Related papers: Scalable Exact Hierarchical Agglomerative Clusteri…

DBSCAN is a fundamental spatial clustering algorithm with numerous practical applications. However, a bottleneck of the algorithm is in the worst case, the run time complexity is $O(n^2)$. To address this limitation, we propose a new…

Geometric Near-neighbor Access Tree (GNAT) is a metric space indexing method based on hierarchical hyperplane partitioning of the space. While GNAT is very efficient in proximity searching, it has a bad reputation of being a memory hog. We…

Hyperspectral image (HSI) clustering is a challenging task due to the high complexity of HSI data. Subspace clustering has been proven to be powerful for exploiting the intrinsic relationship between data points. Despite the impressive…

Reliable extraction of cosmological information from clustering measurements of galaxy surveys requires estimation of the error covariance matrices of observables. The accuracy of covariance matrices is limited by our ability to generate…

Persistence diagrams have been widely used to quantify the underlying features of filtered topological spaces in data visualization. In many applications, computing distances between diagrams is essential; however, computing these distances…

Mechanistic interpretability seeks to reverse-engineer neural network computations into human-understandable algorithms, yet extracting sparse computational circuits from billion-parameter language models remains challenging due to…

We consider the problem of testing graph cluster structure: given access to a graph $G=(V, E)$, can we quickly determine whether the graph can be partitioned into a few clusters with good inner conductance, or is far from any such graph?…

This paper considers metric spaces where distances between a pair of nodes are represented by distance intervals. The goal is to study methods for the determination of hierarchical clusters, i.e., a family of nested partitions indexed by a…

Spectral clustering is a novel clustering method which can detect complex shapes of data clusters. However, it requires the eigen decomposition of the graph Laplacian matrix, which is proportion to $O(n^3)$ and thus is not suitable for…

Hyperspectral image classification (HIC) is an important but challenging task, and a problem that limits the algorithmic development in this field is that the ground truths of hyperspectral images (HSIs) are extremely hard to obtain.…

Hierarchical clustering is a widely used approach for clustering datasets at multiple levels of granularity. Despite its popularity, existing algorithms such as hierarchical agglomerative clustering (HAC) are limited to the offline setting,…

A fundamental procedure in the analysis of massive datasets is the construction of similarity graphs. Such graphs play a key role for many downstream tasks, including clustering, classification, graph learning, and nearest neighbor search.…

We construct geohashing procedure based on using of space-filling H-curve. This curve provides a way to construct geohash with less computations than the construction based on usage of Hilbert curve. At the same time, H-curve has better…

A common problem appearing across the field of data science is $k$-NN ($k$-nearest neighbours), particularly within the context of Geographic Information Systems. In this article, we present a novel data structure, the GeoTree, which holds…

A simple model to study subspace clustering is the high-dimensional $k$-Gaussian mixture model where the cluster means are sparse vectors. Here we provide an exact asymptotic characterization of the statistically optimal reconstruction…

Many networks in real-life typically contain parts in which some nodes are more highly connected to each other than the other nodes of the network. The collection of such nodes are usually called clusters, communities, cohesive groups or…

This paper investigates a generation expansion planning (GEP) problem encompassing renewable, thermal, and storage technologies while simultaneously optimizing market participation, operational expenditures, and capital investment. To…

Typical R-convolution graph kernels invoke the kernel functions that decompose graphs into non-isomorphic substructures and compare them. However, overlooking implicit similarities and topological position information between those…

Graph neural networks (GNNs) realize great success in graph learning but suffer from performance loss when meeting heterophily, i.e. neighboring nodes are dissimilar, due to their local and uniform aggregation. Existing attempts of…

Across many areas, from neural tracking to database entity resolution, manual assessment of clusters by human experts presents a bottleneck in rapid development of scalable and specialized clustering methods. To solve this problem we…