相关论文: Batch and median neural gas

Neural gas (NG) is a robust vector quantization algorithm with a well-known mathematical model. According to this, the neural gas samples the underlying data distribution following a power law with a magnification exponent that depends on…

Within scientific and real life problems, classification is a typical case of extremely complex tasks in data-driven scenarios, especially if approached with traditional techniques. Machine Learning supervised and unsupervised paradigms,…

We consider the problem of minimizing a sum of $n$ functions over a convex parameter set $\mathcal{C} \subset \mathbb{R}^p$ where $n\gg p\gg 1$. In this regime, algorithms which utilize sub-sampling techniques are known to be effective. In…

Recent years have witnessed the emergence of textual commonsense knowledge bases, aimed at providing more nuanced and context-rich knowledge. The integration of external commonsense into language models has been shown to be a key enabler in…

Gaussian processes are ubiquitous as the primary tool for modeling spatial data. However, the Gaussian process is limited by its $\mathcal{O}(n^3)$ cost, making direct parameter fitting algorithms infeasible for the scale of modern data…

Optimization problem, which is aimed at finding the global minimal value of a given cost function, is one of the central problem in science and engineering. Various numerical methods have been proposed to solve this problem, among which the…

A new maximum approximate likelihood (ML) estimation algorithm for the mixture of Kent distribution is proposed. The new algorithm is constructed via the BSLM (block successive lower-bound maximization) framework and incorporates manifold…

The combination of Markov state modeling (MSM) and molecular dynamics (MD) simulations has been shown in recent years to be a valuable approach to unravel the slow processes of molecular systems with increasing complexity. While the…

In this paper we describe a new brute force algorithm for building the $k$-Nearest Neighbor Graph ($k$-NNG). The $k$-NNG algorithm has many applications in areas such as machine learning, bio-informatics, and clustering analysis. While…

Normalization techniques such as Batch Normalization have been applied successfully for training deep neural networks. Yet, despite its apparent empirical benefits, the reasons behind the success of Batch Normalization are mostly…

Clustering may be the most fundamental problem in unsupervised learning which is still active in machine learning research because its importance in many applications. Popular methods like K-means, may suffer from instability as they are…

Superlinear convergence has been an elusive goal for black-box nonsmooth optimization. Even in the convex case, the subgradient method is very slow, and while some cutting plane algorithms, including traditional bundle methods, are popular…

Median clustering extends popular neural data analysis methods such as the self-organizing map or neural gas to general data structures given by a dissimilarity matrix only. This offers flexible and robust global data inspection methods…

Natural gradient (NG) is an information-geometric optimization method that plays a crucial role, especially in the estimation of parameters for machine learning models like neural networks. To apply NG to quantum systems, the quantum…

Multimarginal optimal transport (MOT) is a powerful framework for modeling interactions between multiple distributions, yet its applicability is bottlenecked by a high computational overhead. Entropic regularization provides computational…

Spectral clustering (SC) is one of the most popular clustering methods and often outperforms traditional clustering methods. SC uses the eigenvectors of a Laplacian matrix calculated from a similarity matrix of a dataset. SC has serious…

Numerical simulation is a predominant tool for studying the dynamics in complex systems, but large-scale simulations are often intractable due to computational limitations. Here, we introduce the Neural Graph Simulator (NGS) for simulating…

Clustering is a fundamental problem in unsupervised learning, and has been studied widely both as a problem of learning mixture models and as an optimization problem. In this paper, we study clustering with respect the emph{k-median}…

Parameter estimation for model-based clustering using a finite mixture of normal inverse Gaussian (NIG) distributions is achieved through variational Bayes approximations. Univariate NIG mixtures and multivariate NIG mixtures are…

The recently emerged spectral clustering surpasses conventional clustering methods by detecting clusters of any shape without the convexity assumption. Unfortunately, with a computational complexity of $O(n^3)$, it was infeasible for…