Related papers: Unimodal clustering using isotonic regression: ISO…
Spectral clustering has found extensive use in many areas. Most traditional spectral clustering algorithms work in three separate steps: similarity graph construction; continuous labels learning; discretizing the learned labels by k-means…
We study the clustering task under anisotropic Gaussian Mixture Models where the covariance matrices from different clusters are unknown and are not necessarily the identical matrix. We characterize the dependence of signal-to-noise ratios…
Clustering algorithms remain valuable tools for grouping and summarizing the most important aspects of data. Example areas where this is the case include image segmentation, dimension reduction, signals analysis, model order reduction,…
Recent spectral clustering methods are a propular and powerful technique for data clustering. These methods need to solve the eigenproblem whose computational complexity is $O(n^3)$, where $n$ is the number of data samples. In this paper, a…
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…
Clustering partitions a dataset such that observations placed together in a group are similar but different from those in other groups. Hierarchical and $K$-means clustering are two approaches but have different strengths and weaknesses.…
Datasets in high-dimension do not typically form clusters in their original space; the issue is worse when the number of points in the dataset is small. We propose a low-computation method to find statistically significant clustering…
Many clustering problems in computer vision and other contexts are also classification problems, where each cluster shares a meaningful label. Subspace clustering algorithms in particular are often applied to problems that fit this…
This paper presents a neural network-based end-to-end clustering framework. We design a novel strategy to utilize the contrastive criteria for pushing data-forming clusters directly from raw data, in addition to learning a feature embedding…
This paper studies a factor modeling-based approach for clustering high-dimensional data generated from a mixture of strongly correlated variables. Statistical modeling with correlated structures pervades modern applications in economics,…
We discuss topological aspects of cluster analysis and show that inferring the topological structure of a dataset before clustering it can considerably enhance cluster detection: theoretical arguments and empirical evidence show that…
Clustering is widely used in unsupervised learning to find homogeneous groups of observations within a dataset. However, clustering mixed-type data remains a challenge, as few existing approaches are suited for this task. This study…
Any approach aimed at pasteurizing and quantifying a particular phenomenon must include the use of robust statistical methodologies for data analysis. With this in mind, the purpose of this study is to present statistical approaches that…
We consider the problem of estimating the number of clusters (k) in a dataset. We propose a non-parametric approach to the problem that utilizes similarity graphs to construct a robust statistic that effectively captures similarity…
We propose a new class of models for variable clustering called Asymptotic Independent block (AI-block) models, which defines population-level clusters based on the independence of the maxima of a multivariate stationary mixing random…
Recent advancements in Mixed Integer Optimization (MIO) algorithms, paired with hardware enhancements, have led to significant speedups in resolving MIO problems. These strategies have been utilized for optimal subset selection,…
We address the classical problem of hierarchical clustering, but in a framework where one does not have access to a representation of the objects or their pairwise similarities. Instead, we assume that only a set of comparisons between…
The increasing needs of clustering massive datasets and the high cost of running clustering algorithms poses difficult problems for users. In this context it is important to determine if a data set is clusterable, that is, it may be…
Cluster analysis methods seek to partition a data set into homogeneous subgroups. It is useful in a wide variety of applications, including document processing and modern genetics. Conventional clustering methods are unsupervised, meaning…
In this work, we introduce a novel methodology for divisive hierarchical clustering. Our divisive (``top-down'') approach is motivated by the fact that agglomerative hierarchical clustering (``bottom-up''), which is commonly used for…