Related papers: Log-Time K-Means Clustering for 1D Data: Novel App…
Clustering is widely used in unsupervised learning to find homogeneous groups of observations within a dataset. However, clustering mixed-type data remains a challenge, as few existing approaches are suited for this task. This study…
Most learning approaches treat dimensionality reduction (DR) and clustering separately (i.e., sequentially), but recent research has shown that optimizing the two tasks jointly can substantially improve the performance of both. The premise…
The metric $k$-median problem is a textbook clustering problem. As input, we are given a metric space $V$ of size $n$ and an integer $k$, and our task is to find a subset $S \subseteq V$ of at most $k$ `centers' that minimizes the total…
This thesis aims to invent new approaches for making inferences with the k-means algorithm. k-means is an iterative clustering algorithm that randomly assigns k centroids, then assigns data points to the nearest centroid, and updates…
Conventional machine learning algorithms cannot be applied until a data matrix is available to process. When the data matrix needs to be obtained from a relational database via a feature extraction query, the computation cost can be…
Clustering is a NP-hard problem. Thus, no optimal algorithm exists, heuristics are applied to cluster the data. Heuristics can be very resource-intensive, if not applied properly. For substantially large data sets computational efficiencies…
We study the problem of list-decodable mean estimation, where an adversary can corrupt a majority of the dataset. Specifically, we are given a set $T$ of $n$ points in $\mathbb{R}^d$ and a parameter $0< \alpha <\frac 1 2$ such that an…
The diameter $k$-clustering problem is the problem of partitioning a finite subset of $\mathbb{R}^d$ into $k$ subsets called clusters such that the maximum diameter of the clusters is minimized. One early clustering algorithm that computes…
Clustering is a fundamental task in data science that aims to group data based on their similarities. However, defining similarity is often ambiguous, making it challenging to determine the most appropriate objective function for a given…
The K-Modes algorithm, developed for clustering categorical data, is of high algorithmic simplicity but suffers from unreliable performances in clustering quality and clustering efficiency, both heavily influenced by the choice of initial…
With the development of information technology, the application of artificial intelligence and machine learning in the field of education shows great potential. This study aims to explore how to utilize K-means clustering algorithm to…
The $k$-means algorithm is often used in clustering applications but its usage requires a complete data matrix. Missing data, however, is common in many applications. Mainstream approaches to clustering missing data reduce the missing data…
We provide a new bi-criteria $\tilde{O}(\log^2 k)$ competitive algorithm for explainable $k$-means clustering. Explainable $k$-means was recently introduced by Dasgupta, Frost, Moshkovitz, and Rashtchian (ICML 2020). It is described by an…
Clustering samples according to an effective metric and/or vector space representation is a challenging unsupervised learning task with a wide spectrum of applications. Among several clustering algorithms, k-means and its kernelized version…
We study the topic of dimensionality reduction for $k$-means clustering. Dimensionality reduction encompasses the union of two approaches: \emph{feature selection} and \emph{feature extraction}. A feature selection based algorithm for…
The Tabu Search (TS) metaheuristic has been proposed for K-Means clustering as an alternative to Lloyd's algorithm, which for all its ease of implementation and fast runtime, has the major drawback of being trapped at local optima. While…
Load shapes derived from smart meter data are frequently employed to analyze daily energy consumption patterns, particularly in the context of applications like Demand Response (DR). Nevertheless, one of the most important challenges to…
The input to the \emph{sets-$k$-means} problem is an integer $k\geq 1$ and a set $\mathcal{P}=\{P_1,\cdots,P_n\}$ of sets in $\mathbb{R}^d$. The goal is to compute a set $C$ of $k$ centers (points) in $\mathbb{R}^d$ that minimizes the sum…
We investigate $k$-means clustering in the online no-substitution setting when the input arrives in \emph{arbitrary} order. In this setting, points arrive one after another, and the algorithm is required to instantly decide whether to take…
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…