A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Breathing k-means outperforms greedy k-means++ in clustering.
Modified K-means ensures local optimality with same complexity.
Clustering is a separation of data into groups of similar objects. Every group called cluster consists of objects that are similar to one another and dissimilar to objects of other groups. In this paper, the K-Means algorithm is implemented by three distance functions and to identify the optimal distance function for c…
Two algorithms improve K-means clustering speed without sacrificing quality.
K-means fails catastrophically in high dimensions, Hartigan's avoids it.
A faster Wasserstein k-means algorithm for histogram data reduces computation and maintains clustering quality.
Improved K-Means++ and K-Means with faster run-time.
-means algorithm is one of the most classical clustering methods, which has been widely and successfully used in signal processing. However, due to the thin-tailed property of the Gaussian distribution, -means algorithm suffers from relatively poor performance on the dataset containing heavy-tailed data or outlie…
Study reduces dimensions for -means clustering for better accuracy.
Efficient algorithms for -means clustering frequently converge to suboptimal partitions, and given a partition, it is difficult to detect -means optimality. In this paper, we develop an a posteriori certifier of approximate optimality for -means clustering. The certifier is a sub-linear Monte Carlo algorithm b…
Ball k-means reduces point-centroid distance computations for faster k-means clustering.
Fair k-means algorithm ensures equitable costs for different groups.
K-means algorithm improves financial market risk prediction accuracy.
K-means fails in high dimensions with noise and few samples.
This article briefly introduced Arthur and Vassilvitshii's work on \textbf{k-means++} algorithm and further generalized the center initialization process. It is found that choosing the most distant sample point from the nearest center as new center can mostly have the same effect as the center initialization process in…
The K-means algorithm is arguably the most popular data clustering method, commonly applied to processed datasets in some "feature spaces", as is in spectral clustering. Highly sensitive to initializations, however, K-means encounters a scalability bottleneck with respect to the number of clusters K as this number grow…
Traditionally, practitioners initialize the {\tt k-means} algorithm with centers chosen uniformly at random. Randomized initialization with uneven weights ({\tt k-means++}) has recently been used to improve the performance over this strategy in cost and run-time. We consider the k-means problem with semi-supervised inf…
Mixed datasets consist of both numeric and categorical attributes. Various k-means-based clustering algorithms have been developed for these datasets. Generally, these algorithms use random partition as a starting point, which tends to produce different clustering results for different runs. In this paper, we propose, …
A new k-means algorithm using cover trees accelerates clustering.
We propose the Lasso Weighted -means (--means) algorithm as a simple yet efficient sparse clustering procedure for high-dimensional data where the number of features () can be much larger compared to the number of observations (). In the --means algorithm, we introduce a lasso-based penalty term,…
Robust Trimmed k-means improves clustering with outliers and mixed data.
We show that -means (Lloyd's algorithm) is obtained as a special case when truncated variational EM approximations are applied to Gaussian Mixture Models (GMM) with isotropic Gaussians. In contrast to the standard way to relate -means and GMMs, the provided derivation shows that it is not required to consider Gau…
Generalizes k-means to graphs using PageRank.
The present work proposes hybridization of Expectation-Maximization (EM) and K-Means techniques as an attempt to speed-up the clustering process. Though both K-Means and EM techniques look into different areas, K-means can be viewed as an approximate way to obtain maximum likelihood estimates for the means. Along with …
One of the applications of center-based clustering algorithms such as K-Means is partitioning data points into K clusters. In some examples, the feature space relates to the underlying problem we are trying to solve, and sometimes we can obtain a suitable feature space. Nevertheless, while K-Means is one of the most ef…
Many clustering algorithms exist that estimate a cluster centroid, such as K-means, K-medoids or mean-shift, but no algorithm seems to exist that clusters data by returning exactly K meaningful modes. We propose a natural definition of a K-modes objective function by combining the notions of density and cluster assignm…
Identifying a set of homogeneous clusters in a heterogeneous dataset is one of the most important classes of problems in statistical modeling. In the realm of unsupervised partitional clustering, k-means is a very important algorithm for this. In this technical report, we develop a new k-means variant called Augmented …
Kernel -means clustering can correctly identify and extract a far more varied collection of cluster structures than the linear -means clustering algorithm. However, kernel -means clustering is computationally expensive when the non-linear feature map is high-dimensional and there are many input points. Kernel …
Bayesian models offer great flexibility for clustering applications---Bayesian nonparametrics can be used for modeling infinite mixtures, and hierarchical Bayesian models can be utilized for sharing clusters across multiple data sets. For the most part, such flexibility is lacking in classical clustering methods such a…
Due to the progressive growth of the amount of data available in a wide variety of scientific fields, it has become more difficult to ma- nipulate and analyze such information. Even though datasets have grown in size, the K-means algorithm remains as one of the most popular clustering methods, in spite of its dependenc…
Replicable clustering algorithms for k-medians, k-means, and k-centers are proposed.
New algorithm improves clustering accuracy without sacrificing scalability.
The original k-means clustering method works only if the exact vectors representing the data points are known. Therefore calculating the distances from the centroids needs vector operations, since the average of abstract data points is undefined. Existing algorithms can be extended for those cases when the sole input i…
Proposes ARSK for robust and sparse clustering.
This paper proposes the use of an optimization algorithm, namely PSO to decide the initial centroids in K-means, to eventually get better accuracy. The vectorized notation of the optimal centroids can be thought of as entities in an optimization space, where the accuracy of K-means over a random subset of the data coul…
PNN-smoothing improves -means clustering by merging subsets' clusterings.
Kernel k-Means algorithm improves clustering of non-linear data.
The -means algorithm is extended to allow for partitioning of skewed groups. Our algorithm is called TiK-Means and contributes a -means type algorithm that assigns observations to groups while estimating their skewness-transformation parameters. The resulting groups and transformation reveal general-structured cl…
Combines k-means and hill climbing for stratification and allocation.
A new algorithm balances fairness in clustering to avoid discrimination.
We introduce a model-free relax-and-round algorithm for k-means clustering based on a semidefinite relaxation due to Peng and Wei. The algorithm interprets the SDP output as a denoised version of the original data and then rounds this output to a hard clustering. We provide a generic method for proving performance guar…
The -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 missing-completely-at-random mechanism or to ignore the incomplete records, and apply the …
In many situations where the interest lies in identifying clusters one might expect that not all available variables carry information about these groups. Furthermore, data quality (e.g. outliers or missing entries) might present a serious and sometimes hard-to-assess problem for large and complex datasets. In this pap…
Proposes a semi-supervised K-Means algorithm for better feature selection.
Despite its well-known shortcomings, -means remains one of the most widely used approaches to data clustering. Current research continues to tackle its flaws while attempting to preserve its simplicity. Recently, the \textit{power -means} algorithm was proposed to avoid trapping in local minima by annealing throu…
-means clustering is a fundamental problem in unsupervised learning. The problem concerns finding a partition of the data points into clusters such that the within-cluster variation is minimized. Despite its importance and wide applicability, a theoretical understanding of the -means problem has not been comp…
We design a new algorithm for the Euclidean -means problem that operates in the local model of differential privacy. Unlike in the non-private literature, differentially private algorithms for the -means objective incur both additive and multiplicative errors. Our algorithm significantly reduces the additive erro…
The paper assesses conditions for the uniqueness of k-means clustering.