Related papers: Coresets for Clustering in Graphs of Bounded Treew…
A $k$-decision tree $t$ (or $k$-tree) is a recursive partition of a matrix (2D-signal) into $k\geq 1$ block matrices (axis-parallel rectangles, leaves) where each rectangle is assigned a real label. Its regression or classification loss to…
Coresets are small data summaries that are sufficient for model training. They can be maintained online, enabling efficient handling of large data streams under resource constraints. However, existing constructions are limited to simple…
Clustering algorithms are of fundamental importance when dealing with large unstructured datasets and discovering new patterns and correlations therein, with applications ranging from scientific research to medical imaging and marketing…
We study sublinear algorithms for two fundamental graph problems, MAXCUT and correlation clustering. Our focus is on constructing core-sets as well as developing streaming algorithms for these problems. Constant space algorithms are known…
We investigate coresets - succinct, small summaries of large data sets - so that solutions found on the summary are provably competitive with solution found on the full data set. We provide an overview over the state-of-the-art in coreset…
Coresets are efficient representations of data sets such that models trained on the coreset are provably competitive with models trained on the original data set. As such, they have been successfully used to scale up clustering models such…
We present algorithms for the computation of $\varepsilon$-coresets for $k$-median clustering of point sequences in $\mathbb{R}^d$ under the $p$-dynamic time warping (DTW) distance. Coresets under DTW have not been investigated before, and…
Clustering a graph means identifying internally dense subgraphs which are only sparsely interconnected. Formalizations of this notion lead to measures that quantify the quality of a clustering and to algorithms that actually find…
Clustering large datasets is a fundamental problem with a number of applications in machine learning. Data is often collected on different sites and clustering needs to be performed in a distributed manner with low communication. We would…
Conductance-based graph clustering has been recognized as a fundamental operator in numerous graph analysis applications. Despite the significant success of conductance-based graph clustering, existing algorithms are either hard to obtain…
The k-means clustering algorithm is a popular algorithm that partitions data into k clusters. There are many improvements to accelerate the standard algorithm. Most current research employs upper and lower bounds on point-to-cluster…
In the era of big data, k-means clustering has been widely adopted as a basic processing tool in various contexts. However, its computational cost could be prohibitively high as the data size and the cluster number are large. It is well…
Coreset (or core-set) is a small weighted \emph{subset} $Q$ of an input set $P$ with respect to a given \emph{monotonic} function $f:\mathbb{R}\to\mathbb{R}$ that \emph{provably} approximates its fitting loss $\sum_{p\in P}f(p\cdot x)$ to…
The treewidth of a graph is an important invariant in structural and algorithmic graph theory. This paper studies the treewidth of line graphs. We show that determining the treewidth of the line graph of a graph $G$ is equivalent to…
The clustering problem, in its many variants, has numerous applications in operations research and computer science (e.g., in applications in bioinformatics, image processing, social network analysis, etc.). As sizes of data sets have grown…
Hypergraphs are a useful abstraction for modeling multiway relationships in data, and hypergraph clustering is the task of detecting groups of closely related nodes in such data. Graph clustering has been studied extensively, and there are…
Graph-based clustering has shown promising performance in many tasks. A key step of graph-based approach is the similarity graph construction. In general, learning graph in kernel space can enhance clustering accuracy due to the…
A coreset (or core-set) of a dataset is its semantic compression with respect to a set of queries, such that querying the (small) coreset provably yields an approximate answer to querying the original (full) dataset. In the last decade,…
How do graph clustering techniques compare with respect to their summarization power? How well can they summarize a million-node graph with a few representative structures? Graph clustering or community detection algorithms can summarize a…
Coresets are among the most popular paradigms for summarizing data. In particular, there exist many high performance coresets for clustering problems such as $k$-means in both theory and practice. Curiously, there exists no work on…