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In this paper, we first propose a new iterative algorithm, called the K-sets+ algorithm for clustering data points in a semi-metric space, where the distance measure does not necessarily satisfy the triangular inequality. We show that the…

Minimum sum-of-squares clustering (MSSC) is a widely used clustering model, of which the popular K-means algorithm constitutes a local minimizer. It is well known that the solutions of K-means can be arbitrarily distant from the true MSSC…

With the development of information technology, the application of artificial intelligence and machine learning in the field of education shows great potential. This study aims to explore how to utilize K-means clustering algorithm to…

The learning of mixture models can be viewed as a clustering problem. Indeed, given data samples independently generated from a mixture of distributions, we often would like to find the {\it correct target clustering} of the samples…

Clustering data is a popular feature in the field of unsupervised machine learning. Most algorithms aim to find the best method to extract consistent clusters of data, but very few of them intend to cluster data that share the same…

In general, the clustering problem is NP-hard, and global optimality cannot be established for non-trivial instances. For high-dimensional data, distance-based methods for clustering or classification face an additional difficulty, the…

It has been shown that community detection algorithms work better for clustering tasks than other, more popular methods, such as k-means. In fact, network analysis based methods often outperform more widely used methods and do not suffer…

$k$-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,…

We consider the problem of clustering in the learning-augmented setting, where we are given a data set in $d$-dimensional Euclidean space, and a label for each data point given by an oracle indicating what subsets of points should be…

There is a long history of research into time series clustering using distance-based partitional clustering. Many of the most popular algorithms adapt k-means (also known as Lloyd's algorithm) to exploit time dependencies in the data by…

For very large values of $k$, we consider methods for fast $k$-means clustering of massive datasets with $10^7\sim10^9$ points in high-dimensions ($d\geq100$). All current practical methods for this problem have runtimes at least…

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…

Clustering analysis has received considerable attention in spatial data mining for several years. With the rapid development of the geospatial information technologies, the size of spatial information data is growing exponentially which…

Clustering is a widely used technique with a long and rich history in a variety of areas. However, most existing algorithms do not scale well to large datasets, or are missing theoretical guarantees of convergence. This paper introduces a…

Clustering is often used for discovering structure in data. Clustering systems differ in the objective function used to evaluate clustering quality and the control strategy used to search the space of clusterings. Ideally, the search…

Object-centric representations using slots have shown the advances towards efficient, flexible and interpretable abstraction from low-level perceptual features in a compositional scene. Current approaches randomize the initial state of…

Traditionally, practitioners initialize the {\tt k-means} algorithm with centers chosen uniformly at random. Randomized initialization with uneven weights ({\tt k-means++}) has recently been used to improve the performance over this…

Clustering is an important exploratory data analysis technique to group objects based on their similarity. The widely used $K$-means clustering method relies on some notion of distance to partition data into a fewer number of groups. In the…

Clustering plays a crucial role in computer science, facilitating data analysis and problem-solving across numerous fields. By partitioning large datasets into meaningful groups, clustering reveals hidden structures and relationships within…

Fast and high quality document clustering is an important task in organizing information, search engine results obtaining from user query, enhancing web crawling and information retrieval. With the large amount of data available and with a…