Related papers: Scalable K-Means++

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…

We give a quantum approximation scheme (i.e., $(1 + \varepsilon)$-approximation for every $\varepsilon > 0$) for the classical $k$-means clustering problem in the QRAM model with a running time that has only polylogarithmic dependence on…

K-means is a popular clustering method used in data mining area. To work with large datasets, researchers propose PKMeans, which is a parallel k-means on MapReduce. However, the existing k-means parallelization methods including PKMeans…

The $k$-means algorithm (Lloyd's algorithm) is a widely used method for clustering unlabeled data. A key bottleneck of the $k$-means algorithm is that each iteration requires time linear in the number of data points, which can be expensive…

Due to its simplicity and versatility, k-means remains popular since it was proposed three decades ago. The performance of k-means has been enhanced from different perspectives over the years. Unfortunately, a good trade-off between quality…

In the era of big data, k-means clustering has been widely adopted as a basic processing tool in various contexts. However, its computational cost could be prohibitively high as the data size and the cluster number are large. It is well…

The $k$-means algorithm is arguably the most popular nonparametric clustering method but cannot generally be applied to datasets with incomplete records. The usual practice then is to either impute missing values under an assumed…

In this paper, the decades-old clustering method k-means is revisited. The original distortion minimization model of k-means is addressed by a pure stochastic minimization procedure. In each step of the iteration, one sample is tentatively…

In this paper, we compare three initialization schemes for the KMEANS clustering algorithm: 1) random initialization (KMEANSRAND), 2) KMEANS++, and 3) KMEANSD++. Both KMEANSRAND and KMEANS++ have a major that the value of k needs to be set…

The k-means clustering is one of the most popular clustering algorithms in data mining. Recently a lot of research has been concentrated on the algorithm when the dataset is divided into multiple parties or when the dataset is too large to…

We introduce the breathing k-means algorithm, which on average significantly improves solutions obtained by the widely-known greedy k-means++ algorithm, the default method for k-means clustering in the scikit-learn package. The improvements…

$k$-means clustering is a well-studied problem due to its wide applicability. Unfortunately, there exist strong theoretical limits on the performance of any algorithm for the $k$-means problem on worst-case inputs. To overcome this barrier,…

Quantum computing is a promising paradigm based on quantum theory for performing fast computations. Quantum algorithms are expected to surpass their classical counterparts in terms of computational complexity for certain tasks, including…

The Incremental K-means (IKM), an improved version of K-means (KM), was introduced to improve the clustering quality of KM significantly. However, the speed of IKM is slower than KM. My thesis proposes two algorithms to speed up IKM while…

Color quantization is an important operation with many applications in graphics and image processing. Most quantization methods are essentially based on data clustering algorithms. However, despite its popularity as a general purpose…

The $k$-means++ algorithm by Arthur and Vassilvitskii [SODA 2007] is a classical and time-tested algorithm for the $k$-means problem. While being very practical, the algorithm also has good theoretical guarantees: its solution is $O(\log…

The fuzzy $K$-means problem is a generalization of the classical $K$-means problem to soft clusterings, i.e. clusterings where each points belongs to each cluster to some degree. Although popular in practice, prior to this work the fuzzy…

Kernel-based K-means clustering has gained popularity due to its simplicity and the power of its implicit non-linear representation of the data. A dominant concern is the memory requirement since memory scales as the square of the number of…

Fueled by massive data, important decision making is being automated with the help of algorithms, therefore, fairness in algorithms has become an especially important research topic. In this work, we design new streaming and distributed…

We prove in this paper that the expected value of the objective function of the $k$-means++ algorithm for samples converges to population expected value. As $k$-means++, for samples, provides with constant factor approximation for $k$-means…