Related papers: Information theoretical clustering is hard to appr…
Handling visual complexity is a challenging problem in visualization owing to the subjectiveness of its definition and the difficulty in devising generalizable quantitative metrics. In this paper we address this challenge by measuring the…
In machine learning and data mining, Cluster analysis is one of the most widely used unsupervised learning technique. Philosophy of this algorithm is to find similar data items and group them together based on any distance function in…
The input to the \emph{sets-$k$-means} problem is an integer $k\geq 1$ and a set $\mathcal{P}=\{P_1,\cdots,P_n\}$ of sets in $\mathbb{R}^d$. The goal is to compute a set $C$ of $k$ centers (points) in $\mathbb{R}^d$ that minimizes the sum…
Projection Pursuit methodology permits to solve the difficult problem of finding an estimate of a density defined on a set of very large dimension. In his seminal article, Huber (see "Projection pursuit", Annals of Statistics, 1985)…
Spectral clustering refers to a family of unsupervised learning algorithms that compute a spectral embedding of the original data based on the eigenvectors of a similarity graph. This non-linear transformation of the data is both the key of…
In this paper, we initiate the study of fair clustering that ensures distributional similarity among similar individuals. In response to improving fairness in machine learning, recent papers have investigated fairness in clustering…
This paper defines pointwise clustering metrics, a collection of metrics for characterizing the similarity of two clusterings. These metrics have several interesting properties which make them attractive for practical applications. They can…
Motivated by the observation and prediction of clustering behavior for impurities substituted into the host lattice of a real material, and the dramatic impact this can have on electronic properties, we develop a simple approach to describe…
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.…
Finding "true" clusters in a data set is a challenging problem. Clustering solutions obtained using different models and algorithms do not necessarily provide compact and well-separated clusters or the optimal number of clusters. Cluster…
We propose some axioms for hierarchical clustering of probability measures and investigate their ramifications. The basic idea is to let the user stipulate the clusters for some elementary measures. This is done without the need of any…
Unsupervised classification called clustering is a process of organizing objects into groups whose members are similar in some way. Clustering of uncertain data objects is a challenge in spatial data bases. In this paper we use Probability…
Invariant coordinate selection (ICS) and projection pursuit (PP) are two methods that can be used to detect clustering directions in multivariate data by optimizing criteria sensitive to non-normality. In particular, ICS finds clustering…
The group testing problem concerns discovering a small number of defective items within a large population by performing tests on pools of items. A test is positive if the pool contains at least one defective, and negative if it contains no…
Multitarget tracking in the interference environments suffers from the nonuniform, unknown and time-varying clutter, resulting in dramatic performance deterioration. We address this challenge by proposing a robust multitarget tracking…
Traditionally, clustering algorithms focus on partitioning the data into groups of similar instances. The similarity objective, however, is not sufficient in applications where a fair-representation of the groups in terms of protected…
A new cluster validity index is proposed for fuzzy clusters obtained from fuzzy c-means algorithm. The proposed validity index exploits inter-cluster proximity between fuzzy clusters. Inter-cluster proximity is used to measure the degree of…
We propose two probability-like measures of individual cluster-membership certainty which can be applied to a hard partition of the sample such as that obtained from the Partitioning Around Medoids (PAM) algorithm, hierarchical clustering…
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…
Approximating adequate number of clusters in multidimensional data is an open area of research, given a level of compromise made on the quality of acceptable results. The manuscript addresses the issue by formulating a transductive…