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This paper addresses the limitations of conventional vector quantization algorithms, particularly K-Means and its variant K-Means++, and investigates the Stochastic Quantization (SQ) algorithm as a scalable alternative for high-dimensional…
Clustering is an important exploratory data analysis technique to group objects based on their similarity. The widely used $K$-means clustering method relies on some notion of distance to partition data into a fewer number of groups. In the…
Numerous papers ask how difficult it is to cluster data. We suggest that the more relevant and interesting question is how difficult it is to cluster data sets {\em that can be clustered well}. More generally, despite the ubiquity and the…
A recent literature in econometrics models unobserved cross-sectional heterogeneity in panel data by assigning each cross-sectional unit a one-dimensional, discrete latent type. Such models have been shown to allow estimation and inference…
We consider the problem of estimating the number of clusters (k) in a dataset. We propose a non-parametric approach to the problem that utilizes similarity graphs to construct a robust statistic that effectively captures similarity…
The task of clustering a set of objects based on multiple sources of data arises in several modern applications. We propose an integrative statistical model that permits a separate clustering of the objects for each data source. These…
Mean shift is a simple interactive procedure that gradually shifts data points towards the mode which denotes the highest density of data points in the region. Mean shift algorithms have been effectively used for data denoising, mode…
Data analysis plays an indispensable role for value creation in industry. Cluster analysis in this context is able to explore given datasets with little or no prior knowledge and to identify unknown patterns. As (big) data complexity…
Existing approaches remain largely constrained by traditional distance metrics, limiting their effectiveness in handling random data. In this work, we introduce the first k-means variant in the literature that operates within a…
Lloyd's k-means algorithm is one of the most widely used clustering methods. We prove that in high-dimensional, high-noise settings, the algorithm exhibits catastrophic failure: with high probability, essentially every partition of the data…
This paper addresses the statistical significance of structures in random data: Given a set of vectors and a measure of mutual similarity, how likely does a subset of these vectors form a cluster with enhanced similarity among its elements?…
A new clustering accuracy measure is proposed to determine the unknown number of clusters and to assess the quality of clustering of a data set given in any dimensional space. Our validity index applies the classical nonparametric…
Clustering using neural networks has recently demonstrated promising performance in machine learning and computer vision applications. However, the performance of current approaches is limited either by unsupervised learning or their…
Center-based clustering (e.g., $k$-means, $k$-medians) and clustering using linear subspaces are two most popular techniques to partition real-world data into smaller clusters. However, when the data consists of sensitive demographic…
In general, the clustering problem is NP-hard, and global optimality cannot be established for non-trivial instances. For high-dimensional data, distance-based methods for clustering or classification face an additional difficulty, the…
We introduce a new method for performing clustering with the aim of fitting clusters with different scatters and weights. It is designed by allowing to handle a proportion $\alpha$ of contaminating data to guarantee the robustness of the…
Advances made to the traditional clustering algorithms solves the various problems such as curse of dimensionality and sparsity of data for multiple attributes. The traditional H-K clustering algorithm can solve the randomness and apriority…
It has always been a great challenge for clustering algorithms to automatically determine the cluster numbers according to the distribution of datasets. Several approaches have been proposed to address this issue, including the recent…
Distributed data mining techniques and mainly distributed clustering are widely used in the last decade because they deal with very large and heterogeneous datasets which cannot be gathered centrally. Current distributed clustering…
Clustering algorithms aim to organize data into groups or clusters based on the inherent patterns and similarities within the data. They play an important role in today's life, such as in marketing and e-commerce, healthcare, data…