Related papers: On the Communication Complexity of Distributed Clu…
In the era of big data, it is necessary to split extremely large data sets across multiple computing nodes and construct estimators using the distributed data. When designing distributed estimators, it is desirable to minimize the amount of…
Suppose $k$ centers are fit to $m$ points by heuristically minimizing the $k$-means cost; what is the corresponding fit over the source distribution? This question is resolved here for distributions with $p\geq 4$ bounded moments; in…
$\renewcommand{\Re}{{\rm I\!\hspace{-0.025em} R}} \newcommand{\eps}{{\varepsilon}} \newcommand{\Coreset}{{\mathcal{S}}} $ In this paper, we show the existence of small coresets for the problems of computing $k$-median and $k$-means…
The area of constrained clustering has been extensively explored by researchers and used by practitioners. Constrained clustering formulations exist for popular algorithms such as k-means, mixture models, and spectral clustering but have…
Motivated by the increasing need for fast processing of large-scale graphs, we study a number of fundamental graph problems in a message-passing model for distributed computing, called $k$-machine model, where we have $k$ machines that…
Ensuring data trustworthiness within individual edge nodes while facilitating collaborative data processing poses a critical challenge in edge computing systems (ECS), particularly in resource-constrained scenarios such as autonomous…
With the huge upsurge of information in day-to-days life, it has become difficult to assemble relevant information in nick of time. But people, always are in dearth of time, they need everything quick. Hence clustering was introduced to…
K-Means clustering still plays an important role in many computer vision problems. While the conventional Lloyd method, which alternates between centroid update and cluster assignment, is primarily used in practice, it may converge to a…
Efficient extraction of useful knowledge from these data is still a challenge, mainly when the data is distributed, heterogeneous and of different quality depending on its corresponding local infrastructure. To reduce the overhead cost,…
We study statistical problems, such as planted clique, its variants, and sparse principal component analysis in the context of average-case communication complexity. Our motivation is to understand the statistical-computational trade-offs…
Center-based clustering (e.g., $k$-means, $k$-medians) and clustering using linear subspaces are two most popular techniques to partition real-world data into smaller clusters. However, when the data consists of sensitive demographic…
$k$-means and $k$-median clustering are powerful unsupervised machine learning techniques. However, due to complicated dependences on all the features, it is challenging to interpret the resulting cluster assignments. Moshkovitz, Dasgupta,…
We study the communication complexity of linear algebraic problems over finite fields in the multi-player message passing model, proving a number of tight lower bounds. Specifically, for a matrix which is distributed among a number of…
This paper investigates the capability of correctly recovering well-separated clusters by various brands of the $k$-means algorithm. The concept of well-separatedness used here is derived directly from the common definition of clusters,…
We describe new lower bounds for randomized communication complexity and query complexity which we call the partition bounds. They are expressed as the optimum value of linear programs. For communication complexity we show that the…
We study the effect that the amount of correlation in a bipartite distribution has on the communication complexity of a problem under that distribution. We introduce a new family of complexity measures that interpolates between the two…
In this work we propose a clustering framework based on the paradigm of transform learning. In simple terms the representation from transform learning is used for K-means clustering; however, the problem is not solved in such a na\"ive…
We consider parameter estimation in distributed networks, where each sensor in the network observes an independent sample from an underlying distribution and has $k$ bits to communicate its sample to a centralized processor which computes…
This paper shows that one can be competitive with the k-means objective while operating online. In this model, the algorithm receives vectors v_1,...,v_n one by one in an arbitrary order. For each vector the algorithm outputs a cluster…
Clustering is a usual unsupervised machine learning technique for grouping the data points into groups based upon similar features. We focus here on unsupervised clustering for contaminated data, i.e in the case where K-medians should be…