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This paper presents a comparative analysis of different optimization techniques for the K-means algorithm in the context of big data. K-means is a widely used clustering algorithm, but it can suffer from scalability issues when dealing with…
$k$-means clustering is a well-studied problem due to its wide applicability. Unfortunately, there exist strong theoretical limits on the performance of any algorithm for the $k$-means problem on worst-case inputs. To overcome this barrier,…
Clustering is a critical component of decision-making in todays data-driven environments. It has been widely used in a variety of fields such as bioinformatics, social network analysis, and image processing. However, clustering accuracy…
K-means is undoubtedly the most widely used partitional clustering algorithm. Unfortunately, due to its gradient descent nature, this algorithm is highly sensitive to the initial placement of the cluster centers. Numerous initialization…
This paper concerns the critical decision process of extracting or selecting the features before applying a clustering algorithm. It is not obvious to evaluate the importance of the features since the most popular methods to do it are…
This paper deals with the clustering of univariate observations: given a set of observations coming from $K$ possible clusters, one has to estimate the cluster means. We propose an algorithm based on the minimization of the "KP" criterion…
Clustering is a popular form of unsupervised learning for geometric data. Unfortunately, many clustering algorithms lead to cluster assignments that are hard to explain, partially because they depend on all the features of the data in a…
Kernel $k$-means clustering is a powerful tool for unsupervised learning of non-linearly separable data. Since the earliest attempts, researchers have noted that such algorithms often become trapped by local minima arising from…
The problem of estimating the number of clusters (say k) is one of the major challenges for the partitional clustering. This paper proposes an algorithm named k-SCC to estimate the optimal k in categorical data clustering. For the…
Clustering is an unsupervised learning task that aims to partition data into a set of clusters. In many applications, these clusters correspond to real-world constructs (e.g. electoral districts) whose benefit can only be attained by groups…
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…
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…
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…
In many statistical linear inverse problems, one needs to recover classes of similar curves from their noisy images under an operator that does not have a bounded inverse. Problems of this kind appear in many areas of application.…
We consider the classical $k$-means clustering problem in the setting bi-criteria approximation, in which an algoithm is allowed to output $\beta k > k$ clusters, and must produce a clustering with cost at most $\alpha$ times the to the…
We consider a clustering problem where we observe feature vectors $X_i \in R^p$, $i = 1, 2, \ldots, n$, from $K$ possible classes. The class labels are unknown and the main interest is to estimate them. We are primarily interested in the…
One of the applications of center-based clustering algorithms such as K-Means is partitioning data points into K clusters. In some examples, the feature space relates to the underlying problem we are trying to solve, and sometimes we can…
Even with the rise in popularity of over-parameterized models, simple dimensionality reduction and clustering methods, such as PCA and k-means, are still routinely used in an amazing variety of settings. A primary reason is the combination…
Determining the correct number of clusters (CNC) is an important task in data clustering and has a critical effect on finalizing the partitioning results. K-means is one of the popular methods of clustering that requires CNC. Validity index…
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…