Common methods for spatial distribution, such as hydrologic response units, are subjective, time-consuming, and fail to capture the full range of basin attributes. Recent advances in statistical-learning techniques allow new approaches this problem. We propose use Gaussian Mixture Models (GMMs) distribution models. GMMs objectively select set modeling locations that best represent watershed fea...

The mixture of Gaussian distributions, a soft version of k-means ( [2]), is considered a stateof-the-art clustering algorithm. It is widely used in computer vision for selecting classes, e.g., color[4, 1, 5],texture[1, 9], shapes [12, 10]. In this algorithm, each class is described by a Gaussian distribution, defined by its mean and covariance. The data is described by a weighted sum of these G...

In this paper, we study denoising of multicomponent images. The presented procedures are spatial wavelet-based denoising techniques, based on Bayesian leastsquares optimization procedures, using prior models for the wavelet coefficients that account for the correlations between the spectral bands. We analyze three mixture priors: Gaussian scale mixture models, Bernoulli-Gaussian mixture models ...

In this paper, an improved nonlinear Gaussian mixture probability hypothesis density (GM-PHD) filter is proposed to address bearings-only measurements in multi-target tracking. The proposed method, called the Gaussian mixture measurements-probability hypothesis density (GMM-PHD) filter, not only approximates the posterior intensity using a Gaussian mixture, but also models the likelihood functi...

We explore the use of Optimal Mixture Models to represent topics. We analyze two broad classes of mixture models: set-based and weighted. We provide an original proof that estimation of set-based models is NP-hard, and therefore not feasible. We argue that weighted models are superior to set-based models, and the solution can be estimated by a simple gradient descent technique. We demonstrate t...

Figure 1.1: Visualization of Tensors of different orders. gained popularity in parameter estimation for a variety of problems. In this lecture, the focus is on how they may be used in estimating the parameters of Gaussian Mixture Models and Hidden Markov Models. In a Gaussian mixture model, there are k unknown n-dimensional multivariate Gaussian distributions. Samples are generated by first pic...

We address the problem of probability density function estimation using a Gaussian mixture model updated with the expectationmaximization (EM) algorithm. To deal with the case of an unknown number of mixing kernels, we define a new measure for Gaussian mixtures, called total kurtosis, which is based on the weighted sample kurtoses of the kernels. This measure provides an indication of how well ...

| We address the problem of probability density function estimation using a Gaussian mixture model updated with the expectation-maximization (EM) algorithm. To deal with the case of an unknown number of mixing kernels , we deene a new measure for Gaussian mixtures, called total kurtosis, which is based on the weighted sample kur-toses of the kernels. This measure provides an indication of how w...

| We address the problem of probability density function estimation using a Gaussian mixture model updated with the EM algorithm. To deal with the case of an unknown number of mixing kernels, we deene a new measure for Gaussian mixtures, called total kurtosis, which is based on the weighted sample kurtoses of the kernels. This measure provides an indication of how well the Gaussian mixture ts t...