Related papers: Fully dynamic hierarchical diameter k-clustering a…

Consider observation data, comprised of n observation vectors with values on a set of attributes. This gives us n points in attribute space. Having data structured as a tree, implied by having our observations embedded in an ultrametric…

We give new deterministic bounds for fully-dynamic graph connectivity. Our data structure supports updates (edge insertions/deletions) in $O(\log^2n/\log\log n)$ amortized time and connectivity queries in $O(\log n/\log\log n)$ worst-case…

This paper presents Orthogonal Subspace Clustering (OSC), an innovative method for high-dimensional data clustering. We first establish a theoretical theorem proving that high-dimensional data can be decomposed into orthogonal subspaces in…

Clustering plays a crucial role in computer science, facilitating data analysis and problem-solving across numerous fields. By partitioning large datasets into meaningful groups, clustering reveals hidden structures and relationships within…

We present a deterministic dynamic algorithm for maintaining a $(1+\epsilon)f$-approximate minimum cost set cover with $O(f\log(Cn)/\epsilon^2)$ amortized update time, when the input set system is undergoing element insertions and…

We propose a new anytime hierarchical clustering method that iteratively transforms an arbitrary initial hierarchy on the configuration of measurements along a sequence of trees we prove for a fixed data set must terminate in a chain of…

This paper is about metric data structures in high-dimensional or non-Euclidean space that permit cached sufficient statistics accelerations of learning algorithms. It has recently been shown that for less than about 10 dimensions,…

We present an efficient dynamic data structure that supports geodesic nearest neighbor queries for a set of point sites $S$ in a static simple polygon $P$. Our data structure allows us to insert a new site in $S$, delete a site from $S$,…

We study the density estimation problem defined as follows: given $k$ distributions $p_1, \ldots, p_k$ over a discrete domain $[n]$, as well as a collection of samples chosen from a ``query'' distribution $q$ over $[n]$, output $p_i$ that…

The $k$-center problem is a fundamental optimization problem with numerous applications in machine learning, data analysis, data mining, and communication networks. The $k$-center problem has been extensively studied in the classical…

We present a dynamic data structure for maintaining the persistent homology of a time series of real numbers. The data structure supports local operations, including the insertion and deletion of an item and the cutting and concatenating of…

Co-clustering simultaneously clusters rows and columns, revealing more fine-grained groups. However, existing co-clustering methods suffer from poor scalability and cannot handle large-scale data. This paper presents a novel and scalable…

Geometric data structures have been extensively studied in the regime where the dimension is much smaller than the number of input points. But in many scenarios in Machine Learning, the dimension can be much higher than the number of points…

We show how to approximate a data matrix $\mathbf{A}$ with a much smaller sketch $\mathbf{\tilde A}$ that can be used to solve a general class of constrained k-rank approximation problems to within $(1+\epsilon)$ error. Importantly, this…

This paper introduces a new clustering technique, called {\em dimensional clustering}, which clusters each data point by its latent {\em pointwise dimension}, which is a measure of the dimensionality of the data set local to that point.…

We give a new construction for a small space summary satisfying the coreset guarantee of a data set with respect to the $k$-means objective function. The number of points required in an offline construction is in $\tilde{O}(k…

Advances made to the traditional clustering algorithms solves the various problems such as curse of dimensionality and sparsity of data for multiple attributes. The traditional H-K clustering algorithm can solve the randomness and apriority…

We study the problem of clustering sequences of unlabeled point sets taken from a common metric space. Such scenarios arise naturally in applications where a system or process is observed in distinct time intervals, such as biological…

Clustering is a fundamental primitive in unsupervised learning. However, classical algorithms for $k$-clustering (such as $k$-median and $k$-means) assume access to exact pairwise distances -- an unrealistic requirement in many modern…

We study the metric facility location problem with client insertions and deletions. This setting differs from the classic dynamic facility location problem, where the set of clients remains the same, but the metric space can change over…