Related papers: On the Communication Complexity of Distributed Clu…
Motivated by the increasing need to understand the distributed algorithmic foundations of large-scale graph computations, we study some fundamental graph problems in a message-passing model for distributed computing where $k \geq 2$…
Clustering is a well-studied unsupervised learning task that aims to partition data points into a number of clusters. In many applications, these clusters correspond to real-world constructs (e.g., electoral districts, playlists, TV…
We present an asymptotic criterion to determine the optimal number of clusters in k-means. We consider k-means as data compression, and propose to adopt the number of clusters that minimizes the estimated description length after…
Comparison of three kind of the clustering and find cost function and loss function and calculate them. Error rate of the clustering methods and how to calculate the error percentage always be one on the important factor for evaluating the…
In this work, we study the $k$-median clustering problem with an additional equal-size constraint on the clusters, from the perspective of parameterized preprocessing. Our main result is the first lossy ($2$-approximate) polynomial kernel…
This paper studies clustering of data sequences using the k-medoids algorithm. All the data sequences are assumed to be generated from \emph{unknown} continuous distributions, which form clusters with each cluster containing a composite set…
There has been much interest recently in developing fair clustering algorithms that seek to do justice to the representation of groups defined along sensitive attributes such as race and gender. We observe that clustering algorithms could…
Many algorithms for approximate nearest neighbor search in high-dimensional spaces partition the data into clusters. At query time, in order to avoid exhaustive search, an index selects the few (or a single) clusters nearest to the query…
Determining the randomized (or distributional) communication complexity of disjointness is a central problem in communication complexity, having roots in the foundational work of Babai, Frankl, and Simon in the 1980s and culminating in the…
Clustering is a fundamental data processing task used for grouping records based on one or more features. In the vertically partitioned setting, data is distributed among entities, with each holding only a subset of those features. A key…
We consider the distributed source coding problem in which correlated data picked up by scattered sensors has to be encoded separately and transmitted to a common receiver, subject to a rate-distortion constraint. Although near-tooptimal…
We study the problem of discrete distribution estimation in KL divergence and provide concentration bounds for the Laplace estimator. We show that the deviation from mean scales as $\sqrt{k}/n$ when $n \ge k$, improving upon the best prior…
In this paper, we study clustering with respect to the k-modes objective function, a natural formulation of clustering for categorical data. One of the main contributions of this paper is to establish the connection between k-modes and…
Recent works try to optimise collective communication in grid systems focusing mostly on the optimisation of communications among different clusters. We believe that intra-cluster collective communications should also be optimised, as a way…
The use of distributed optimization in machine learning can be motivated either by the resulting preservation of privacy or the increase in computational efficiency. On the one hand, training data might be stored across multiple devices.…
Clustering is an important tool in data analysis, with K-means being popular for its simplicity and versatility. However, it cannot handle non-linearly separable clusters. Kernel K-means addresses this limitation but requires a large kernel…
Although recent works try to improve collective communication in grid systems by separating intra and inter-cluster communication, the optimisation of communications focus only on inter-cluster communications. We believe, instead, that the…
We initiate the study of a quantity that we call coordination complexity. In a distributed optimization problem, the information defining a problem instance is distributed among $n$ parties, who need to each choose an action, which jointly…
Large data sets often require performing distributed statistical estimation, with a full data set split across multiple machines and limited communication between machines. To study such scenarios, we define and study some refinements of…
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…