arXiv research

A main task in data analysis is to organize data points into coherent groups or clusters. The stochastic block model is a probabilistic model for the cluster structure. This model prescribes different probabilities for the presence of edges within a cluster and between different clusters. We assume that the cluster ass…

Clusters on simple manifolds have connected boundaries.

A lens cluster minimizes perimeter in the plane with given area constraints.

Construct locally minimizing $(1,2)$-clusters with prescribed asymptotic geometry.

A new k-means variant minimizes pairwise distances within clusters.

Network Lasso clusters sparse graph clusters efficiently.

CCMM efficiently solves large-scale convex clustering problems.

SimpleMKKM improves multi-kernel clustering efficiency.

The paper proves an infinite double bubble theorem in higher dimensions.

Proposes a new clustering method based on expectiles for non-spherical clusters.

CLASSIX is a fast and explainable clustering method that sorts data and merges groups.

We consider a decomposition method for compressive streaming data in the context of online compressive Robust Principle Component Analysis (RPCA). The proposed decomposition solves an $n$-$\ell_1$ cluster-weighted minimization to decompose a sequence of frames (or vectors), into sparse and low-rank components, from com…

ALMA improves clustering of multilayer networks.

Convex clustering solves a stable optimization problem for clustering.

Connectedness of small clusters in Riemannian and Finsler manifolds proven.

Paper introduces scalable clustering for large datasets with outliers.

New spectral clustering method using LASSO regularization for robust graph partitioning.

Adaptive clustering and personalization algorithms minimize regret in multi-agent stochastic linear bandits.

A new framework for predictive clustering and optimization.

New framework minimizes interference and selection bias in network A/B testing.

Hierarchical clustering is a popular method for analyzing data which associates a tree to a dataset. Hartigan consistency has been used extensively as a framework to analyze such clustering algorithms from a statistical point of view. Still, as we show in the paper, a tree which is Hartigan consistent with a given dens…

The main contribution of the paper is a new approach to subspace clustering that is significantly more computationally efficient and scalable than existing state-of-the-art methods. The central idea is to modify the regression technique in sparse subspace clustering (SSC) by replacing the $\ell_1$ minimization with a g…

Clustering is a fundamental problem in many scientific applications. Standard methods such as $k$-means, Gaussian mixture models, and hierarchical clustering, however, are beset by local minima, which are sometimes drastically suboptimal. Recently introduced convex relaxations of $k$-means and hierarchical clustering s…

The paper tackles fair correlation clustering with fairness constraints.

Clustering analysis by nonnegative low-rank approximations has achieved remarkable progress in the past decade. However, most approximation approaches in this direction are still restricted to matrix factorization. We propose a new low-rank learning method to improve the clustering performance, which is beyond matrix f…

Classical clustering algorithms typically either lack an underlying probability framework to make them predictive or focus on parameter estimation rather than defining and minimizing a notion of error. Recent work addresses these issues by developing a probabilistic framework based on the theory of random labeled point…

We present a framework for clustering with cluster-specific feature selection. The framework, CRAFT, is derived from asymptotic log posterior formulations of nonparametric MAP-based clustering models. CRAFT handles assorted data, i.e., both numeric and categorical data, and the underlying objective functions are intuit…

The MBO scheme for data clustering is analyzed in the large data limit, proving convergence to optimal partition problems.

This paper considers the problem of clustering a partially observed unweighted graph---i.e., one where for some node pairs we know there is an edge between them, for some others we know there is no edge, and for the remaining we do not know whether or not there is an edge. We want to organize the nodes into disjoint cl…

We introduce a principled method for the signed clustering problem, where the goal is to partition a graph whose edge weights take both positive and negative values, such that edges within the same cluster are mostly positive, while edges spanning across clusters are mostly negative. Our method relies on a graph-based …

Data de-duplication is the task of detecting multiple records that correspond to the same real-world entity in a database. In this work, we view de-duplication as a clustering problem where the goal is to put records corresponding to the same physical entity in the same cluster and putting records corresponding to diff…

A novel k-means method for MNAR data improves clustering accuracy.

Efficiently clusters millions of data points with learnable subspace clustering.

In this paper we propose a Deep Autoencoder MIxture Clustering (DAMIC) algorithm based on a mixture of deep autoencoders where each cluster is represented by an autoencoder. A clustering network transforms the data into another space and then selects one of the clusters. Next, the autoencoder associated with this clust…

This paper proposes a novel deep subspace clustering approach which uses convolutional autoencoders to transform input images into new representations lying on a union of linear subspaces. The first contribution of our work is to insert multiple fully-connected linear layers between the encoder layers and their corresp…

The geometrical features of the (non-convex) loss landscape of neural network models are crucial in ensuring successful optimization and, most importantly, the capability to generalize well. While minimizers' flatness consistently correlates with good generalization, there has been little rigorous work in exploring the…

The paper extends fairness to hierarchical clustering, finding efficient algorithms with minimal loss.

One of the longstanding problems in spectral graph clustering (SGC) is the so-called model order selection problem: automated selection of the correct number of clusters. This is equivalent to the problem of finding the number of connected components or communities in an undirected graph. In this paper, we propose AMOS…

Combines OT and PCA for DR, preserving clusters.

The problem of maximizing (or minimizing) the agreement between clusterings, subject to given marginals, can be formally posed under a common framework for several agreement measures. Until now, it was possible to find its solution only through numerical algorithms. Here, an explicit solution is shown for the case wher…

Proposes ITISC for clustering with minimized worst-case expected distortions.

We prove that the optimal way to enclose and separate four planar regions with equal area using the less possible perimeter requires all regions to be connected. Moreover, the topology of such optimal clusters is uniquely determined.

Unsupervised clustering of series using dynamic programming.

Multi-cell cooperative processing with limited backhaul traffic is studied for cellular uplinks. Aiming at reduced backhaul overhead, a sparsity-regularized multi-cell receive-filter design problem is formulated. Both unstructured distributed cooperation as well as clustered cooperation, in which base station groups ar…

By analyzing the foreign exchange market data of various currencies, we derive a hierarchical taxonomy of currencies constructing minimal-spanning trees. Clustered structure of the currencies and the key currency in each cluster are found. The clusters match nicely with the geographical regions of corresponding countri…

Multi-view clustering aims at integrating complementary information from multiple heterogeneous views to improve clustering results. Existing multi-view clustering solutions can only output a single clustering of the data. Due to their multiplicity, multi-view data, can have different groupings that are reasonable and …

We generalize the setting of online clustering of bandits by allowing non-uniform distribution over user frequencies. A more efficient algorithm is proposed with simple set structures to represent clusters. We prove a regret bound for the new algorithm which is free of the minimal frequency over users. The experiments …

Matrix rank minimization problem is in general NP-hard. The nuclear norm is used to substitute the rank function in many recent studies. Nevertheless, the nuclear norm approximation adds all singular values together and the approximation error may depend heavily on the magnitudes of singular values. This might restrict…