Related papers: Using Ripley's K-function to Characterize Clusteri…

This paper addresses the limitations of conventional vector quantization algorithms, particularly K-Means and its variant K-Means++, and investigates the Stochastic Quantization (SQ) algorithm as a scalable alternative for high-dimensional…

Kinetic turbulence in magnetized space plasmas has been extensively studied via in situ observations, numerical simulations and theoretical models. In this context, a key point concerns the formation of coherent current structures and their…

A quantum coherent screening cloud around a magnetic impurity in metallic systems is the hallmark of the antiferromagnetic Kondo effect. Despite the central role of the Kondo effect in quantum materials, the structure of quantum…

Clustering is one of the most fundamental problems in unsupervised learning with a large number of applications. However, classical clustering algorithms assume that the data is static, thus failing to capture many real-world applications…

Self-supervised methods for learning object-centric representations have recently been applied successfully to various datasets. This progress is largely fueled by slot-based methods, whose ability to cluster visual scenes into meaningful…

In this chapter we review some examples, methods, and recent results involving comparison of clustering properties of point processes. Our approach is founded on some basic observations allowing us to consider void probabilities and moment…

We consider the problem of metric learning subject to a set of constraints on relative-distance comparisons between the data items. Such constraints are meant to reflect side-information that is not expressed directly in the feature vectors…

Amorphous materials are coming within reach of realistic computer simulations, but new approaches are needed to fully understand their intricate atomic structures. Here, we show how machine-learning (ML)-based techniques can give new,…

In this paper, we study the strong consistency of the sparse K-means clustering for high dimensional data. We prove the consistency in both risk and clustering for the Euclidean distance. We discuss the characterization of the limit of the…

Given a set of points $P \subset \mathbb{R}^d$, the $k$-means clustering problem is to find a set of $k$ {\em centers} $C = \{c_1,...,c_k\}, c_i \in \mathbb{R}^d,$ such that the objective function $\sum_{x \in P} d(x,C)^2$, where $d(x,C)$…

We propose clustering algorithms based on a recently developed geometric digraph family called cluster catch digraphs (CCDs). These digraphs are used to devise clustering methods that are hybrids of density-based and graph-based clustering…

Recent spectral clustering methods are a propular and powerful technique for data clustering. These methods need to solve the eigenproblem whose computational complexity is $O(n^3)$, where $n$ is the number of data samples. In this paper, a…

Two important optimization problems in the analysis of geometric data sets are clustering and sketching. Here, clustering refers to the problem of partitioning some input metric measure space (mm-space) into k clusters, minimizing some…

Kernel mean embeddings have recently attracted the attention of the machine learning community. They map measures $\mu$ from some set $M$ to functions in a reproducing kernel Hilbert space (RKHS) with kernel $k$. The RKHS distance of two…

A model for quantum tunnelling of a cluster comprising A identical particles, coupled by oscillator-type potential, through short-range repulsive potential barriers is introduced for the first time in the new symmetrized-coordinate…

Clustering plays a crucial role in computer science, facilitating data analysis and problem-solving across numerous fields. By partitioning large datasets into meaningful groups, clustering reveals hidden structures and relationships within…

Helly's theorem is a fundamental result in discrete geometry, describing the ways in which convex sets intersect with each other. If $S$ is a set of $n$ points in $R^d$, we say that $S$ is $(k,G)$-clusterable if it can be partitioned into…

Sharpened dimensionality reduction (SDR), which belongs to the class of multidimensional projection techniques, has recently been introduced to tackle the challenges in the exploratory and visual analysis of high-dimensional data. SDR has…

We consider the problem of feature detection in the presence of clutter in spatial point processes. Classification methods have been developed in previous studies. Among these, Byers and Raftery (1998) models the observed Kth nearest…

We propose an algorithm for clustering high dimensional data. If $P$ features for $N$ objects are represented in an $N\times P$ matrix ${\bf X}$, where $N\ll P$, the method is based on exploiting the cluster-dependent structure of the…