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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…
This paper introduces a novel K-means clustering algorithm, an advancement on the conventional Big-means methodology. The proposed method efficiently integrates parallel processing, stochastic sampling, and competitive optimization to…
Clustering is one of the most fundamental tools in the artificial intelligence area, particularly in the pattern recognition and learning theory. In this paper, we propose a simple, but novel approach for variance-based k-clustering tasks,…
A new cluster analysis method, $K$-quantiles clustering, is introduced. $K$-quantiles clustering can be computed by a simple greedy algorithm in the style of the classical Lloyd's algorithm for $K$-means. It can be applied to large and…
Clustering is a key task in machine learning, with $k$-means being widely used for its simplicity and effectiveness. While 1D clustering is common, existing methods often fail to exploit the structure of 1D data, leading to inefficiencies.…
Clustering is one of the most fundamental tools in data science and machine learning, and k-means clustering is one of the most common such methods. There is a variety of approximate algorithms for the k-means problem, but computing the…
The k-means clustering algorithm is a popular algorithm that partitions data into k clusters. There are many improvements to accelerate the standard algorithm. Most current research employs upper and lower bounds on point-to-cluster…
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…
Assignment methods are at the heart of many algorithms for unsupervised learning and clustering - in particular, the well-known K-means and Expectation-Maximization (EM) algorithms. In this work, we study several different methods of…
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 one of the most important tools for analysis of large datasets, and perhaps the most popular clustering algorithm is Lloyd's algorithm for $k$-means. This algorithm takes $n$ vectors $V=[v_1,\dots,v_n]\in\mathbb{R}^{d\times…
Clustering techniques are very attractive for extracting and identifying patterns in datasets. However, their application to very large spatial datasets presents numerous challenges such as high-dimensionality data, heterogeneity, and high…
We investigate the complexity of solving stable or perturbation-resilient instances of $k$-Means and $k$-Median clustering in fixed dimension Euclidean metrics (more generally doubling metrics). The notion of stable (perturbation resilient)…
We consider a network of binary-valued sensors with a fusion center. The fusion center has to perform K-means clustering on the binary data transmitted by the sensors. In order to reduce the amount of data transmitted within the network,…
We propose a robust clustering framework for high-dimensional data with heavy tails and a large fraction of irrelevant variables. The method replaces the mean updates of Lloyd's $K$-means with \emph{spatial medians} to enhance robustness.…
A new procedure for simultaneously finding the optimal cluster structure of multivariate functional objects and finding the subspace to represent the cluster structure is presented. The method is based on the $k$-means criterion for…
Advances made to the traditional clustering algorithms solves the various problems such as curse of dimensionality and sparsity of data for multiple attributes. The traditional H-K clustering algorithm can solve the randomness and apriority…
In traditional k-fold cross-validation, each instance is used ($k-1$) times for training and once for testing, leading to redundancy that lets many instances disproportionately influence the learning phase. We introduce Irredundant $k$-fold…
In this contribution, the clustering procedure based on K-Means algorithm is studied as an inverse problem, which is a special case of the illposed problems. The attempts to improve the quality of the clustering inverse problem drive to…
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…