Related papers: A Geometric Approach to $k$-means

This work proposes a clusterization algorithm called k-Morphological Sets (k-MS), based on morphological reconstruction and heuristics. k-MS is faster than the CPU-parallel k-Means in worst case scenarios and produces enhanced…

We propose a localized approach to multiple kernel learning that can be formulated as a convex optimization problem over a given cluster structure. For which we obtain generalization error guarantees and derive an optimization algorithm…

Clustering is a fundamental unsupervised learning approach. Many clustering algorithms -- such as $k$-means -- rely on the euclidean distance as a similarity measure, which is often not the most relevant metric for high dimensional data…

Mining clusters from data is an important endeavor in many applications. The $k$-means method is a popular, efficient, and distribution-free approach for clustering numerical-valued data, but does not apply for categorical-valued…

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The $k$-Means clustering problem on $n$ points is NP-Hard for any dimension $d\ge 2$, however, for the 1D case there exists exact polynomial time algorithms. Previous literature reported an $O(kn^2)$ time dynamic programming algorithm that…

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Sum-of-norms clustering is a convex optimization problem whose solution can be used for the clustering of multivariate data. We propose and study a localized version of this method, and show in particular that it can separate arbitrarily…

In this paper, we present a new iterative rounding framework for many clustering problems. Using this, we obtain an $(\alpha_1 + \epsilon \leq 7.081 + \epsilon)$-approximation algorithm for $k$-median with outliers, greatly improving upon…

K-means clustering is widely used in psychological and psychometric research to identify profiles, subgroups, and potential typologies, yet its classical formulation does not test whether such groups exist as latent psychological…

Clustering is an effective technique in data mining to generate groups that are the matter of interest. Among various clustering approaches, the family of k-means algorithms and min-cut algorithms gain most popularity due to their…

We propose k^2-means, a new clustering method which efficiently copes with large numbers of clusters and achieves low energy solutions. k^2-means builds upon the standard k-means (Lloyd's algorithm) and combines a new strategy to accelerate…

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One of the fundamental problems in network analysis is detecting community structure in multi-layer networks, of which each layer represents one type of edge information among the nodes. We propose integrative spectral clustering approaches…

We consider the problem of data clustering with unidentified feature quality and when a small amount of labelled data is provided. An unsupervised sparse clustering method can be employed in order to detect the subgroup of features…

This paper proposes a variant of the normalized cut algorithm for spectral clustering. Although the normalized cut algorithm applies the K-means algorithm to the eigenvectors of a normalized graph Laplacian for finding clusters, our…

Clustering is one of the most fundamental problems in data analysis and it has been studied extensively in the literature. Though many clustering algorithms have been proposed, clustering theories that justify the use of these clustering…

Clustering is a powerful machine learning technique that groups "similar" data points based on their characteristics. Many clustering algorithms work by approximating the minimization of an objective function, namely the sum of…

In this work we propose a clustering framework based on the paradigm of transform learning. In simple terms the representation from transform learning is used for K-means clustering; however, the problem is not solved in such a na\"ive…

We study how to learn multiple dictionaries from a dataset, and approximate any data point by the sum of the codewords each chosen from the corresponding dictionary. Although theoretically low approximation errors can be achieved by the…