$K$-Means and Gaussian Mixture Modeling with a Separation Constraint

基于正态逆高斯分布的变分贝叶斯聚类方法

Variational Bayes Approximations for Clustering via Mixtures of Normal Inverse Gaussian Distributions

通过变分贝叶斯近似实现了基于模型的聚类的参数估计。考虑了单变量NIG混合物和多变量NIG混合物。变分贝叶斯近似的使用在这里是从传统的EM方法的实质性偏离，并消除了一些相关的计算复杂性和不确定性。我们的变分算法适用于模拟和真实数据。最后，本文进行了讨论，并对今后的工作提出了建议。

Clustering of non-Gaussian data by variational Bayes for normal inverse Gaussian mixture models

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) distributions are normal-variance mean which mixing densities are inverse Gaussian distributions and can be used for both haavy-tail and asymmetry. For NIG mixture models, both expectation-maximization method and variational Bayesian (VB) algorithms have been proposed. However, the existing VB algorithm for NIG mixture have a disadvantage that the shape of th…

An Adaptive Covariance Parameterization Technique for the Ensemble Gaussian Mixture Filter

The ensemble Gaussian mixture filter combines the simplicity and power of Gaussian mixture models with the provable convergence and power of particle filters. The quality of the ensemble Gaussian mixture filter heavily depends on the choice of covariance matrix in each Gaussian mixture. This work extends the ensemble Gaussian mixture filter to an adaptive choice of covariance based on the parameterized estimates of the sample covariance matrix. Through the use of the expectation maximization algorithm, optimal choices of the covariance matrix parameters are computed in an online fashion. Numer…

A Bayesian approach for clustering skewed data using mixtures of multivariate normal-inverse Gaussian distributions

Non-Gaussian mixture models are gaining increasing attention for mixture model-based clustering particularly when dealing with data that exhibit features such as skewness and heavy tails. Here, such a mixture distribution is presented, based on the multivariate normal inverse Gaussian (MNIG) distribution. For parameter estimation of the mixture, a Bayesian approach via Gibbs sampler is used; for this, a novel approach to simulate univariate generalized inverse Gaussian random variables and matrix generalized inverse Gaussian random matrices is provided. The proposed algorithm will be applied t…

卷积声音混合盲分离的动态算法

A Dynamic Algorithm for Blind Separation of Convolutive Sound Mixtures

提出一种基于频域统计信息更新和时域解混滤波器支撑最小化的动态盲源分离算法，通过优化多时滞互相关系数的l1×l∞范数解决排列和缩放模糊性，实现无迭代自适应分离。

高斯混合模型的矩量法：实现与基准测试

Method of moments for Gaussian mixtures: Implementation and benchmarks

针对高斯混合模型参数恢复问题，本文记录高维场景下矩量法性能，概述矩选择及对应多项式，实现为Julia包GMMParameterEstimation并提供计算基准，助力相关领域参数恢复应用。