Related papers: Recovering Trees with Convex Clustering
We investigate the problem of exact cluster recovery using oracle queries. Previous results show that clusters in Euclidean spaces that are convex and separated with a margin can be reconstructed exactly using only $O(\log n)$ same-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…
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 generalize finite-sample bounds for convex clustering to the setting where affinity weights appearing in the objective correspond to a general connected graph. These bounds and their analysis lead to a better understanding of clustering…
Convex clustering has recently garnered increasing interest due to its attractive theoretical and computational properties, but its merits become limited in the face of high-dimensional data. In such settings, pairwise affinity terms that…
Clustering, like covariate selection for classification, is an important step to compress and interpret the data. However, clustering of covariates is often performed independently of the classification step, which can lead to undesirable…
Convex clustering is an attractive clustering algorithm with favorable properties such as efficiency and optimality owing to its convex formulation. It is thought to generalize both k-means clustering and agglomerative clustering. However,…
Convex clustering is a modern clustering framework that guarantees globally optimal solutions and performs comparably to other advanced clustering methods. However, obtaining a complete dendrogram (clusterpath) for large-scale datasets…
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…
Convex clustering is a modern method with both hierarchical and $k$-means clustering characteristics. Although convex clustering can capture complex clustering structures hidden in data, the existing convex clustering algorithms are not…
In this paper, we study the strength of convex relaxations obtained by convexification of aggregation of constraints for a set $S$ described by two bilinear bipartite equalities. Aggregation is the process of rescaling the original…
This survey reviews a clustering method based on solving a convex optimization problem. Despite the plethora of existing clustering methods, convex clustering has several uncommon features that distinguish it from prior art. The…
Clustering is a fundamental problem in unsupervised learning. Popular methods like K-means, may suffer from poor performance as they are prone to get stuck in its local minima. Recently, the sum-of-norms (SON) model (also known as the…
Network models provide a powerful and flexible framework for analyzing a wide range of structured data sources. In many situations of interest, however, multiple networks can be constructed to capture different aspects of an underlying…
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…
Sum-of-norms clustering is a method for assigning $n$ points in $\mathbb{R}^d$ to $K$ clusters, $1\le K\le n$, using convex optimization. Recently, Panahi et al.\ proved that sum-of-norms clustering is guaranteed to recover a mixture of…
We study the problem of clustering with relative constraints, where each constraint specifies relative similarities among instances. In particular, each constraint $(x_i, x_j, x_k)$ is acquired by posing a query: is instance $x_i$ more…
Locating the center of convex objects is important in both image processing and unsupervised machine learning/data clustering fields. The automated analysis of biological images uses both of these fields for locating cell nuclei and for…
We study the problem of decomposing (clustering) a tree with respect to costs attributed to pairs of nodes, so as to minimize the sum of costs for those pairs of nodes that are in the same component (cluster). For the general case and for…
Convex clustering is a well-regarded clustering method, resembling the similar centroid-based approach of Lloyd's $k$-means, without requiring a predefined cluster count. It starts with each data point as its centroid and iteratively merges…