Related papers: Sliding Window Algorithms for k-Clustering Problem…
This paper addresses the limitations of conventional vector quantization algorithms, particularly K-Means and its variant K-Means++, and investigates the Stochastic Quantization (SQ) algorithm as a scalable alternative for high-dimensional…
The $k$-means method is an iterative clustering algorithm which associates each observation with one of $k$ clusters. It traditionally employs cluster centers in the same space as the observed data. By relaxing this requirement, it is…
Clustering is a widely used and powerful machine learning technique, but its effectiveness is often limited by the need to specify the number of clusters, k, or by relying on thresholds that implicitly determine k. We introduce k*-means, a…
In addition to finding meaningful clusters, centroid-based clustering algorithms such as K-means or mean-shift should ideally find centroids that are valid patterns in the input space, representative of data in their cluster. This is…
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…
Clustering is an important data mining technique where we will be interested in maximizing intracluster distance and also minimizing intercluster distance. We have utilized clustering techniques for detecting deviation in product sales and…
We study the classic $k$-means/median clustering, which are fundamental problems in unsupervised learning, in the setting where data are partitioned across multiple sites, and where we are allowed to discard a small portion of the data by…
Common clustering algorithms require multiple scans of all the data to achieve convergence, and this is prohibitive when large databases, with data arriving in streams, must be processed. Some algorithms to extend the popular K-means method…
K-Means clustering algorithm is one of the most commonly used clustering algorithms because of its simplicity and efficiency. K-Means clustering algorithm based on Euclidean distance only pays attention to the linear distance between…
The input to the $k$-median for lines problem is a set $L$ of $n$ lines in $\mathbb{R}^d$, and the goal is to compute a set of $k$ centers (points) in $\mathbb{R}^d$ that minimizes the sum of squared distances over every line in $L$ and its…
We present data streaming algorithms for the $k$-median problem in high-dimensional dynamic geometric data streams, i.e. streams allowing both insertions and deletions of points from a discrete Euclidean space $\{1, 2, \ldots \Delta\}^d$.…
Low-latency sliding window algorithms for regular and context-free languages are studied, where latency refers to the worst-case time spent for a single window update or query. For every regular language $L$ it is shown that there exists a…
The field of learning-augmented algorithms seeks to use ML techniques on past instances of a problem to inform an algorithm designed for a future instance. In this paper, we introduce a novel model for learning-augmented algorithms inspired…
We consider the problem of clustering with $K$-means and Gaussian mixture models with a constraint on the separation between the centers in the context of real-valued data. We first propose a dynamic programming approach to solving the…
We study the $k$-median with discounts problem, wherein we are given clients with non-negative discounts and seek to open at most $k$ facilities. The goal is to minimize the sum of distances from each client to its nearest open facility…
In this paper we introduce and study the online consistent $k$-clustering with outliers problem, generalizing the non-outlier version of the problem studied in [Lattanzi-Vassilvitskii, ICML17]. We show that a simple local-search based…
Analytic function, also called window function, is to query the aggregation of data over a sliding window. For example, a simple query over the online stock platform is to return the average price of a stock of the last three days. These…
In this work, we show the first worst-case to average-case reduction for the classical $k$-SUM problem. A $k$-SUM instance is a collection of $m$ integers, and the goal of the $k$-SUM problem is to find a subset of $k$ elements that sums to…
With the advancement of technology and reduced storage costs, individuals and organizations are tending towards the usage of electronic media for storing textual information and documents. It is time consuming for readers to retrieve…
Clustering serves as a vital tool for uncovering latent data structures, and achieving both high accuracy and interpretability is essential. To this end, existing methods typically construct binary decision trees by solving mixed-integer…