Related papers: Distributionally Robust K-Means Clustering
Distributional (or distribution-valued) data are a new type of data arising from several sources and are considered as realizations of distributional variables. A new set of fuzzy c-means algorithms for data described by distributional…
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…
Biclustering is the task of simultaneously clustering the rows and columns of the data matrix into different subgroups such that the rows and columns within a subgroup exhibit similar patterns. In this paper, we consider the case of…
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…
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…
Clustering is one of the most fundamental problems in unsupervised learning with a large number of applications. However, classical clustering algorithms assume that the data is static, thus failing to capture many real-world applications…
This paper presents a novel Wasserstein distributionally robust control and state estimation algorithm for partially observable linear stochastic systems, where the probability distributions of disturbances and measurement noises are…
We propose a novel approach to the problem of multilevel clustering, which aims to simultaneously partition data in each group and discover grouping patterns among groups in a potentially large hierarchically structured corpus of data. Our…
Neural networks are vulnerable to adversarial examples and researchers have proposed many heuristic attack and defense mechanisms. We address this problem through the principled lens of distributionally robust optimization, which guarantees…
We propose a method for high dimensional multivariate regression that is robust to random error distributions that are heavy-tailed or contain outliers, while preserving estimation accuracy in normal random error distributions. We extend…
One of the applications of center-based clustering algorithms such as K-Means is partitioning data points into K clusters. In some examples, the feature space relates to the underlying problem we are trying to solve, and sometimes we can…
Bayesian models offer great flexibility for clustering applications---Bayesian nonparametrics can be used for modeling infinite mixtures, and hierarchical Bayesian models can be utilized for sharing clusters across multiple data sets. For…
There has been considerable work on improving popular clustering algorithm `K-means' in terms of mean squared error (MSE) and speed, both. However, most of the k-means variants tend to compute distance of each data point to each cluster…
$k$-means clustering is a well-studied problem due to its wide applicability. Unfortunately, there exist strong theoretical limits on the performance of any algorithm for the $k$-means problem on worst-case inputs. To overcome this barrier,…
There has been much interest recently in developing fair clustering algorithms that seek to do justice to the representation of groups defined along sensitive attributes such as race and gender. We observe that clustering algorithms could…
K-Means clustering algorithm is one of the most commonly used clustering algorithms because of its simplicity and efficiency. K-Means clustering algorithm based on Euclidean distance only pays attention to the linear distance between…
K-means plays a vital role in data mining and is the simplest and most widely used algorithm under the Euclidean Minimum Sum-of-Squares Clustering (MSSC) model. However, its performance drastically drops when applied to vast amounts of…
Clustering is a fundamental data mining tool that aims to divide data into groups of similar items. Generally, intuition about clustering reflects the ideal case -- exact data sets endowed with flawless dissimilarity between individual…
Certified robustness in machine learning has primarily focused on adversarial perturbations of the input with a fixed attack budget for each point in the data distribution. In this work, we present provable robustness guarantees on the…
We introduce a distributionally robust minimium mean square error estimation model with a Wasserstein ambiguity set to recover an unknown signal from a noisy observation. The proposed model can be viewed as a zero-sum game between a…