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This thesis aims to invent new approaches for making inferences with the k-means algorithm. k-means is an iterative clustering algorithm that randomly assigns k centroids, then assigns data points to the nearest centroid, and updates…

Cluster analysis is one of the primary data analysis technique in data mining and K-means is one of the commonly used partitioning clustering algorithm. In K-means algorithm, resulting set of clusters depend on the choice of initial…

Center-based clustering algorithms (e.g., K-means) are popular for clustering tasks, but they usually struggle to achieve high accuracy on complex datasets. We believe the main reason is that traditional center-based clustering algorithms…

The K-means algorithm is arguably the most popular data clustering method, commonly applied to processed datasets in some "feature spaces", as is in spectral clustering. Highly sensitive to initializations, however, K-means encounters a…

Clustering is one of the widely used techniques to find out patterns from a dataset that can be applied in different applications or analyses. K-means, the most popular and simple clustering algorithm, might get trapped into local minima if…

The aim of the k-means is to minimize squared sum of Euclidean distance from the mean (SSEDM) of each cluster. The k-means can effectively optimize this function, but it is too sensitive for initial centers (seeds). This paper proposed a…

k-means has recently been recognized as one of the best algorithms for clustering unsupervised data. Since k-means depends mainly on distance calculation between all data points and the centers, the time cost will be high when the size of…

K-means defines one of the most employed centroid-based clustering algorithms with performances tied to the data's embedding. Intricate data embeddings have been designed to push $K$-means performances at the cost of reduced theoretical…

We study feature selection for $k$-means clustering. Although the literature contains many methods with good empirical performance, algorithms with provable theoretical behavior have only recently been developed. Unfortunately, these…

We propose a simple and efficient clustering method for high-dimensional data with a large number of clusters. Our algorithm achieves high-performance by evaluating distances of datapoints with a subset of the cluster centres. Our…

In addition to finding meaningful clusters, centroid-based clustering algorithms such as K-means or mean-shift should ideally find centroids that are valid patterns in the input space, representative of data in their cluster. This is…

Due to its simplicity and versatility, k-means remains popular since it was proposed three decades ago. The performance of k-means has been enhanced from different perspectives over the years. Unfortunately, a good trade-off between quality…

The analysis of continously larger datasets is a task of major importance in a wide variety of scientific fields. In this sense, cluster analysis algorithms are a key element of exploratory data analysis, due to their easiness in the…

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…

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…

We study the effects of center initialization on the performance of a family of distributed gradient-based clustering algorithms introduced in [1], that work over connected networks of users. In the considered scenario, each user contains a…

$k$-means algorithm is one of the most classical clustering methods, which has been widely and successfully used in signal processing. However, due to the thin-tailed property of the Gaussian distribution, $k$-means algorithm suffers from…

This paper presents a new way of selecting an initial solution for the k-modes algorithm that allows for a notion of mathematical fairness and a leverage of the data that the common initialisations from literature do not. The method, which…

The k-means algorithm is one of the well-known and most popular clustering algorithms. K-means seeks an optimal partition of the data by minimizing the sum of squared error with an iterative optimization procedure, which belongs to the…

Fuzzy K-Means clustering is a critical technique in unsupervised data analysis. Unlike traditional hard clustering algorithms such as K-Means, it allows data points to belong to multiple clusters with varying degrees of membership,…