相关论文: Helly-Type Theorems in Property Testing

We present a simple sublinear time algorithm for testing the following geometric property. Let $P_1, ..., P_n$ be $n$ convex sets in $\mathbb{R}^d$ ($n \gg d$), such as polytopes, balls, etc. We assume that the complexity of each set…

We discuss an "operational" approach to testing convex composite hypotheses when the underlying distributions are heavy-tailed. It relies upon Euclidean separation of convex sets and can be seen as an extension of the approach to testing by…

A family of sets has the $(p,q)$ property if among any $p$ members of the family some $q$ have a nonempty intersection. It is shown that for every $p\ge q\ge d+1$ there is a $c=c(p,q,d)<\infty$ such that for every family $\scr F$ of…

Designing efficient, effective, and consistent metric clustering algorithms is a significant challenge attracting growing attention. Traditional approaches focus on the stability of cluster centers; unfortunately, this neglects the…

Probabilistic clustering models (or equivalently, mixture models) are basic building blocks in countless statistical models and involve latent random variables over discrete spaces. For these models, posterior inference methods can be…

Cluster analysis is a fundamental research issue in statistics and machine learning. In many modern clustering methods, we need to determine whether two subsets of samples come from the same cluster. Since these subsets are usually…

We show that for any compact convex set $K$ in $\mathbb{R}^d$ and any finite family $\mathcal{F}$ of convex sets in $\mathbb{R}^d$, if the intersection of every sufficiently small subfamily of $\mathcal{F}$ contains an isometric copy of $K$…

The $K$-hull of a compact set $A\subset\mathbb{R}^d$, where $K\subset \mathbb{R}^d$ is a fixed compact convex body, is the intersection of all translates of $K$ that contain $A$. A set is called $K$-strongly convex if it coincides with its…

The problem of constrained $k$-center clustering has attracted significant attention in the past decades. In this paper, we study balanced $k$-center cluster where the size of each cluster is constrained by the given lower and upper bounds.…

Clustering is the problem of separating a set of objects into groups (called clusters) so that objects within the same cluster are more similar to each other than to those in different clusters. Spectral clustering is a now well-known…

Clustering is a widely used unsupervised learning method for finding structure in the data. However, the resulting clusters are typically presented without any guarantees on their robustness; slightly changing the used data sample or…

We analyze the clustering problem through a flexible probabilistic model that aims to identify an optimal partition on the sample X 1 , ..., X n. We perform exact clustering with high probability using a convex semidefinite estimator that…

This paper explores hierarchical clustering in the case where pairs of points have dissimilarity scores (e.g. distances) as a part of the input. The recently introduced objective for points with dissimilarity scores results in every tree…

Subspace clustering has been extensively studied from the hypothesis-and-test, algebraic, and spectral clustering based perspectives. Most assume that only a single type/class of subspace is present. Generalizations to multiple types are…

Testing graph cluster structure has been a central object of study in property testing since the foundational work of Goldreich and Ron [STOC'96] on expansion testing, i.e. the problem of distinguishing between a single cluster (an…

The clustering algorithms that view each object data as a single sample drawn from a certain distribution, Gaussian distribution, for example, has been a hot topic for decades. Many clustering algorithms: such as k-means and spectral…

Machine learning and data mining techniques are effective tools to classify large amounts of data. But they tend to preserve any inherent bias in the data, for example, with regards to gender or race. Removing such bias from data or the…

High-dimensional clustering analysis is a challenging problem in statistics and machine learning, with broad applications such as the analysis of microarray data and RNA-seq data. In this paper, we propose a new clustering procedure called…

The clustering of a data set is one of the core tasks in data analytics. Many clustering algorithms exhibit a strong contrast between a favorable performance in practice and bad theoretical worst-cases. Prime examples are least-squares…

We study clustering on graphs with multiple edge types. Our main motivation is that similarities between objects can be measured in many different metrics. For instance similarity between two papers can be based on common authors, where…