相关论文: Local Search k-means++ with Foresight

We present a technique that allows for improving on some relative greedy procedures by well-chosen (non-oblivious) local search algorithms. Relative greedy procedures are a particular type of greedy algorithm that start with a simple,…

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…

In the classical NP-hard metric $k$-median problem, we are given a set of $n$ clients and centers with metric distances between them, along with an integer parameter $k\geq 1$. The objective is to select a subset of $k$ open centers that…

We study the problem of $k$-means clustering in the space of straight-line segments in $\mathbb{R}^{2}$ under the Hausdorff distance. For this problem, we give a $(1+\epsilon)$-approximation algorithm that, for an input of $n$ segments, for…

We consider a composite optimization problem where the sum of a continuously differentiable and a merely lower semicontinuous function has to be minimized. The proximal gradient algorithm is the classical method for solving such a problem…

Stochastic local search (SLS) algorithms have exhibited great effectiveness in finding models of random instances of the Boolean satisfiability problem (SAT). As one of the most widely known and used SLS algorithm, WalkSAT plays a key role…

The invention of the transformer architecture has revolutionized Artificial Intelligence (AI), yielding unprecedented success in areas such as natural language processing, computer vision, and multimodal reasoning. Despite these advances,…

We introduce a probabilistic approach to the LMS filter. By means of an efficient approximation, this approach provides an adaptable step-size LMS algorithm together with a measure of uncertainty about the estimation. In addition, the…

This paper shows that one can be competitive with the k-means objective while operating online. In this model, the algorithm receives vectors v_1,...,v_n one by one in an arbitrary order. For each vector the algorithm outputs a cluster…

Many large multimedia applications require efficient processing of nearest neighbor queries. Often, multimedia data are represented as a collection of important high-dimensional feature vectors. Existing Locality Sensitive Hashing (LSH)…

The $k$-means is one of the most important unsupervised learning techniques in statistics and computer science. The goal is to partition a data set into many clusters, such that observations within clusters are the most homogeneous and…

Local search algorithms use the neighborhood relations among search states and often perform well for a variety of NP-hard combinatorial search problems. This paper shows how quantum computers can also use these neighborhood relations. An…

Approximate Nearest Neighbor Search (ANNS) is a fundamental problem in many areas of machine learning and data mining. During the past decade, numerous hashing algorithms are proposed to solve this problem. Every proposed algorithm claims…

$k$-means clustering is NP-hard in the worst case but previous work has shown efficient algorithms assuming the optimal $k$-means clusters are \emph{stable} under additive or multiplicative perturbation of data. This has two caveats. First,…

The k-Nearest Neighbor (k-NN) classification algorithm is one of the most widely-used lazy classifiers because of its simplicity and ease of implementation. It is considered to be an effective classifier and has many applications. However,…

Clustering algorithms have long been the topic of research, representing the more popular side of unsupervised learning. Since clustering analysis is one of the best ways to find some clarity and structure within raw data, this paper…

Efficient algorithms for $k$-means clustering frequently converge to suboptimal partitions, and given a partition, it is difficult to detect $k$-means optimality. In this paper, we develop an a posteriori certifier of approximate optimality…

K-medoids clustering is a popular variant of k-means clustering and widely used in pattern recognition and machine learning. A main drawback of k-medoids clustering is that an improper initialization can cause it to get trapped in local…

Existing methods for retrieving k-nearest neighbours suffer from the curse of dimensionality. We argue this is caused in part by inherent deficiencies of space partitioning, which is the underlying strategy used by most existing methods. We…

As data volumes continue to grow, clustering and outlier detection algorithms are becoming increasingly time-consuming. Classical index structures for neighbor search are no longer sustainable due to the "curse of dimensionality". Instead,…