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Subspace clustering is the unsupervised grouping of points lying near a union of low-dimensional linear subspaces. Algorithms based directly on geometric properties of such data tend to either provide poor empirical performance, lack…
Clustering is one of the widely used techniques to find out patterns from a dataset that can be applied in different applications or analyses. K-means, the most popular and simple clustering algorithm, might get trapped into local minima if…
Clustering is a critical component of decision-making in todays data-driven environments. It has been widely used in a variety of fields such as bioinformatics, social network analysis, and image processing. However, clustering accuracy…
In this work, we address the unsupervised classification issue by exploiting the general idea of Random Projection Ensemble. Specifically, we propose to generate a set of low dimensional independent random projections and to perform…
Kernel $k$-means clustering can correctly identify and extract a far more varied collection of cluster structures than the linear $k$-means clustering algorithm. However, kernel $k$-means clustering is computationally expensive when the…
The Lloyd-Max algorithm is a classical approach to perform K-means clustering. Unfortunately, its cost becomes prohibitive as the training dataset grows large. We propose a compressive version of K-means (CKM), that estimates cluster…
The primary goal in cluster analysis is to discover natural groupings of objects. The field of cluster analysis is crowded with diverse methods that make special assumptions about data and address different scientific aims. Despite its…
We propose a computationally simple framework for clustering functional data based on Gaussian-process-generated random projections. In this approach, each curve is first projected onto a large collection of independent Gaussian process…
Spectral clustering is a fundamental technique in the field of data mining and information processing. Most existing spectral clustering algorithms integrate dimensionality reduction into the clustering process assisted by manifold learning…
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 propose a novel probabilistic dimensionality reduction framework that can naturally integrate the generative model and the locality information of data. Based on this framework, we present a new model, which is able to learn a smooth…
Given a set of points, clustering consists of finding a partition of a point set into $k$ clusters such that the center to which a point is assigned is as close as possible. Most commonly, centers are points themselves, which leads to the…
Clustering in high-dimensional spaces is a difficult problem which is recurrent in many domains, for example in image analysis. The difficulty is due to the fact that high-dimensional data usually live in different low-dimensional subspaces…
Multidimensional scaling is an important dimension reduction tool in statistics and machine learning. Yet few theoretical results characterizing its statistical performance exist, not to mention any in high dimensions. By considering a…
One key use of k-means clustering is to identify cluster prototypes which can serve as representative points for a dataset. However, a drawback of using k-means cluster centers as representative points is that such points distort the…
This paper presents Orthogonal Subspace Clustering (OSC), an innovative method for high-dimensional data clustering. We first establish a theoretical theorem proving that high-dimensional data can be decomposed into orthogonal subspaces in…
We consider the problem of jointly modeling and clustering populations of tensors by introducing a high-dimensional tensor mixture model with heterogeneous covariances. To effectively tackle the high dimensionality of tensor objects, we…
Convex clustering is a recent stable alternative to hierarchical clustering. It formulates the recovery of progressively coalescing clusters as a regularized convex problem. While convex clustering was originally designed for handling…
We study in this paper the problem of jointly clustering and learning representations. As several previous studies have shown, learning representations that are both faithful to the data to be clustered and adapted to the clustering…
Clustering plays a crucial role in computer science, facilitating data analysis and problem-solving across numerous fields. By partitioning large datasets into meaningful groups, clustering reveals hidden structures and relationships within…