Gaussian mixture density modeling, decomposition, and applications

1996 ◽  
Vol 5 (9) ◽  
pp. 1293-1302 ◽  
Author(s):  
Xinhua Zhuang ◽  
Yan Huang ◽  
K. Palaniappan ◽  
Yunxin Zhao
Keyword(s):  
Gaussian Mixture ◽  
Mixture Density ◽  
Density Modeling

Kernel-Based Topographic Map Formation by Local Density Modeling

2002 ◽  
Vol 14 (7) ◽  
pp. 1561-1573 ◽  
Author(s):  
Marc M. Van Hulle
Keyword(s):  
Learning Algorithm ◽  
Local Density ◽  
Gaussian Mixture ◽  
Density Model ◽  
Topographic Map ◽  
Mixture Density ◽  
Gaussian Kernels ◽  
New Learning ◽  
Local Input ◽  
Density Modeling

We introduce a new learning algorithm for kernel-based topographic map formation. The algorithm generates a gaussian mixture density model by individually adapting the gaussian kernels' centers and radii to the assumed gaussian local input densities.

Edgeworth-Expanded Gaussian Mixture Density Modeling

2005 ◽  
Vol 17 (8) ◽  
pp. 1706-1714 ◽  
Author(s):  
Marc M. Van Hulle
Keyword(s):  
Edgeworth Expansion ◽  
Closed Form Solution ◽  
Gaussian Mixture ◽  
Form Solution ◽  
Gaussian Kernel ◽  
Moment Matching ◽  
Mixture Density ◽  
Gaussian Kernels ◽  
Kernel Parameters ◽  
Density Modeling

Instead of increasing the order of the Edgeworth expansion of a single gaussian kernel, we suggest using mixtures of Edgeworth-expanded gaussian kernels of moderate order. We introduce a simple closed-form solution for estimating the kernel parameters based on weighted moment matching. Furthermore, we formulate the extension to the multivariate case, which is not always feasible with algebraic density approximation procedures.

scholarly journals Reconciling differences in stratospheric ozone composites

2017 ◽  
Vol 17 (20) ◽  
pp. 12269-12302 ◽  
Author(s):  
William T. Ball ◽  
Justin Alsing ◽  
Daniel J. Mortlock ◽  
Eugene V. Rozanov ◽  
Fiona Tummon ◽  
...  
Keyword(s):  
Time Series ◽  
Likelihood Function ◽  
Stratospheric Ozone ◽  
Gaussian Mixture ◽  
Robust Estimate ◽  
Mixture Density ◽  
Source Data ◽  
Ozone Trends ◽  
Decadal Trend

Abstract. Observations of stratospheric ozone from multiple instruments now span three decades; combining these into composite datasets allows long-term ozone trends to be estimated. Recently, several ozone composites have been published, but trends disagree by latitude and altitude, even between composites built upon the same instrument data. We confirm that the main causes of differences in decadal trend estimates lie in (i) steps in the composite time series when the instrument source data changes and (ii) artificial sub-decadal trends in the underlying instrument data. These artefacts introduce features that can alias with regressors in multiple linear regression (MLR) analysis; both can lead to inaccurate trend estimates. Here, we aim to remove these artefacts using Bayesian methods to infer the underlying ozone time series from a set of composites by building a joint-likelihood function using a Gaussian-mixture density to model outliers introduced by data artefacts, together with a data-driven prior on ozone variability that incorporates knowledge of problems during instrument operation. We apply this Bayesian self-calibration approach to stratospheric ozone in 10° bands from 60° S to 60° N and from 46 to 1 hPa (∼ 21–48 km) for 1985–2012. There are two main outcomes: (i) we independently identify and confirm many of the data problems previously identified, but which remain unaccounted for in existing composites; (ii) we construct an ozone composite, with uncertainties, that is free from most of these problems – we call this the BAyeSian Integrated and Consolidated (BASIC) composite. To analyse the new BASIC composite, we use dynamical linear modelling (DLM), which provides a more robust estimate of long-term changes through Bayesian inference than MLR. BASIC and DLM, together, provide a step forward in improving estimates of decadal trends. Our results indicate a significant recovery of ozone since 1998 in the upper stratosphere, of both northern and southern midlatitudes, in all four composites analysed, and particularly in the BASIC composite. The BASIC results also show no hemispheric difference in the recovery at midlatitudes, in contrast to an apparent feature that is present, but not consistent, in the four composites. Our overall conclusion is that it is possible to effectively combine different ozone composites and account for artefacts and drifts, and that this leads to a clear and significant result that upper stratospheric ozone levels have increased since 1998, following an earlier decline.

scholarly journals Bayesian classification of vegetation types with Gaussian mixture density fitting to indicator values

2007 ◽  
Vol 18 (4) ◽  
pp. 605-612 ◽  
Author(s):  
Jan‐Philip M. Witte ◽  
Rafał B. Wójcik ◽  
Paul J.J.F. Torfs ◽  
Martin W.H. Haan ◽  
Stephan Hennekens
Keyword(s):  
Gaussian Mixture ◽  
Bayesian Classification ◽  
Vegetation Types ◽  
Indicator Values ◽  
Mixture Density ◽  
Density Fitting

scholarly journals An Improved Gaussian Mixture CKF Algorithm under Non-Gaussian Observation Noise

2016 ◽  
Vol 2016 ◽  
pp. 1-10
Author(s):  
Hongjian Wang ◽  
Cun Li
Keyword(s):  
Target Tracking ◽  
Computation Time ◽  
Velocity Model ◽  
Gaussian Mixture ◽  
Fast Tracking ◽  
Mixture Density ◽  
Cubature Kalman Filter ◽  
Observation Noise ◽  
Non Gaussian ◽  
Time Update

In order to solve the problems that the weight of Gaussian components of Gaussian mixture filter remains constant during the time update stage, an improved Gaussian Mixture Cubature Kalman Filter (IGMCKF) algorithm is designed by combining a Gaussian mixture density model with a CKF for target tracking. The algorithm adopts Gaussian mixture density function to approximately estimate the observation noise. The observation models based on Mini RadaScan for target tracking on offing are introduced, and the observation noise is modelled as glint noise. The Gaussian components are predicted and updated using CKF. A cost function is designed by integral square difference to update the weight of Gaussian components on the time update stage. Based on comparison experiments of constant angular velocity model and maneuver model with different algorithms, the proposed algorithm has the advantages of fast tracking response and high estimation precision, and the computation time should satisfy real-time target tracking requirements.

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