Related papers: Fitting a Simplicial Complex using a Variation of …

We study the sample complexity of learning a high-dimensional simplex from a set of points uniformly sampled from its interior. Learning of simplices is a long studied problem in computer science and has applications in computational…

Classical methods to model topological properties of point clouds, such as the Vietoris-Rips complex, suffer from the combinatorial explosion of complex sizes. We propose a novel technique to approximate a multi-scale filtration of the Rips…

We consider the problem of clustering with $K$-means and Gaussian mixture models with a constraint on the separation between the centers in the context of real-valued data. We first propose a dynamic programming approach to solving the…

We propose a new method for clustering based on the local minimization of the \gamma-divergence, which we call the spontaneous clustering. The greatest advantage of the proposed method is that it automatically detects the number of clusters…

This paper presents a comparative analysis of different optimization techniques for the K-means algorithm in the context of big data. K-means is a widely used clustering algorithm, but it can suffer from scalability issues when dealing with…

Minimum sum-of-squares clustering (MSSC) is a widely used clustering model, of which the popular K-means algorithm constitutes a local minimizer. It is well known that the solutions of K-means can be arbitrarily distant from the true MSSC…

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…

$k$-center is one of the most popular clustering models. While it admits a simple 2-approximation in polynomial time in general metrics, the Euclidean version is NP-hard to approximate within a factor of 1.93, even in the plane, if one…

The minimum sum-of-squares clustering (MSSC), or k-means type clustering, is traditionally considered an unsupervised learning task. In recent years, the use of background knowledge to improve the cluster quality and promote…

Point cloud panoptic segmentation is a challenging task that seeks a holistic solution for both semantic and instance segmentation to predict groupings of coherent points. Previous approaches treat semantic and instance segmentation as…

Given a stream of points in a metric space, is it possible to maintain a constant approximate clustering by changing the cluster centers only a small number of times during the entire execution of the algorithm? This question received…

Multi-objective optimization problems require simultaneously optimizing two or more objective functions. Many studies have reported that the solution set of an M-objective optimization problem often forms an (M-1)-dimensional topological…

Clustering can be defined as the process of assembling objects into a number of groups whose elements are similar to each other in some manner. As a technique that is used in many domains, such as face clustering, plant categorization,…

Subspace clustering (SC) aims to cluster data lying in a union of low-dimensional subspaces. Usually, SC learns an affinity matrix and then performs spectral clustering. Both steps suffer from high time and space complexity, which leads to…

We study the classical metric $k$-median clustering problem over a set of input rankings (i.e., permutations), which has myriad applications, from social-choice theory to web search and databases. A folklore algorithm provides a…

This thesis aims to invent new approaches for making inferences with the k-means algorithm. k-means is an iterative clustering algorithm that randomly assigns k centroids, then assigns data points to the nearest centroid, and updates…

We show a new reduction method on a simplicial complex. This reduction works well with relations and Dowker complexes. The idea is to add a dummy vertex $ z $ to the simplicial complex $K$. We add the simplicial cone $ z * L $ to $K$ where…

Organizing data into semantically more meaningful is one of the fundamental modes of understanding and learning. Cluster analysis is a formal study of methods for understanding and algorithm for learning. K-mean clustering algorithm is one…

We present in this paper two different classes of general $K$-splitting algorithms for solving finite-dimensional convex optimization problems. Under the assumption that the function being minimized has a Lipschitz continuous gradient, we…

In this work, we study diversity-aware clustering problems where the data points are associated with multiple attributes resulting in intersecting groups. A clustering solution needs to ensure that the number of chosen cluster centers from…