Related papers: Faster and Simpler Greedy Algorithm for $k$-Median…
Sparsity learning with known grouping structure has received considerable attention due to wide modern applications in high-dimensional data analysis. Although advantages of using group information have been well-studied by shrinkage-based…
The analysis of continously larger datasets is a task of major importance in a wide variety of scientific fields. In this sense, cluster analysis algorithms are a key element of exploratory data analysis, due to their easiness in the…
In this paper, we propose an implicit gradient descent algorithm for the classic $k$-means problem. The implicit gradient step or backward Euler is solved via stochastic fixed-point iteration, in which we randomly sample a mini-batch…
In [25], T. Oikhberg introduced and studied variants of the greedy and weak greedy algorithms for sequences with gaps, with a focus on the $\mathbf n$-$t$-quasi-greedy property that is based on them. Building upon this foundation, our…
We analyse the performance of several iterative algorithms for the quantisation of a probability measure $\mu$, based on the minimisation of a Maximum Mean Discrepancy (MMD). Our analysis includes kernel herding, greedy MMD minimisation and…
We explore the problems of classification of composite object (images, speech signals) with low number of models per class. We study the question of improving recognition performance for medium-sized database (thousands of classes). The key…
This paper extends k-means algorithms from the Euclidean domain to the domain of graphs. To recompute the centroids, we apply subgradient methods for solving the optimization-based formulation of the sample mean of graphs. To accelerate the…
We develop an algorithm that finds the consensus of many different clustering solutions of a graph. We formulate the problem as a median set partitioning problem and propose a greedy optimization technique. Unlike other approaches that find…
Kernel based methods provide a way to reconstruct potentially high-dimensional functions from meshfree samples, i.e., sampling points and corresponding target values. A crucial ingredient for this to be successful is the distribution of the…
Recently, due to an increasing interest for transparency in artificial intelligence, several methods of explainable machine learning have been developed with the simultaneous goal of accuracy and interpretability by humans. In this paper,…
For the past 25 years, one of the most studied algorithms in the field of Nonlinear Approximation Theory has been the Thresholding Greedy Algorithm. In this paper, we propose new summability methods for this algorithm, generating two new…
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…
We study two generalizations of classic clustering problems called dynamic ordered $k$-median and dynamic $k$-supplier, where the points that need clustering evolve over time, and we are allowed to move the cluster centers between…
We introduce a greedy algorithm optimizing arrangements of lines with respect to a property. We apply this algorithm to the case of simpliciality: it recovers all known simplicial arrangements of lines in a very short time and also produces…
We present SimultaneousGreedys, a deterministic algorithm for constrained submodular maximization. At a high level, the algorithm maintains $\ell$ solutions and greedily updates them in a simultaneous fashion. SimultaneousGreedys achieves…
Gaussian mixture models (GMM) are the most widely used statistical model for the $k$-means clustering problem and form a popular framework for clustering in machine learning and data analysis. In this paper, we propose a natural semi-random…
Motivated by applications in redistricting, we consider the uniform capacitated k-median and uniform capacitated k-means problems in bounded doubling metrics. We provide the first QPTAS for both problems and the first PTAS for the uniform…
We give the first polynomial-time approximation schemes (PTASs) for the following problems: (1) uniform facility location in edge-weighted planar graphs; (2) $k$-median and $k$-means in edge-weighted planar graphs; (3) $k$-means in…
A greedy randomized nonlinear Bregman-Kaczmarz method by sampling the working index with residual information is developed for the solution of the constrained nonlinear system of equations. Theoretical analyses prove the convergence of the…
The $k$-Means clustering problem on $n$ points is NP-Hard for any dimension $d\ge 2$, however, for the 1D case there exists exact polynomial time algorithms. Previous literature reported an $O(kn^2)$ time dynamic programming algorithm that…