Related papers: Batch and median neural gas
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…
Gaussian mixture models (GMM) are the most widely used statistical model for the $k$-means clustering problem and form a popular framework for clustering in machine learning and data analysis. In this paper, we propose a natural semi-random…
A new scheme of approximation in quantum theory is proposed which is potentially applicable to arbtrary interacting systems. The method consists in in approximating the original Hamiltonian by one corresponding to a suitable exactly…
The Random Batch Method (RBM) is an effective technique to reduce the computational complexity when solving certain stochastic differential problems (SDEs) involving interacting particles. It can transform the computational complexity from…
Lambda quantiles, originally introduced as lambda value at risk, generalise the classical value at risk by allowing for a variable confidence level. This work presents efficient algorithms for computing lambda quantiles and demonstrates…
This research aims to develop kernel GNG, a kernelized version of the growing neural gas (GNG) algorithm, and to investigate the features of the networks generated by the kernel GNG. The GNG is an unsupervised artificial neural network that…
Clustering is a popular form of unsupervised learning for geometric data. Unfortunately, many clustering algorithms lead to cluster assignments that are hard to explain, partially because they depend on all the features of the data in a…
This paper studies the application of the blended dynamics approach towards distributed optimization problem where the global cost function is given by a sum of local cost functions. The benefits include (i) individual cost function need…
Molecular dynamics (MD) simulation is applied to the condensation process of supersaturated vapors of methane, ethane, and carbon dioxide. Simulations of systems with up to a million particles were conducted with a massively parallel MD…
This paper presents universal algorithms for clustering problems, including the widely studied $k$-median, $k$-means, and $k$-center objectives. The input is a metric space containing all potential client locations. The algorithm must…
Finite mixture models, typically Gaussian mixtures, are well known and widely used as model-based clustering. In practical situations, there are many non-Gaussian data that are heavy-tailed and/or asymmetric. Normal inverse Gaussian (NIG)…
In the modal approach to clustering, clusters are defined as the local maxima of the underlying probability density function, where the latter can be estimated either non-parametrically or using finite mixture models. Thus, clusters are…
We show that model-based Bayesian clustering, the probabilistically most systematic approach to the partitioning of data, can be mapped into a statistical physics problem for a gas of particles, and as a result becomes amenable to a…
Heuristic search has traditionally relied on hand-crafted or programmatically derived heuristics. Neural networks (NNs) are newer powerful tools which can be used to learn complex mappings from states to cost-to-go heuristics. However,…
Maximum entropy inference and learning of graphical models are pivotal tasks in learning theory and optimization. This work extends algorithms for these problems, including generalized iterative scaling (GIS) and gradient descent (GD), to…
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…
We derive an efficient method to perform clustering of nodes in Gaussian graphical models directly from sample data. Nodes are clustered based on the similarity of their network neighborhoods, with edge weights defined by partial…
Molecular dynamics simulations are widely used to investigate nucleation in first-order phase transitions. Brute-force simulations, though popular, are limited to conditions of high metastability, where the critical cluster and the…
$k$-center is one of the most popular clustering models. While it admits a simple 2-approximation in polynomial time in general metrics, the Euclidean version is NP-hard to approximate within a factor of 1.93, even in the plane, if one…
Clustering is a widely used technique with a long and rich history in a variety of areas. However, most existing algorithms do not scale well to large datasets, or are missing theoretical guarantees of convergence. This paper introduces a…