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This work proposes a hierarchical clustering algorithm for high-dimensional datasets using the cyclic space of reversible finite cellular automata. In cellular automaton (CA) based clustering, if two objects belong to the same cycle, they…

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…

The joint optimization of representation learning and clustering in the embedding space has experienced a breakthrough in recent years. In spite of the advance, clustering with representation learning has been limited to flat-level…

This paper studies the hierarchical clustering problem, where the goal is to produce a dendrogram that represents clusters at varying scales of a data set. We propose the ParChain framework for designing parallel hierarchical agglomerative…

Metrics on rooted phylogenetic trees are integral to a number of areas of phylogenetic analysis. Cluster-similarity metrics have recently been introduced in order to limit skew in the distribution of distances, and to ensure that trees in…

Spectral clustering algorithms typically require a priori selection of input parameters such as the number of clusters, a scaling parameter for the affinity measure, or ranges of these values for parameter tuning. Despite efforts for…

Efficient extraction of useful knowledge from these data is still a challenge, mainly when the data is distributed, heterogeneous and of different quality depending on its corresponding local infrastructure. To reduce the overhead cost,…

State-of-the-art clustering algorithms use heuristics to partition the feature space and provide little insight into the rationale for cluster membership, limiting their interpretability. In healthcare applications, the latter poses a…

Agglomerative hierarchical clustering is one of the most widely used approaches for exploring how observations in a dataset relate to each other. However, its greedy nature makes it highly sensitive to small perturbations in the data, often…

This paper studies the statistical and computational limits of high-order clustering with planted structures. We focus on two clustering models, constant high-order clustering (CHC) and rank-one higher-order clustering (ROHC), and study the…

When solving ill-posed inverse problems, one often desires to explore the space of potential solutions rather than be presented with a single plausible reconstruction. Valuable insights into these feasible solutions and their associated…

Hierarchical graph clustering is a common technique to reveal the multi-scale structure of complex networks. We propose a novel metric for assessing the quality of a hierarchical clustering. This metric reflects the ability to reconstruct…

Understanding the global organization of complicated and high dimensional data is of primary interest for many branches of applied sciences. It is typically achieved by applying dimensionality reduction techniques mapping the considered…

Recently, a number of competitive methods have tackled unsupervised representation learning by maximising the mutual information between the representations produced from augmentations. The resulting representations are then invariant to…

Merge trees are fundamental structures in topological data analysis. Interleaving distance is a widely accepted metric for comparing merge trees, with applications in visualization and scientific computing. While a greedy algorithm exists…

We present a new method for clustering based on compression. The method doesn't use subject-specific features or background knowledge, and works as follows: First, we determine a universal similarity distance, the normalized compression…

In a world abundant with diverse data arising from complex acquisition techniques, there is a growing need for new data analysis methods. In this paper we focus on high-dimensional data that are organized into several hierarchical datasets.…

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…

After generalizing the concept of clusters to incorporate clusters that are linked to other clusters through some relatively narrow bridges, an approach for detecting patches of separation between these clusters is developed based on an…

The objective of clustering is to discover natural groups in datasets and to identify geometrical structures which might reside there, without assuming any prior knowledge on the characteristics of the data. The problem can be seen as…