相关论文: Clustering, Hamming Embedding, Generalized LSH and…

Metric clustering is fundamental in areas ranging from Combinatorial Optimization and Data Mining, to Machine Learning and Operations Research. However, in a variety of situations we may have additional requirements or knowledge, distinct…

We associate with each convex optimization problem posed on some locally convex space with an infinite index set T, and a given non-empty family H formed by finite subsets of T, a suitable Lagrangian-Haar dual problem. We provide reverse…

After generalizing the concept of clusters to incorporate clusters that are linked to other clusters through some relatively narrow bridges, an approach for detecting patches of separation between these clusters is developed based on an…

We use SPH simulations to investigate the gravitational fragmentation of expanding shells through the linear and non--linear regimes. The results are analysed using spherical harmonic decomposition to capture the initiation of structure…

Phase structure of rapidly quenched solid helium samples is studied by the NMR technique. The pulse NMR method is used for measurements of spin-lattice $T_1$ and spin-spin $T_2$ relaxation times and spin diffusion coefficient $D$ for all…

Convex clustering is a recent stable alternative to hierarchical clustering. It formulates the recovery of progressively coalescing clusters as a regularized convex problem. While convex clustering was originally designed for handling…

Clustering approaches that utilize convex loss functions have recently attracted growing interest in the formation of compact data clusters. Although classical methods like k-means and its wide family of variants are still widely used, all…

We investigate the spatial dependence of the density of vibrated granular beds, using simulations based on a hybrid Monte Carlo algorithm. We find that the initial consolidation is typically inhmogeneous, both in the presence of a constant…

While personalized recommendations systems have become increasingly popular, ensuring user data protection remains a top concern in the development of these learning systems. A common approach to enhancing privacy involves training models…

Choosing appropriate hyperparameters for unsupervised clustering algorithms in an optimal way depending on the problem under study is a long standing challenge, which we tackle while adapting clustering algorithms for immune disorder…

Using a set of hydrodynamical simulations of 62 galaxy clusters and groups we study the ICM of inhomogeneities, focusing on the ones on the large scale that, unlike clumps, are the most difficult to identify. To this purpose we introduce…

In many fundamental combinatorial optimization problems, a feasible solution induces some real cost vectors as an intermediate result, and the optimization objective is a certain function of the vectors. For example, in the problem of…

The problem of multimodal clustering arises whenever the data are gathered with several physically different sensors. Observations from different modalities are not necessarily aligned in the sense there there is no obvious way to associate…

The dipole in the angular distribution of the cosmic microwave background (CMB) is attributed to the Doppler effect and our motion relative to the CMB rest frame. It is expected that observations of large-scale structures (LSSs) would also…

We study the convex hull membership (CHM) problem in the pure exploration setting where one aims to efficiently and accurately determine if a given point lies in the convex hull of means of a finite set of distributions. We give a complete…

We describe a quantitative construction of almost-normal diffeomorphisms between embedded orientable manifolds with boundary to be used in the study of geometric variational problems with stratified singular sets. We then apply this…

We introduce and study several measures of complexity of functions from the convex hull of a given base class. These complexity measures take into account the sparsity of the weights of a convex combination as well as certain clustering…

We focus on the task of unsupervised lemmatization, i.e. grouping together inflected forms of one word under one label (a lemma) without the use of annotated training data. We propose to perform agglomerative clustering of word forms with a…

This paper deals with four symmetrizations of a convex set $C$: the intersection, the harmonic and the arithmetic mean, and the convex hull of $C$ and $-C$. A well-known result of Firey shows that those means build up a subset-chain in the…

Data clustering is a fundamental problem with a wide range of applications. Standard methods, eg the $k$-means method, usually require solving a non-convex optimization problem. Recently, total variation based convex relaxation to the…