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Mode clustering is a nonparametric method for clustering that defines clusters using the basins of attraction of a density estimator's modes. We provide several enhancements to mode clustering: (i) a soft variant of cluster assignment, (ii)…
We present a new model-based integrative method for clustering objects given both vectorial data, which describes the feature of each object, and network data, which indicates the similarity of connected objects. The proposed general model…
Sentence embedding methods offer a powerful approach for working with short textual constructs or sequences of words. By representing sentences as dense numerical vectors, many natural language processing (NLP) applications have improved…
We investigate the problem of segmenting unlabeled speech into word-like units and clustering these to create a lexicon. Prior work can be categorized into two frameworks. Bottom-up methods first determine boundaries and then cluster the…
This paper makes a combinatorial study of the two monoids and the two types of tableaux that arise from the two possible generalizations of the Patience Sorting algorithm from permutations (or standard words) to words. For both types of…
Let $\Lambda^{\ast}$ be the free monoid of (finite) words over a not necessarily finite alphabet $\Lambda$, which is equipped with some (partial) order. This ordering lifts to $\Lambda^{\ast}$, where it extends the divisibility ordering of…
Multilayer graph has garnered plenty of research attention in many areas due to their high utility in modeling interdependent systems. However, clustering of multilayer graph, which aims at dividing the graph nodes into categories or…
Generative approaches to clustering provide information on geometric properties of clusters, whereas discriminative approaches provide boundaries between clusters. Ideas from both approaches are incorporated to present a fully unsupervised,…
In this work we seek clusters of genomic words in human DNA by studying their inter-word lag distributions. Due to the particularly spiked nature of these histograms, a clustering procedure is proposed that first decomposes each…
The paper tackles the problem of clustering multiple networks, directed or not, that do not share the same set of vertices, into groups of networks with similar topology. A statistical model-based approach based on a finite mixture of…
More and more languages in the world are under study nowadays, as a result, the traditional way of historical linguistics study is facing some challenges. For example, the linguistic comparative research among languages needs manual…
We present a global optimization algorithm for clustering data given the ratio of likelihoods that each pair of data points is in the same cluster or in different clusters. To define a clustering solution in terms of pairwise relationships,…
Document clustering as an unsupervised approach extensively used to navigate, filter, summarize and manage large collection of document repositories like the World Wide Web (WWW). Recently, focuses in this domain shifted from traditional…
Over the past decade, a combinatorial framework for discrete, finite, and irreversibly aggregating systems has emerged. This work reviews its progress, practical applications, and limitations. We outline the approach's assumptions and…
Word embedding maps words into a low-dimensional continuous embedding space by exploiting the local word collocation patterns in a small context window. On the other hand, topic modeling maps documents onto a low-dimensional topic space, by…
Here, we propose a clustering technique for general clustering problems including those that have non-convex clusters. For a given desired number of clusters $K$, we use three stages to find a clustering. The first stage uses a hybrid…
We give an efficient algorithm for robustly clustering of a mixture of two arbitrary Gaussians, a central open problem in the theory of computationally efficient robust estimation, assuming only that the the means of the component Gaussians…
Kan extensions provide a natural general framework for a variety of combinatorial problems. We have developed rewriting procedures for Kan extensions (over the category of sets) and this enables one program to address a wide range of…
Motivated by the concept of "generating operators" for a countable family of operators introduced in the recent paper (arXiv:2306.16800), we find a method to reconstruct the Rankin--Cohen brackets from a very simple multivariable contour…
In longitudinal data analysis, observation points of repeated measurements over time often vary among subjects except in well-designed experimental studies. Additionally, measurements for each subject are typically obtained at only a few…