Related papers: On $p$-adic Classification

We investigate different approaches to transform a given binomial into a monomial via blowing up appropriate centers. In particular, we develop explicit implementations in {\sc Singular}, which allow to make a comparison on the basis of…

As a kind of basic machine learning method, clustering algorithms group data points into different categories based on their similarity or distribution. We present a clustering algorithm by finding hyper-planes to distinguish the data…

The efficacy of family-based approaches to mixture model-based clustering and classification depends on the selection of parsimonious models. Current wisdom suggests the Bayesian information criterion (BIC) for mixture model selection.…

We study the problem of explainability-first clustering where explainability becomes a first-class citizen for clustering. Previous clustering approaches use decision trees for explanation, but only after the clustering is completed. In…

We introduce a differentiable clustering method based on stochastic perturbations of minimum-weight spanning forests. This allows us to include clustering in end-to-end trainable pipelines, with efficient gradients. We show that our method…

Clustering has become an indispensable tool in the presence of increasingly large and complex data sets. Most clustering algorithms depend, either explicitly or implicitly, on the sampled density. However, estimated densities are fragile…

We explore the geometrical interpretation of the PCA based clustering algorithm Principal Direction Divisive Partitioning (PDDP). We give several examples where this algorithm breaks down, and suggest a new method, gap partitioning, which…

Given primes $\ell\ne p$, we record here a $p$-adic valued Fourier theory on a local field over $\mathbf{Q}_\ell$, which is developed under the perspective of group schemes. As an application, by substituting rigid analysis for complex…

In this paper adapting to $p$-adic case some methods of real valued Gibbs measures on Cayley trees we construct several $p$-adic distributions on the set $\mathbb{Z}_p$ of $p$-adic integers. Moreover, we give conditions under which these…

In this work, we introduce a novel methodology for divisive hierarchical clustering. Our divisive (``top-down'') approach is motivated by the fact that agglomerative hierarchical clustering (``bottom-up''), which is commonly used for…

The K-Modes algorithm, developed for clustering categorical data, is of high algorithmic simplicity but suffers from unreliable performances in clustering quality and clustering efficiency, both heavily influenced by the choice of initial…

In the framework of model-based clustering, a model allowing several latent class variables is proposed. This model assumes that the distribution of the observed data can be factorized into several independent blocks of variables. Each…

Clustering is a core task in machine learning with wide-ranging applications in data mining and pattern recognition. However, its unsupervised nature makes it inherently challenging. Many existing clustering algorithms suffer from critical…

Using methods of associative algebras, Lie theory, group cohomology, and modular representation theory, we construct profinite $p$-adic analytic groups such that the centralizer of each of their non-trivial elements is abelian. The paper…

We give a classification of irreducible admissible modulo $p$ representations of a split $p$-adic reductive group in terms of supersingular representations. This is a generalization of a theorem of Herzig.

An extension of the latent class model is presented for clustering categorical data by relaxing the classical "class conditional independence assumption" of variables. This model consists in grouping the variables into inter-independent and…

We consider a problem of clustering a sequence of multinomial observations by way of a model selection criterion. We propose a form of a penalty term for the model selection procedure. Our approach subsumes both the conventional AIC and BIC…

The determination of cluster centers generally depends on the scale that we use to analyze the data to be clustered. Inappropriate scale usually leads to unreasonable cluster centers and thus unreasonable results. In this study, we first…

We design algorithms for computing values of many p-adic elementary and special functions, including logarithms, exponentials, polylogarithms, and hypergeometric functions. All our algorithms feature a quasi-linear complexity with respect…

Supervised classification can be effective for prediction but sometimes weak on interpretability or explainability (XAI). Clustering, on the other hand, tends to isolate categories or profiles that can be meaningful but there is no…