相关论文: Generalization of k-means Related Algorithms

A stochastic algorithm is proposed, finding the set of generalized means associated to a probability measure on a compact Riemannian manifold M and a continuous cost function on the product of M by itself. Generalized means include p-means…

Clustering samples according to an effective metric and/or vector space representation is a challenging unsupervised learning task with a wide spectrum of applications. Among several clustering algorithms, k-means and its kernelized version…

Data-driven algorithm selection is a powerful approach for choosing effective heuristics for computational problems. It operates by evaluating a set of candidate algorithms on a collection of representative training instances and selecting…

The $k$-means clustering algorithm is popular but has the following main drawbacks: 1) the number of clusters, $k$, needs to be provided by the user in advance, 2) it can easily reach local minima with randomly selected initial centers, 3)…

The complexity of matrix multiplication is a central topic in computer science. While the focus has traditionally been on exact algorithms, a long line of literature also considers randomized algorithms, which return an approximate solution…

Tackling output sampling noise due to finite shots of quantum measurement is an unavoidable challenge when extracting information in machine learning with physical systems. A technique called Eigentask Learning was developed recently as a…

Color quantization is an important operation with numerous applications in graphics and image processing. Most quantization methods are essentially based on data clustering algorithms. However, despite its popularity as a general purpose…

Adaptive importance sampling is a powerful tool to sample from complicated target densities, but its success depends sensitively on the initial proposal density. An algorithm is presented to automatically perform the initialization using…

Historically, the notion of effective algorithm is closely related to the Church-Turing thesis. But effectivity imposes no restriction on computation time or any other resource; in that sense, it is incompatible with engineering or physics.…

This paper introduces k-splits, an improved hierarchical algorithm based on k-means to cluster data without prior knowledge of the number of clusters. K-splits starts from a small number of clusters and uses the most significant data…

In this work, we study the socially fair $k$-median/$k$-means problem. We are given a set of points $P$ in a metric space $\mathcal{X}$ with a distance function $d(.,.)$. There are $\ell$ groups: $P_1,\dotsc,P_{\ell} \subseteq P$. We are…

Recent results suggest that reinitializing a subset of the parameters of a neural network during training can improve generalization, particularly for small training sets. We study the impact of different reinitialization methods in several…

Mean shift is a simple interactive procedure that gradually shifts data points towards the mode which denotes the highest density of data points in the region. Mean shift algorithms have been effectively used for data denoising, mode…

In the k-center problem, given a metric space V and a positive integer k, one wants to select k elements (centers) of V and an assignment from V to centers, minimizing the maximum distance between an element of V and its assigned center.…

Quantum machine learning is one of the most promising applications of a full-scale quantum computer. Over the past few years, many quantum machine learning algorithms have been proposed that can potentially offer considerable speedups over…

Majorization-minimization schemes are a broad class of iterative methods targeting general optimization problems, including nonconvex, nonsmooth and stochastic. These algorithms minimize successively a sequence of upper bounds of the…

This paper investigates the following natural greedy procedure for clustering in the bi-criterion setting: iteratively grow a set of centers, in each round adding the center from a candidate set that maximally decreases clustering cost. In…

In the present paper we introduce new optimization algorithms for the task of density ratio estimation. More precisely, we consider extending the well-known KMM method using the construction of a suitable loss function, in order to…

We design replicable algorithms in the context of statistical clustering under the recently introduced notion of replicability from Impagliazzo et al. [2022]. According to this definition, a clustering algorithm is replicable if, with high…

Although deep learning based approximation algorithms have been applied very successfully to numerous problems, at the moment the reasons for their performance are not entirely understood from a mathematical point of view. Recently,…