Related papers: Clustering with Queries under Semi-Random Noise
We show that every language in NP has a PCP verifier that tosses $O(\log n)$ random coins, has perfect completeness, and a soundness error of at most $1/\text{poly}(n)$, while making at most $O(\text{poly}\log\log n)$ queries into a proof…
In the context of unsupervised learning, Lloyd's algorithm is one of the most widely used clustering algorithms. It has inspired a plethora of work investigating the correctness of the algorithm under various settings with ground truth…
Recently, there has been substantial interest in clustering research that takes a beyond worst-case approach to the analysis of algorithms. The typical idea is to design a clustering algorithm that outputs a near-optimal solution, provided…
This paper studies problems of inferring order given noisy information. In these problems there is an unknown order (permutation) $\pi$ on $n$ elements denoted by $1,...,n$. We assume that information is generated in a way correlated with…
We study the problem of clustering a set of items from binary user feedback. Such a problem arises in crowdsourcing platforms solving large-scale labeling tasks with minimal effort put on the users. For example, in some of the recent…
We present a framework for the partitioning of a spatial trajectory in a sequence of segments based on spatial density and temporal criteria. The result is a set of temporally separated clusters interleaved by sub-sequences of unclustered…
We consider the problem of learning overcomplete dictionaries in the context of sparse coding, where each sample selects a sparse subset of dictionary elements. Our main result is a strategy to approximately recover the unknown dictionary…
We provide a novel computer-assisted technique for systematically analyzing first-order methods for optimization. In contrast with previous works, the approach is particularly suited for handling sublinear convergence rates and stochastic…
The large size of nowadays' online multimedia databases makes retrieving their content a difficult and time-consuming task. Users of online sound collections typically submit search queries that express a broad intent, often making the…
In this paper we propose a novel methodology to construct Optimal Classification Trees that takes into account that noisy labels may occur in the training sample. Our approach rests on two main elements: (1) the splitting rules for the…
This paper investigates graph clustering in the planted cluster model in the presence of {\em small clusters}. Traditional results dictate that for an algorithm to provably correctly recover the clusters, {\em all} clusters must be…
Clustering may be the most fundamental problem in unsupervised learning which is still active in machine learning research because its importance in many applications. Popular methods like K-means, may suffer from instability as they are…
We consider the problem of center-based clustering in low-dimensional Euclidean spaces under the perturbation stability assumption. An instance is $\alpha$-stable if the underlying optimal clustering continues to remain optimal even when…
In a geometric $k$-clustering problem the goal is to partition a set of points in $\mathbb{R}^d$ into $k$ subsets such that a certain cost function of the clustering is minimized. We present data structures for orthogonal range-clustering…
Density-based clustering methods often surpass centroid-based counterparts, when addressing data with noise or arbitrary data distributions common in real-world problems. In this study, we reveal a key property intrinsic to density-based…
We introduce a general semiparametric clusterwise elliptical distribution to assess how latent cluster structure shapes continuous outcomes. Using a subjectwise representation, we first estimate cluster-specific mean vectors and a…
The clustering problem, in its many variants, has numerous applications in operations research and computer science (e.g., in applications in bioinformatics, image processing, social network analysis, etc.). As sizes of data sets have grown…
Machine learning algorithms perform well on identifying patterns in many different datasets due to their versatility. However, as one increases the size of the dataset, the computation time for training and using these statistical models…
Most convex and nonconvex clustering algorithms come with one crucial parameter: the $k$ in $k$-means. To this day, there is not one generally accepted way to accurately determine this parameter. Popular methods are simple yet theoretically…
We study a Faulty Congested Clique model, in which an adversary may fail nodes in the network throughout the computation. We show that any task of $O(n\log{n})$-bit input per node can be solved in roughly $n$ rounds, where $n$ is the size…