paradigm integration and outlines future research directions.
arXiv:2608.22044v1 Announce Type: new Abstract: Modern machine learning (ML) methods are highly effective for prediction tasks, but many commonly used representations reduce complex data to fixed dim...
arXiv:2608. 09214v1 Announce Type: cross Abstract: Recent Retrieval-Augmented Generation (RAG) systems increasingly combine vector retrieval with structured knowledge, such as Graph RAG and Filtered vector search.
The paper evaluates seven graph database engines, including Corvic AI, on a synthetic biomedical property graph with 1.02 million nodes and 5.34 million rows. It benchmarks query latency, bulk‑ingest throughput, point‑update latency, and correctness across a twenty‑query workload that covers neighborhood lookups, bounded paths, set intersections, anti‑joins, aggregation, ranking, temporal filters, full scans, and relational joins. The study finds that no single engine is universally fastest; performance depends on query shape, and the largest cost difference arises from bulk‑ingest throughput, which varies by three orders of magnitude and dominates total cost for workloads with fewer than about 10⁵ queries per data refresh.
The paper introduces Topology-Preserving Adaptive Graph Pooling (TPAGP), a method that partitions graphs into granular balls by combining node features and topology to create multi-granularity representations. TPAGP captures both global and local structural patterns, unlike prior pooling methods that coarsen graphs by removing or clustering nodes. Experiments show TPAGP outperforms existing pooling techniques on benchmark datasets, reducing information loss from fixed-granularity strategies.
arXiv:2609.01525v1 Announce Type: cross Abstract: A durable assumption holds that graph analytics requires a purpose-built graph engine, and that relational systems are ill-suited to connected data....
arXiv:2607. 24766v1 Announce Type: new Abstract: Large language models (LLMs) can generate individual charts, but coordinated multi-view visualizations (CMVs), where views share data flows and cross-view interactions, remain out of reach.