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We study the distances of edges within cliques in a soft random geometric graph on a torus, where the vertices are points of a homogeneous Poisson point process, and far-away points are less likely to be connected than nearby points. We…
Finding the number of meaningful clusters in an unlabeled dataset is important in many applications. Regularized k-means algorithm is a possible approach frequently used to find the correct number of distinct clusters in datasets. The most…
Spectral clustering (SC) and graph-based semi-supervised learning (SSL) algorithms are sensitive to how graphs are constructed from data. In particular if the data has proximal and unbalanced clusters these algorithms can lead to poor…
A new cluster analysis method, $K$-quantiles clustering, is introduced. $K$-quantiles clustering can be computed by a simple greedy algorithm in the style of the classical Lloyd's algorithm for $K$-means. It can be applied to large and…
A commonly used characteristic of statistical dependence of adjacency relations in real networks, the clustering coefficient, evaluates chances that two neighbours of a given vertex are adjacent. An extension is obtained by considering…
Important data mining problems such as nearest-neighbor search and clustering admit theoretical guarantees when restricted to objects embedded in a metric space. Graphs are ubiquitous, and clustering and classification over graphs arise in…
The k-means algorithm is a partitional clustering method. Over 60 years old, it has been successfully used for a variety of problems. The popularity of k-means is in large part a consequence of its simplicity and efficiency. In this paper…
We initiate the study of coresets for clustering in graph metrics, i.e., the shortest-path metric of edge-weighted graphs. Such clustering problems are essential to data analysis and used for example in road networks and data visualization.…
This paper describes a method for clustering data that are spread out over large regions and which dimensions are on different scales of measurement. Such an algorithm was developed to implement a robotics application consisting in sorting…
Standard conformal prediction methods provide a marginal coverage guarantee, which means that for a random test point, the conformal prediction set contains the true label with a user-specified probability. In many classification problems,…
Data clustering is a process of arranging similar data into groups. A clustering algorithm partitions a data set into several groups such that the similarity within a group is better than among groups. In this paper a hybrid clustering…
Classes of graphs with bounded expansion are a generalization of both proper minor closed classes and degree bounded classes. Such classes are based on a new invariant, the greatest reduced average density (grad) of G with rank r,…
A random intersection graph is constructed by assigning independently to each vertex a subset of a given set and drawing an edge between two vertices if and only if their respective subsets intersect. In this paper a model is developed in…
Given a point set S and an unknown metric d on S, we study the problem of efficiently partitioning S into k clusters while querying few distances between the points. In our model we assume that we have access to one versus all queries that…
This paper develops a threshold regression model where an unknown relationship between two variables nonparametrically determines the threshold. We allow the observations to be cross-sectionally dependent so that the model can be applied to…
We propose a new method for clustering based on the local minimization of the \gamma-divergence, which we call the spontaneous clustering. The greatest advantage of the proposed method is that it automatically detects the number of clusters…
We introduce $k$-variance, a generalization of variance built on the machinery of random bipartite matchings. $K$-variance measures the expected cost of matching two sets of $k$ samples from a distribution to each other, capturing local…
Clustering categorical data is an integral part of data mining and has attracted much attention recently. In this paper, we present k-ANMI, a new efficient algorithm for clustering categorical data. The k-ANMI algorithm works in a way that…
K-means is one of the most widely used algorithms for clustering in Data Mining applications, which attempts to minimize the sum of the square of the Euclidean distance of the points in the clusters from the respective means of the…
The threshold network model is a type of finite random graphs. In this paper, we introduce a generalized threshold network model. A pair of vertices with random weights is connected by an edge when real-valued functions of the pair of…