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- Adrian G. Bors, Nikolaos Nasios
- IEEE Trans. Systems, Man, and Cybernetics, Part B
- 2009

Kernel density estimation is a nonparametric procedure for probability density modeling, which has found several applications in various fields. The smoothness and modeling ability of the functional approximation are controlled by the kernel bandwidth. In this paper, we describe a Bayesian estimation method for finding the bandwidth from a given data set.… (More)

- Nikolaos Nasios, Adrian G. Bors
- IEEE transactions on systems, man, and…
- 2006

This paper proposes a joint maximum likelihood and Bayesian methodology for estimating Gaussian mixture models. In Bayesian inference, the distributions of parameters are modeled, characterized by hyperparameters. In the case of Gaussian mixtures, the distributions of parameters are considered as Gaussian for the mean, Wishart for the covariance, and… (More)

- Nikolaos Nasios, Adrian G. Bors
- Pattern Recognition
- 2007

This paper introduces a new nonparametric estimation approach inspired from quantum mechanics. Kernel density estimation associates a function to each data sample. In classical kernel estimation theory the probability density function is calculated by summing up all the kernels. The proposed approach assumes that each data sample is associated with a… (More)

- Nikolaos Nasios, Adrian G. Bors
- CAIP
- 2003

In this paper we suggest a new variational Bayesian approach. Variational Expectation-Maximization (VEM) algorithm is proposed in order to estimate a set of hyperparameters modelling distributions of parameters characterizing mixtures of Gaussians. We consider maximum log-likelihood (ML) estimation for the initialization of the hyperparameters. The ML… (More)

- Nikolaos Nasios, Adrian G. Bors
- NNSP
- 2003

This paper introduces variational expectation-maximization (VEM) algorithm for training Gaussian networks. Hyperparameters model distributions of parameters characterizing Gaussian mixture densities. The proposed algorithm employs a hierarchical learning strategy for estimating a set of hyperparameters and the number of Gaussian mixture components. A dual… (More)

- Nikolaos Nasios, Adrian G. Bors
- IEEE International Conference on Image Processing…
- 2005

This paper introduces a new nonparametric estimation approach that can be used for data that is not necessarily Gaussian distributed. The proposed approach employs the Shrodinger partial differential equation. We assume that each data sample is associated with a quantum physics particle that has a radial field around its value. We consider a statistical… (More)

- Adrian G. Bors, Nikolaos Nasios
- ICANN
- 2009

Kernel density estimation (KDE) has been used in many computational intelligence and computer vision applications. In this paper we propose a Bayesian estimation method for finding the bandwidth in KDE applications. A Gamma density function is fitted to distributions of variances of K-nearest neighbours data populations while uniform distribution priors are… (More)

- Nikolaos Nasios, Adrian G. Bors
- IEEE International Conference on Image Processing…
- 2005

A variational Bayesian framework is employed in the paper for image segmentation using color clustering. A Gaussian mixture model is used to represent color distributions. Variational expectation-maximization (VEM) algorithm takes into account the uncertainty in the parameter estimation ensuring a lower bound on the approximation error. In the variational… (More)

- Adrian G. Bors, Nikolaos Nasios
- ICPR
- 2008

In kernel density estimation methods, an approximation of the data probability density function is achieved by locating a kernel function at each data location. The smoothness of the functional approximation and the modelling ability are controlled by the kernel bandwidth. In this paper we propose a Bayesian estimation method for finding the kernel… (More)

- Nikolaos Nasios, Adrian G. Bors
- CAIP
- 2005

Non-parametric data representation can be done by means of a potential function. This paper introduces a methodology for finding modes of the potential function. Two different methods are considered for the potential function representation: by using summations of Gaussian kernels, and by employing quantum clustering. In the second case each data sample is… (More)