Related papers: Are Cluster Validity Measures (In)valid?
An important issue in clustering concerns the avoidance of false positives while searching for clusters. This work addressed this problem considering agglomerative methods, namely single, average, median, complete, centroid and Ward's…
The paper presents a cursory examination of clustering, focusing on a rarely explored field of hierarchy of clusters. Based on this, a short discussion of clustering quality measures is presented and the F-score measure is examined more…
Clustering is one of the main tasks in exploratory data analysis and descriptive statistics where the main objective is partitioning observations in groups. Clustering has a broad range of application in varied domains like climate,…
Unsupervised clustering of feature matrix data is an indispensible technique for exploratory data analysis and quality control of experimental data. However, clusters are difficult to assess for statistical significance in an objective way.…
The performance (accuracy and robustness) of several clustering algorithms is studied for linearly dependent random variables in the presence of noise. It turns out that the error percentage quickly increases when the number of observations…
This report provides an exploration of different distance measures that can be used with the $K$-means algorithm for cluster analysis. Specifically, we investigate the Mahalanobis distance, and critically assess any benefits it may have…
While clustering is ubiquitously used across science and industry, uncertainty in cluster assignments is rarely quantified with rigorous guarantees. We propose a novel conformal inference framework for clustering that returns confidence…
Many studies in data mining have proposed a new learning called semi-Supervised. Such type of learning combines unlabeled and labeled data which are hard to obtain. However, in unsupervised methods, the only unlabeled data are used. The…
Model selection in clustering requires (i) to specify a suitable clustering principle and (ii) to control the model order complexity by choosing an appropriate number of clusters depending on the noise level in the data. We advocate an…
The input of most clustering algorithms is a symmetric matrix quantifying similarity within data pairs. Such a matrix is here turned into a quadratic set function measuring cluster score or similarity within data subsets larger than pairs.…
This paper is a chapter in the forthcoming Handbook of Cluster Analysis, Hennig et al. (2015). For definitions of basic clustering methods and some further methodology, other chapters of the Handbook are referred to. To read this version of…
We define the notion of a well-clusterable data set combining the point of view of the objective of $k$-means clustering algorithm (minimising the centric spread of data elements) and common sense (clusters shall be separated by gaps). We…
Deep image clustering methods are typically evaluated on small-scale balanced classification datasets while feature-based $k$-means has been applied on proprietary billion-scale datasets. In this work, we explore the performance of…
Comparing clusterings is central to evaluating unsupervised models, yet the many existing similarity measures can produce widely divergent, sometimes contradictory, evaluations. Clustering similarity measures are typically organized into…
We introduce a cluster evaluation technique called Tree Index. Our Tree Index algorithm aims at describing the structural information of the clustering rather than the quantitative format of cluster-quality indexes (where the representation…
Determining the number of clusters is a central challenge in unsupervised learning, where ground-truth labels are unavailable. The Silhouette coefficient is a widely used internal validation metric for this task, yet its standard…
Clustering algorithms are an essential part of the unsupervised data science ecosystem, and extrinsic evaluation of clustering algorithms requires a method for comparing the detected clustering to a ground truth clustering. In a general…
Metric clustering is fundamental in areas ranging from Combinatorial Optimization and Data Mining, to Machine Learning and Operations Research. However, in a variety of situations we may have additional requirements or knowledge, distinct…
Clustering a graph means identifying internally dense subgraphs which are only sparsely interconnected. Formalizations of this notion lead to measures that quantify the quality of a clustering and to algorithms that actually find…
Assessing how adequate clusters fit a dataset and finding an optimum number of clusters is a difficult process. A membership matrix and the degree of membership matrix is suggested to determine the homogeneity of a cluster fit. Maximisation…