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There are many distance-based methods for classification and clustering, and for data with a high number of dimensions and a lower number of observations, processing distances is computationally advantageous compared to the raw data matrix.…
We study augmenting a plane Euclidean network with a segment, called a shortcut, to minimize the largest distance between any two points along the edges of the resulting network. Problems of this type have received considerable attention…
Clustering high-dimensional datasets is hard because interpoint distances become less informative in high-dimensional spaces. We present a clustering algorithm that performs nonlinear dimensionality reduction and clustering jointly. The…
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…
Many methods have been developed for data clustering, such as k-means, expectation maximization and algorithms based on graph theory. In this latter case, graphs are generally constructed by taking into account the Euclidian distance as a…
The topological patterns exhibited by many real-world networks motivate the development of topology-based methods for assessing the similarity of networks. However, extracting topological structure is difficult, especially for large and…
Clustering methods are a valuable tool for the identification of patterns in high dimensional data with applications in many scientific problems. However, quantifying uncertainty in clustering is a challenging problem, particularly when…
We present a new preprocessing algorithm for embedding the nodes of a given edge-weighted undirected graph into a Euclidean space. The Euclidean distance between any two nodes in this space approximates the length of the shortest path…
Recent work on deep clustering has found new promising methods also for constrained clustering problems. Their typically pairwise constraints often can be used to guide the partitioning of the data. Many problems however, feature…
Efficient algorithms for solving optimal transport problems are important for measuring and optimizing distances between functions. In the $L^2$ semi-discrete context, this problem consists of finding a map from a continuous density…
Recent literature has shown that symbolic data, such as text and graphs, is often better represented by points on a curved manifold, rather than in Euclidean space. However, geometrical operations on manifolds are generally more complicated…
Clustering ensemble, or consensus clustering, has emerged as a powerful tool for improving both the robustness and the stability of results from individual clustering methods. Weighted clustering ensemble arises naturally from clustering…
Many statistical and machine learning approaches rely on pairwise distances between data points. The choice of distance metric has a fundamental impact on performance of these procedures, raising questions about how to appropriately…
Even though clustering trajectory data attracted considerable attention in the last few years, most of prior work assumed that moving objects can move freely in an euclidean space and did not consider the eventual presence of an underlying…
Clustering, as an unsupervised technique, plays a pivotal role in various data analysis applications. Among clustering algorithms, Spectral Clustering on Euclidean Spaces has been extensively studied. However, with the rapid evolution of…
The $(k, z)$-Clustering problem in Euclidean space $\mathbb{R}^d$ has been extensively studied. Given the scale of data involved, compression methods for the Euclidean $(k, z)$-Clustering problem, such as data compression and dimension…
We present a new approach to approximate nearest-neighbor queries in fixed dimension under a variety of non-Euclidean distances. We are given a set $S$ of $n$ points in $\mathbb{R}^d$, an approximation parameter $\varepsilon > 0$, and a…
We propose efficient algorithms for two key tasks in the analysis of large nonuniform networks: uniform node sampling and cluster detection. Our sampling technique is based on augmenting a simple, but slowly mixing uniform MCMC sampler with…
Deep embedding methods have influenced many areas of unsupervised learning. However, the best methods for learning hierarchical structure use non-Euclidean representations, whereas Euclidean geometry underlies the theory behind many…
A novel elastic time distance for sparse multivariate functional data is proposed and used to develop a robust distance-based two-layer partition clustering method. With this proposed distance, the new approach not only can detect correct…