Related papers: Clustering, Hamming Embedding, Generalized LSH and…
Network Lasso (NL for short) is a methodology for estimating models by simultaneously clustering data samples and fitting the models to the samples. It often succeeds in forming clusters thanks to the geometry of the $\ell_1$-regularizer…
In this paper, we investigate whether galaxy assembly bias can reconcile the 20-40% disagreement between the observed galaxy projected clustering signal and the galaxy-galaxy lensing signal in the BOSS CMASS galaxy sample reported in…
Text clustering is a fundamental task in natural language processing, yet traditional clustering algorithms with pre-trained embeddings often struggle in domain-specific contexts without costly fine-tuning. Large language models (LLMs)…
We study (asymmetric) $U$-statistics based on a stationary sequence of $m$-dependent variables; moreover, we consider constrained $U$-statistics, where the defining multiple sum only includes terms satisfying some restrictions on the gaps…
Sparse convex clustering is to cluster observations and conduct variable selection simultaneously in the framework of convex clustering. Although a weighted $L_1$ norm is usually employed for the regularization term in sparse convex…
Ensembling word embeddings to improve distributed word representations has shown good success for natural language processing tasks in recent years. These approaches either carry out straightforward mathematical operations over a set of…
In this paper we consider the convex hull of a spherically symmetric sample in $R^d$. Our main contributions are some new asymptotic results for the expectation of the number of vertices, number of facets, area and the volume of the convex…
(abridged) We present an investigation of the clustering of i'AB<24.5 galaxies in the redshift interval 0.2<z<1.2. Using 100,000 precise photometric redshifts in the four ultra-deep fields of the Canada-France Legacy Survey, we construct a…
Refinements of the worst case complexity over instances of fixed input size consider the input order or the input structure, but rarely both at the same time. Barbay et al. [2016] described ``synergistic'' solutions on multisets, which take…
Matrix valued data has become increasingly prevalent in many applications. Most of the existing clustering methods for this type of data are tailored to the mean model and do not account for the dependence structure of the features, which…
Large language models (LLMs) often rely on user-specific memories distilled from past interactions to enable personalized generation. A common practice is to concatenate these memories with the input prompt, but this approach quickly…
Recent research in clustering face embeddings has found that unsupervised, shallow, heuristic-based methods -- including $k$-means and hierarchical agglomerative clustering -- underperform supervised, deep, inductive methods. While the…
We consider countable linear orders and study the quasi-order of convex embeddability and its induced equivalence relation. We obtain both combinatorial and descriptive set-theoretic results, and further extend our research to the case of…
The clustering of dark halos depends not only on their mass but also on their assembly history, a dependence we term `assembly bias'. Using a galaxy formation model grafted onto the Millennium Simulation of the LCDM cosmogony, we study how…
Matrices are two-dimensional data structures allowing one to conceptually organize information. For example, adjacency matrices are useful to store the links of a network; correlation matrices are simple ways to arrange gene co-expression…
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…
This paper characterizes hierarchical clustering methods that abide by two previously introduced axioms -- thus, denominated admissible methods -- and proposes tractable algorithms for their implementation. We leverage the fact that, for…
We use a very large simulation of structure growth in a LCDM universe -- the Millennium Simulation -- to study assembly bias, the fact that the large-scale clustering of haloes of given mass varies significantly with their assembly history.…
Rational approximations of functions with singularities can converge at a root-exponential rate if the poles are exponentially clustered. We begin by reviewing this effect in minimax, least-squares, and AAA approximations on intervals and…
Co-Clustering, the problem of simultaneously identifying clusters across multiple aspects of a data set, is a natural generalization of clustering to higher-order structured data. Recent convex formulations of bi-clustering and tensor…