Related papers: Towards a Query-Optimal and Time-Efficient Algorit…
Clustering is one of the major tasks in data mining. In the last few years, Clustering of spatial data has received a lot of research attention. Spatial databases are components of many advanced information systems like geographic…
Correlation Clustering is a classic clustering objective arising in numerous machine learning and data mining applications. Given a graph $G=(V,E)$, the goal is to partition the vertex set into clusters so as to minimize the number of edges…
Clustering multidimensional points is a fundamental data mining task, with applications in many fields, such as astronomy, neuroscience, bioinformatics, and computer vision. The goal of clustering algorithms is to group similar objects…
We consider the approximability of center-based clustering problems where the points to be clustered lie in a metric space, and no candidate centers are specified. We call such problems "continuous", to distinguish from "discrete"…
We present a new fast online clustering algorithm that reliably recovers arbitrary-shaped data clusters in high throughout data streams. Unlike the existing state-of-the-art online clustering methods based on k-means or k-medoid, it does…
The goal of clustering is to group similar objects into meaningful partitions. This process is well understood when an explicit similarity measure between the objects is given. However, far less is known when this information is not readily…
Advances in sensing technologies and the growth of the internet have resulted in an explosion in the size of modern datasets, while storage and processing power continue to lag behind. This motivates the need for algorithms that are…
We propose a new clustering approach, called optimality-based clustering, that clusters data points based on their latent decision-making preferences. We assume that each data point is a decision generated by a decision-maker who…
While powerful tools have been developed to analyze quantum query complexity, there are still many natural problems that do not fit neatly into the black box model of oracles. We create a new model that allows multiple oracles with…
Consider unsupervised clustering of objects drawn from a discrete set, through the use of human intelligence available in crowdsourcing platforms. This paper defines and studies the problem of universal clustering using responses of crowd…
We establish sufficient conditions of exact and almost full recovery of the node partition in Bipartite Stochastic Block Model (BSBM) using polynomial time algorithms. First, we improve upon the known conditions of almost full recovery by…
Clustering large, mixed data is a central problem in data mining. Many approaches adopt the idea of k-means, and hence are sensitive to initialisation, detect only spherical clusters, and require a priori the unknown number of clusters. We…
Correlation clustering is a technique for aggregating data based on qualitative information about which pairs of objects are labeled 'similar' or 'dissimilar.' Because the optimization problem is NP-hard, much of the previous literature…
An algorithm for structured database searching is presented and used to solve the set partition problem. O(n) oracle calls are required in order to obtain a solution, but the probability that this solution is optimal decreases exponentially…
Recently, there has been substantial interest in clustering research that takes a beyond worst-case approach to the analysis of algorithms. The typical idea is to design a clustering algorithm that outputs a near-optimal solution, provided…
We consider the following problem, which is useful in applications such as joint image and shape alignment. The goal is to recover $n$ discrete variables $g_i \in \{0, \ldots, k-1\}$ (up to some global offset) given noisy observations of a…
Correlation clustering is perhaps the most natural formulation of clustering. Given $n$ objects and a pairwise similarity measure, the goal is to cluster the objects so that, to the best possible extent, similar objects are put in the same…
Hierarchical clustering is a recursive partitioning of a dataset into clusters at an increasingly finer granularity. Motivated by the fact that most work on hierarchical clustering was based on providing algorithms, rather than optimizing a…
Clustering is one of the most important tools for analysis of large datasets, and perhaps the most popular clustering algorithm is Lloyd's algorithm for $k$-means. This algorithm takes $n$ vectors $V=[v_1,\dots,v_n]\in\mathbb{R}^{d\times…
In many statistical linear inverse problems, one needs to recover classes of similar curves from their noisy images under an operator that does not have a bounded inverse. Problems of this kind appear in many areas of application.…