Core‐sets: An updated survey

Abstract

In optimization or machine learning problems we are given a set of items, usually points in some metric space, and the goal is to minimize or maximize an objective function over some space of candidate solutions. For example, in clustering problems, the input is a set of points in some metric space, and a common goal is to compute a set of centers in some other space (points, lines) that will minimize the sum of distances to these points. In database queries, we may need to compute such a some for a specific query set of k centers. However, traditional algorithms cannot handle modern systems that require parallel real‐time computations of infinite distributed streams from sensors such as GPS, audio or video that arrive to a cloud, or networks of weaker devices such as smartphones or robots. Core‐set is a “small data” summarization of the input “big data,” where every possible query has approximately the same answer on both data sets. Generic techniques enable efficient coreset maintenance of streaming, distributed and dynamic data. Traditional algorithms can then be applied on these coresets to maintain the approximated optimal solutions. The challenge is to design coresets with provable tradeoff between their size and approximation error. This survey summarizes such constructions in a retrospective way, that aims to unified and simplify the state‐of‐the‐art. This article is categorized under Algorithmic Development > Structure Discovery Fundamental Concepts of Data and Knowledge > Big Data Mining Technologies > Machine Learning Algorithmic Development > Scalable Statistical Methods

Understanding Collections of Related Datasets Using Dependent MMD Coresets

“…The primary application of coresets is to create a compact representation of a large dataset, to allow for fast inference on downstream tasks (see [28] for a recent survey). However, such compact representations have also proved beneficial in interpretation of both models and datasets.…”

Coresets for Near-Convex Functions

“…A different approach that is to use data summarization techniques. Coresets in particular were first used to solve problems in computational geometry [1] and got increasing attention in both the industry [3,4,5,17,35] and academy [6,8,23,24] over the recent years; see surveys in [20,44,47]. Informally, coreset is a small weighted subset of the input points (unlike e.g.…”

“…The size of the coreset is usually polynomial in 1/ε but independent or near-logarithmic in the size of the input. Since such a coreset approximates every query (and not just the optimal one), it supports constraint optimization, and the above computation models using merge-and-reduce trees; see details in [20]. Moreover, coresets may be computed in time that is near-linear in the input, even for NP-hard optimization problems.…”

Overview of accurate coresets

“…While this overview covers the accurate coreset constructions in literature, as well as the required background for understanding their correctness and proofs, there are a small number of other, different but related, overviews and surveys. The most related recent survey we are aware of is (Feldman, 2020), which: (a) covers the main advantages and disadvantages of (both accurate and non‐accurate) coresets in general, (b) discusses the applications that coresets can make feasible (e.g., the streaming and distributed data models), (c) discusses the different coreset types, and (d) dives in detail into a general framework for (non‐accurate) coreset construction. However, it does not provide the background needed for understanding those techniques and algorithms, and does not discuss concrete coreset construction algorithms and their correctness.…”