相关论文: Size Matters: Cardinality-Constrained Clustering a…

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…

Motivated by the fact that distances between data points in many real-world clustering instances are often based on heuristic measures, Bilu and Linial~\cite{BL} proposed analyzing objective based clustering problems under the assumption…

We initiate the study of the following general clustering problem. We seek to partition a given set $P$ of data points into $k$ clusters by finding a set $X$ of $k$ centers and assigning each data point to one of the centers. The cost of a…

This paper considers coresets for the robust $k$-medians problem with $m$ outliers, and new constructions in various metric spaces are obtained. Specifically, for metric spaces with a bounded VC or doubling dimension $d$, the coreset size…

We investigate how pair-wise data augmentation techniques like Mixup affect the sample complexity of finding optimal decision boundaries in a binary linear classification problem. For a family of data distributions with a separability…

Machine learning components commonly appear in larger decision-making pipelines; however, the model training process typically focuses only on a loss that measures accuracy between predicted values and ground truth values. Decision-focused…

Due to their conceptual simplicity, k-means algorithm variants have been extensively used for unsupervised cluster analysis. However, one main shortcoming of these algorithms is that they essentially fit a mixture of identical spherical…

Robust classification becomes challenging when each class consists of multiple subclasses. Examples include multi-font optical character recognition and automated protein function prediction. In correlation-based nearest-neighbor…

We study the connections between spectral clustering and the problems of maximum margin clustering, and estimation of the components of level sets of a density function. Specifically, we obtain bounds on the eigenvectors of graph Laplacian…

This paper examines the problem of locating outlier columns in a large, otherwise low-rank, matrix. We propose a simple two-step adaptive sensing and inference approach and establish theoretical guarantees for its performance; our results…

Manifold clustering, with its exceptional ability to capture complex data structures, holds a pivotal position in cluster analysis. However, existing methods often focus only on finding the optimal combination between K-means and manifold…

We study $k$-clustering problems with lower bounds, including $k$-median and $k$-means clustering with lower bounds. In addition to the point set $P$ and the number of centers $k$, a $k$-clustering problem with (uniform) lower bounds gets a…

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…

For a certain class of distributions, we prove that the linear programming relaxation of $k$-medoids clustering---a variant of $k$-means clustering where means are replaced by exemplars from within the dataset---distinguishes points drawn…

The analysis of continously larger datasets is a task of major importance in a wide variety of scientific fields. In this sense, cluster analysis algorithms are a key element of exploratory data analysis, due to their easiness in the…

We examine overlapping clustering schemes with functorial constraints, in the spirit of Carlsson--Memoli. This avoids issues arising from the chaining required by partition-based methods. Our principal result shows that any clustering…

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…

We study the theoretical and practical runtime limits of k-means and k-median clustering on large datasets. Since effectively all clustering methods are slower than the time it takes to read the dataset, the fastest approach is to quickly…

In an industrial context, the activity of sensors is recorded at a high frequency. A challenge is to automatically detect abnormal measurement behavior. Considering the sensor measures as functional data, the problem can be formulated as…

Finding optimal join orders is among the most crucial steps to be performed by query optimisers. Though extensively studied in data management research, the problem remains far from solved: While query optimisers rely on exhaustive search…