Related papers: HG-means: A scalable hybrid genetic algorithm for …

Many clustering algorithms exist that estimate a cluster centroid, such as K-means, K-medoids or mean-shift, but no algorithm seems to exist that clusters data by returning exactly K meaningful modes. We propose a natural definition of a…

The Metropolis-Hastings (MH) algorithm is one of the most widely used Markov Chain Monte Carlo schemes for generating samples from Bayesian posterior distributions. The algorithm is asymptotically exact, flexible and easy to implement.…

Clustering large, mixed data is a central problem in data mining. Many approaches adopt the idea of k-means, and hence are sensitive to initialisation, detect only spherical clusters, and require a priori the unknown number of clusters. We…

In this paper we target the class of modal clustering methods where clusters are defined in terms of the local modes of the probability density function which generates the data. The most well-known modal clustering method is the k-means…

The problem of constrained clustering has attracted significant attention in the past decades. In this paper, we study the balanced $k$-center, $k$-median, and $k$-means clustering problems where the size of each cluster is constrained by…

Among all the partition based clustering algorithms K-means is the most popular and well known method. It generally shows impressive results even in considerably large data sets. The computational complexity of K-means does not suffer from…

We present a new clustering algorithm called k-means-u* which in many cases is able to significantly improve the clusterings found by k-means++, the current de-facto standard for clustering in Euclidean spaces. First we introduce the…

The k-means++ seeding algorithm is one of the most popular algorithms that is used for finding the initial $k$ centers when using the k-means heuristic. The algorithm is a simple sampling procedure and can be described as follows: Pick the…

We study how to learn multiple dictionaries from a dataset, and approximate any data point by the sum of the codewords each chosen from the corresponding dictionary. Although theoretically low approximation errors can be achieved by the…

When solving real-world problems, practitioners often hesitate to implement solutions obtained from mathematical models, especially for important decisions. This hesitation stems from practitioners' lack of trust in optimization models and…

Ashtiani et al. proposed a Semi-Supervised Active Clustering framework (SSAC), where the learner is allowed to make adaptive queries to a domain expert. The queries are of the kind "do two given points belong to the same optimal cluster?"…

We consider the problem of clustering with $K$-means and Gaussian mixture models with a constraint on the separation between the centers in the context of real-valued data. We first propose a dynamic programming approach to solving the…

Clustering algorithms have long been the topic of research, representing the more popular side of unsupervised learning. Since clustering analysis is one of the best ways to find some clarity and structure within raw data, this paper…

The K-Means clustering using LLoyd's algorithm is an iterative approach to partition the given dataset into K different clusters. The algorithm assigns each point to the cluster based on the following objective function \[\ \min…

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…

The k-means clustering is one of the most popular clustering algorithms in data mining. Recently a lot of research has been concentrated on the algorithm when the dataset is divided into multiple parties or when the dataset is too large to…

We propose an effective subspace selection scheme as a post-processing step to improve results obtained by sparse subspace clustering (SSC). Our method starts by the computation of stable subspaces using a novel random sampling scheme. Thus…

Common clustering algorithms require multiple scans of all the data to achieve convergence, and this is prohibitive when large databases, with data arriving in streams, must be processed. Some algorithms to extend the popular K-means method…

A least squares semi-supervised local clustering algorithm based on the idea of compressed sensing is proposed to extract clusters from a graph with known adjacency matrix. The algorithm is based on a two-stage approach similar to the one…

This paper provides new algorithms for distributed clustering for two popular center-based objectives, k-median and k-means. These algorithms have provable guarantees and improve communication complexity over existing approaches. Following…