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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…
K-plane clustering (KPC), hyperplane clustering, and mixture regression all essentially fall within the same class of problems. This problem can be conceptualized as clustering in relatively high-dimensional K subspaces or K linear…
Clustering is one of the most fundamental and wide-spread techniques in exploratory data analysis. Yet, the basic approach to clustering has not really changed: a practitioner hand-picks a task-specific clustering loss to optimize and fit…
In this paper, a novel method to perform model-based clustering of time series is proposed. The procedure relies on two iterative steps: (i) K global forecasting models are fitted via pooling by considering the series pertaining to each…
Loss-based clustering methods, such as k-means and its variants, are standard tools for finding groups in data. However, the lack of quantification of uncertainty in the estimated clusters is a disadvantage. Model-based clustering based on…
Data clustering is a fundamental problem with a wide range of applications. Standard methods, eg the $k$-means method, usually require solving a non-convex optimization problem. Recently, total variation based convex relaxation to the…
As a kind of basic machine learning method, clustering algorithms group data points into different categories based on their similarity or distribution. We present a clustering algorithm by finding hyper-planes to distinguish the data…
This paper presents a novel method for clustering surfaces. The proposal involves first using basis functions in a tensor product to smooth the data and thus reduce the dimension to a finite number of coefficients, and then using these…
This paper presents a practical global optimization algorithm for the K-center clustering problem, which aims to select K samples as the cluster centers to minimize the maximum within-cluster distance. This algorithm is based on a…
We propose a simple and efficient clustering method for high-dimensional data with a large number of clusters. Our algorithm achieves high-performance by evaluating distances of datapoints with a subset of the cluster centres. Our…
We present an approach to model-based hierarchical clustering by formulating an objective function based on a Bayesian analysis. This model organizes the data into a cluster hierarchy while specifying a complex feature-set partitioning that…
This paper considers a canonical clustering problem where one receives unlabeled samples drawn from a balanced mixture of two elliptical distributions and aims for a classifier to estimate the labels. Many popular methods including PCA and…
We review clustering as an analysis tool and the underlying concepts from an introductory perspective. What is clustering and how can clusterings be realised programmatically? How can data be represented and prepared for a clustering task?…
We consider clustering in group decision making where the opinions are given by pairwise comparison matrices. In particular, the k-medoids model is suggested to classify the matrices since it has a linear programming problem formulation…
We introduce a novel end-to-end approach for learning to cluster in the absence of labeled examples. Our clustering objective is based on optimizing normalized cuts, a criterion which measures both intra-cluster similarity as well as…
The classical k-means clustering, based on distances computed from all data features, cannot be directly applied to incomplete data with missing values. A natural extension of k-means to missing data, namely k-POD, uses only the observed…
Mixture models extend the toolbox of clustering methods available to the data analyst. They allow for an explicit definition of the cluster shapes and structure within a probabilistic framework and exploit estimation and inference…
We propose a new clustering approach, called optimality-based clustering, that clusters data points based on their latent decision-making preferences. We assume that each data point is a decision generated by a decision-maker who…
Partially recorded data are frequently encountered in many applications and usually clustered by first removing incomplete cases or features with missing values, or by imputing missing values, followed by application of a clustering…
The goal of lifetime clustering is to develop an inductive model that maps subjects into $K$ clusters according to their underlying (unobserved) lifetime distribution. We introduce a neural-network based lifetime clustering model that can…