scholarly journals EM-LDDMM for 3D to 2D registration

2019 ◽  
Author(s):  
Daniel Tward ◽  
Michael Miller
Keyword(s):  
Hidden Variables ◽  
Expectation Maximization Algorithm ◽  
Target Tissue ◽  
Coordinate Systems ◽  
Target Image ◽  
Unknown Parameters ◽  
Conditional Mean ◽  
New Class ◽  
Tissue Sections ◽  
Diffeomorphic Metric Mapping

AbstractWe examine the problem of mapping dense 3D atlases onto censored, sparsely sampled 2D target sections at micron and meso scales. We introduce a new class of large deformation diffeomorphic metric mapping (LD-DMM) algorithms for generating dense atlas correspondences onto sparse 2D samples by introducing a field of hidden variables which must be estimated representing a large class of target image uncertainties including (i) unknown parameters representing cross stain contrasts, (ii) censoring of tissue due to localized measurements of target subvolumes and (iii) sparse sampling of target tissue sections. For prediction of the hidden fields we introduce the generalized expectation-maximization algorithm (EM) for which the E-step calculates the conditional mean of the hidden variates simultaneously combined with the diffeomorphic correspondences between atlas and target coordinate systems. The algorithm is run to fixed points guaranteeing estimators satisfy the necessary maximizer conditions when interpreted as likelihood estimators. The dense mapping is an injective correspondence to the sparse targets implying all of the 3D variations are performed only on the atlas side with variation in the targets only 2D manipulations.

Bayesian k-Means as a “Maximization-Expectation” Algorithm

2009 ◽  
Vol 21 (4) ◽  
pp. 1145-1172 ◽  
Author(s):  
Kenichi Kurihara ◽  
Max Welling
Keyword(s):  
Data Structures ◽  
Expectation Maximization ◽  
Clustering Algorithm ◽  
Hidden Variables ◽  
Expectation Maximization Algorithm ◽  
Model Structure ◽  
Random Parameters ◽  
Agglomerative Clustering ◽  
Top Down ◽  
New Class

We introduce a new class of “maximization-expectation” (ME) algorithms where we maximize over hidden variables but marginalize over random parameters. This reverses the roles of expectation and maximization in the classical expectation-maximization algorithm. In the context of clustering, we argue that these hard assignments open the door to very fast implementations based on data structures such as kd-trees and conga lines. The marginalization over parameters ensures that we retain the ability to infer model structure (i.e., number of clusters). As an important example, we discuss a top-down Bayesian k-means algorithm and a bottom-up agglomerative clustering algorithm. In experiments, we compare these algorithms against a number of alternative algorithms that have recently appeared in the literature.

scholarly journals New class of Lindley distributions: properties and applications

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Duha Hamed ◽  
Ahmad Alzaghal
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Simulation Study ◽  
Likelihood Estimation ◽  
Statistical Properties ◽  
Data Sets ◽  
Lifetime Data ◽  
Unknown Parameters ◽  
Lindley Distribution ◽  
New Class

AbstractA new generalized class of Lindley distribution is introduced in this paper. This new class is called the T-Lindley{Y} class of distributions, and it is generated by using the quantile functions of uniform, exponential, Weibull, log-logistic, logistic and Cauchy distributions. The statistical properties including the modes, moments and Shannon’s entropy are discussed. Three new generalized Lindley distributions are investigated in more details. For estimating the unknown parameters, the maximum likelihood estimation has been used and a simulation study was carried out. Lastly, the usefulness of this new proposed class in fitting lifetime data is illustrated using four different data sets. In the application section, the strength of members of the T-Lindley{Y} class in modeling both unimodal as well as bimodal data sets is presented. A member of the T-Lindley{Y} class of distributions outperformed other known distributions in modeling unimodal and bimodal lifetime data sets.

Univariate and bivariate extensions of the generalized exponential distributions

2021 ◽  
Vol 71 (6) ◽  
pp. 1581-1598
Author(s):  
Vahid Nekoukhou ◽  
Ashkan Khalifeh ◽  
Hamid Bidram
Keyword(s):  
Em Algorithm ◽  
Exponential Distribution ◽  
Bivariate Distribution ◽  
Generalized Exponential Distribution ◽  
Exponential Distributions ◽  
Unknown Parameters ◽  
Data Set ◽  
New Class ◽  
Special Cases ◽  
Univariate Distribution

Abstract The main aim of this paper is to introduce a new class of continuous generalized exponential distributions, both for the univariate and bivariate cases. This new class of distributions contains some newly developed distributions as special cases, such as the univariate and also bivariate geometric generalized exponential distribution and the exponential-discrete generalized exponential distribution. Several properties of the proposed univariate and bivariate distributions, and their physical interpretations, are investigated. The univariate distribution has four parameters, whereas the bivariate distribution has five parameters. We propose to use an EM algorithm to estimate the unknown parameters. According to extensive simulation studies, we see that the effectiveness of the proposed algorithm, and the performance is quite satisfactory. A bivariate data set is analyzed and it is observed that the proposed models and the EM algorithm work quite well in practice.

scholarly journals Using the properties of vehicles in the conceptof the multi-environment multi-modal quantomobile

2020 ◽  
Vol 17 (6) ◽  
pp. 195-205
Author(s):  
Ju. G. Kotikov ◽  
Keyword(s):  
Numerical Modeling ◽  
Research And Development ◽  
Physical Vacuum ◽  
Motion Model ◽  
Single Family ◽  
Coordinate Systems ◽  
Hypothetical Model ◽  
Ground Vehicle ◽  
New Class ◽  
The One

The development of the concept of the quantum engine, that uses the energy of physical vacuum, makes it possible to create a new class of vehicles, namely, the quantomobile, designed as a quantum - powered vehicle. The type of quantum vehicles can be versatile, starting from the simplest version (with the ground vehicle driving modes) to the multi-environment multi-modal quantomobile that can function on land, in the air and in water. To work out a hypothetical model of the multi-environment multi-modal quantomobile, it is necessary to use all the heritage of research and development in the sphere of transport engineering. For 10 variants of the multi-environment multi-modal quantomobile movement - from the air quantum helicopter (quantocraft) to a quantum submarine (quantomarine) - there has been made an analysis of the numerical modeling specifics, the use of coordinate systems, the implementation of the traffic of existing transport vehicles that can be reflected in the concept of multi-environment quantomobile. Two extreme methods of modeling are distinguished: 1) the one based on a single family of coordinate systems and a common (end-to-end for all types of environment) motion model; 2) the one based on models by type of motion with possible switching of coordinate systems.

scholarly journals The Exponentiated Lindley Geometric Distribution with Applications

Entropy ◽  
2019 ◽  
Vol 21 (5) ◽  
pp. 510
Author(s):  
Bo Peng ◽  
Zhengqiu Xu ◽  
Min Wang
Keyword(s):  
Maximum Likelihood ◽  
Geometric Distribution ◽  
Residual Life ◽  
Information Matrix ◽  
Expectation Maximization Algorithm ◽  
Likelihood Estimation ◽  
Real Data ◽  
Quantile Function ◽  
Maximum Likelihood Estimates ◽  
Unknown Parameters

We introduce a new three-parameter lifetime distribution, the exponentiated Lindley geometric distribution, which exhibits increasing, decreasing, unimodal, and bathtub shaped hazard rates. We provide statistical properties of the new distribution, including shape of the probability density function, hazard rate function, quantile function, order statistics, moments, residual life function, mean deviations, Bonferroni and Lorenz curves, and entropies. We use maximum likelihood estimation of the unknown parameters, and an Expectation-Maximization algorithm is also developed to find the maximum likelihood estimates. The Fisher information matrix is provided to construct the asymptotic confidence intervals. Finally, two real-data examples are analyzed for illustrative purposes.

scholarly journals The complementary Poisson-Lindley class of distributions

2015 ◽  
Vol 3 (2) ◽  
pp. 146 ◽  
Author(s):  
Amal Hassan ◽  
Salwa Assar ◽  
Kareem Ali
Keyword(s):  
Information Matrix ◽  
Real Data ◽  
Formal Proof ◽  
Cumulative Distribution ◽  
Likelihood Method ◽  
Unknown Parameters ◽  
Data Set ◽  
Lifetime Distributions ◽  
New Class ◽  
Rate Functions

<p>This paper proposed a new general class of continuous lifetime distributions, which is a complementary to the Poisson-Lindley family proposed by Asgharzadeh et al. [3]. The new class is derived by compounding the maximum of a random number of independent and identically continuous distributed random variables, and Poisson-Lindley distribution. Several properties of the proposed class are discussed, including a formal proof of probability density, cumulative distribution, and reliability and hazard rate functions. The unknown parameters are estimated by the maximum likelihood method and the Fisher’s information matrix elements are determined. Some sub-models of this class are investigated and studied in some details. Finally, a real data set is analyzed to illustrate the performance of new distributions.</p>

Invariant Manifolds Based Modular Adaptive Control for a Class of Nonlinear Systems with Application to Flight Control

2013 ◽  
Vol 373-375 ◽  
pp. 1488-1492
Author(s):  
Chao Zhang ◽  
Sheng Xiu Zhang ◽  
Yi Nan Liu
Keyword(s):  
Adaptive Control ◽  
Flight Control ◽  
Invariant Manifolds ◽  
Controller Design ◽  
Estimation Error ◽  
Dynamical Behavior ◽  
Unknown Parameters ◽  
Adaptive Controllers ◽  
New Class ◽  
New Type

In this paper a novel modular framework for adaptive control for a class of nonlinear system is developed and applied to flight controller design. The framework is based on the invariant manifolds approach with a new type of reduced-order estimator which allows for stable dynamics to be assigned to the estimation error. We show that this method can be applied to systems with unknown parameters, leading to a new class of modular adaptive controllers which is easier to tune compared to controllers obtained using the classical adaptive approaches and does not suffer from unpredictable dynamical behavior of the parameter update laws.

scholarly journals GTM: The Generative Topographic Mapping

1998 ◽  
Vol 10 (1) ◽  
pp. 215-234 ◽  
Author(s):  
Christopher M. Bishop ◽  
Markus Svensén ◽  
Christopher K. I. Williams
Keyword(s):  
Latent Variable ◽  
Hidden Variables ◽  
Expectation Maximization Algorithm ◽  
Simulated Data ◽  
Topographic Mapping ◽  
Self Organizing Map ◽  
Generative Topographic Mapping ◽  
Variable Model ◽  
Oil Pipeline ◽  
Latent Space

Latent variable models represent the probability density of data in a space of several dimensions in terms of a smaller number of latent, or hidden, variables. A familiar example is factor analysis, which is based on a linear transformation between the latent space and the data space. In this article, we introduce a form of nonlinear latent variable model called the generative topographic mapping, for which the parameters of the model can be determined using the expectation-maximization algorithm. GTM provides a principled alternative to the widely used self-organizing map (SOM) of Kohonen (1982) and overcomes most of the significant limitations of the SOM. We demonstrate the performance of the GTM algorithm on a toy problem and on simulated data from flow diagnostics for a multiphase oil pipeline.

Multivariate finite-support phase-type distributions

2020 ◽  
Vol 57 (4) ◽  
pp. 1260-1275
Author(s):  
Celeste R. Pavithra ◽  
T. G. Deepak
Keyword(s):  
Distribution Function ◽  
Expectation Maximization ◽  
Expectation Maximization Algorithm ◽  
Finite Support ◽  
Marginal Distributions ◽  
New Class ◽  
Phase Type ◽  
Phase Type Distributions ◽  
Support Phase

AbstractWe introduce a multivariate class of distributions with support I, a k-orthotope in $[0,\infty)^{k}$ , which is dense in the set of all k-dimensional distributions with support I. We call this new class ‘multivariate finite-support phase-type distributions’ (MFSPH). Though we generally define MFSPH distributions on any finite k-orthotope in $[0,\infty)^{k}$ , here we mainly deal with MFSPH distributions with support $[0,1)^{k}$ . The distribution function of an MFSPH variate is computed by using that of a variate in the MPH $^{*} $ class, the multivariate class of distributions introduced by Kulkarni (1989). The marginal distributions of MFSPH variates are found as FSPH distributions, the class studied by Ramaswami and Viswanath (2014). Some properties, including the mixture property, of MFSPH distributions are established. Estimates of the parameters of a particular class of bivariate finite-support phase-type distributions are found by using the expectation-maximization algorithm. Simulated samples are used to demonstrate how this class could be used as approximations for bivariate finite-support distributions.

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