Related papers: Coresets and Sketches
We develop a sketching algorithm to find the point on the convex hull of a dataset, closest to a query point outside it. Studying the convex hull of datasets can provide useful information about their geometric structure and their…
Summaries of massive data sets support approximate query processing over the original data. A basic aggregate over a set of records is the weight of subpopulations specified as a predicate over records' attributes. Bottom-k sketches are a…
We study the problem of constructing coresets for clustering problems with time series data. This problem has gained importance across many fields including biology, medicine, and economics due to the proliferation of sensors facilitating…
Recent advancement of the WWW, IOT, social network, e-commerce, etc. have generated a large volume of data. These datasets are mostly represented by high dimensional and sparse datasets. Many fundamental subroutines of common data analytic…
In projective clustering we are given a set of n points in $R^d$ and wish to cluster them to a set $S$ of $k$ linear subspaces in $R^d$ according to some given distance function. An $\eps$-coreset for this problem is a weighted (scaled)…
Which one is better between two representative graph summarization models with and without edge weights? From web graphs to online social networks, large graphs are everywhere. Graph summarization, which is an effective graph compression…
Massive sizes of real-world graphs, such as social networks and web graph, impose serious challenges to process and perform analytics on them. These issues can be resolved by working on a small summary of the graph instead . A summary is a…
Merge trees are a type of topological descriptors that record the connectivity among the sublevel sets of scalar fields. They are among the most widely used topological tools in visualization. In this paper, we are interested in sketching a…
Designing coresets--small-space sketches of the data preserving cost of the solutions within $(1\pm \epsilon)$-approximate factor--is an important research direction in the study of center-based $k$-clustering problems, such as $k$-means or…
In this survey, we explore recent literature on finding the cores of higher graphs using geometric and topological means. We study graphs, hypergraphs, and simplicial complexes, all of which are models of higher graphs. We study the notion…
We study core-set construction algorithms for the task of Diversity Maximization under fairness/partition constraint. Given a set of points $P$ in a metric space partitioned into $m$ groups, and given $k_1,\ldots,k_m$, the goal of this…
Clustering is a fundamental tool for analyzing large data sets. A rich body of work has been devoted to designing data-stream algorithms for the relevant optimization problems such as $k$-center, $k$-median, and $k$-means. Such algorithms…
Data sketching is a critical tool for distinct counting, enabling multisets to be represented by compact summaries that admit fast cardinality estimates. Because sketches may be merged to summarize multiset unions, they are a basic building…
In all state-of-the-art sketching and coreset techniques for clustering, as well as in the best known fixed-parameter tractable approximation algorithms, randomness plays a key role. For the classic $k$-median and $k$-means problems, there…
Visualizing very large matrices involves many formidable problems. Various popular solutions to these problems involve sampling, clustering, projection, or feature selection to reduce the size and complexity of the original task. An…
A coreset is a subset of the training set, using which a machine learning algorithm obtains performances similar to what it would deliver if trained over the whole original data. Coreset discovery is an active and open line of research as…
A coreset is a small set that can approximately preserve the structure of the original input data set. Therefore we can run our algorithm on a coreset so as to reduce the total computational complexity. Conventional coreset techniques…
We introduce a new sub-linear space sketch---the Weight-Median Sketch---for learning compressed linear classifiers over data streams while supporting the efficient recovery of large-magnitude weights in the model. This enables…
There are many methods developed to approximate a cloud of vectors embedded in high-dimensional space by simpler objects: starting from principal points and linear manifolds to self-organizing maps, neural gas, elastic maps, various types…
Core-sets refer to subsets of data that maximize some function that is commonly a diversity or group requirement. These subsets are used in place of the original data to accomplish a given task with comparable or even enhanced performance…