Related papers: K-Means for Noise-Insensitive Multi-Dimensional Fe…
A new cluster analysis method, $K$-quantiles clustering, is introduced. $K$-quantiles clustering can be computed by a simple greedy algorithm in the style of the classical Lloyd's algorithm for $K$-means. It can be applied to large and…
Clustering is a representative unsupervised method widely applied in multi-modal and multi-view scenarios. Multiple kernel clustering (MKC) aims to group data by integrating complementary information from base kernels. As a representative,…
Organizing data into semantically more meaningful is one of the fundamental modes of understanding and learning. Cluster analysis is a formal study of methods for understanding and algorithm for learning. K-mean clustering algorithm is one…
Multidimensional scaling is an important dimension reduction tool in statistics and machine learning. Yet few theoretical results characterizing its statistical performance exist, not to mention any in high dimensions. By considering a…
Feature selection is an important and challenging task in high dimensional clustering. For example, in genomics, there may only be a small number of genes that are differentially expressed, which are informative to the overall clustering…
$K$-means, a simple and effective clustering algorithm, is one of the most widely used algorithms in multimedia and computer vision community. Traditional $k$-means is an iterative algorithm---in each iteration new cluster centers are…
This paper introduces a new clustering technique, called {\em dimensional clustering}, which clusters each data point by its latent {\em pointwise dimension}, which is a measure of the dimensionality of the data set local to that point.…
K-Means algorithm is a popular clustering method. However, it has two limitations: 1) it gets stuck easily in spurious local minima, and 2) the number of clusters k has to be given a priori. To solve these two issues, a multi-prototypes…
We consider the multi-target detection problem of recovering a set of signals that appear multiple times at unknown locations in a noisy measurement. In the low noise regime, one can estimate the signals by first detecting occurrences, then…
Clustering high-dimensional data is a critical challenge in machine learning due to the curse of dimensionality and the presence of noise. Traditional clustering algorithms often fail to capture the intrinsic structures in such data. This…
This paper presents a new fuzzy k-means algorithm for the clustering of high-dimensional data in various subspaces. Since high-dimensional data, some features might be irrelevant and relevant but may have different significance in the…
A new procedure for simultaneously finding the optimal cluster structure of multivariate functional objects and finding the subspace to represent the cluster structure is presented. The method is based on the $k$-means criterion for…
We propose a simple and efficient clustering method for high-dimensional data with a large number of clusters. Our algorithm achieves high-performance by evaluating distances of datapoints with a subset of the cluster centres. Our…
Application of K-Means algorithm is restricted by the fact that the number of clusters should be known beforehand. Previously suggested methods to solve this problem are either ad hoc or require parametric assumptions and complicated…
In this note, we introduce a new algorithm to deal with finite dimensional clustering with errors in variables. The design of this algorithm is based on recent theoretical advances (see Loustau (2013a,b)) in statistical learning with errors…
Subspace clustering has been extensively studied from the hypothesis-and-test, algebraic, and spectral clustering based perspectives. Most assume that only a single type/class of subspace is present. Generalizations to multiple types are…
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…
We consider the problem of clustering in the presence of noise. That is, when on top of cluster structure, the data also contains a subset of \emph{unstructured} points. Our goal is to detect the clusters despite the presence of many…
We propose k^2-means, a new clustering method which efficiently copes with large numbers of clusters and achieves low energy solutions. k^2-means builds upon the standard k-means (Lloyd's algorithm) and combines a new strategy to accelerate…
Supervised classification can be effective for prediction but sometimes weak on interpretability or explainability (XAI). Clustering, on the other hand, tends to isolate categories or profiles that can be meaningful but there is no…