Em Algorithm | Statistics

Em Algorithm | Statistics

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  Introduction  Expectation-maximization (EM)algorithm is a method that is used for finding maximum likelihood or maximum a posteriori (MAP) that is the estimation of parameters in statistical models, and the model depends on unobserved latent variables that is calculated using models  This is an ordinary iterative method and The EM iteration alternates an expectation (E) step, that creates a function for the expectation of the log-likelihood that is evaluated using the current estimation of parameters and it is followed by the maximization (M) step, that computes maximization of the expected log-likelihood that is found on the E-step that is calculated in the previous step  These parameter-estimations are then used to determine the distribution of the latent variables in the next E step that is the final process and the foremost
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  Overview  The EMalgorithm was explained and developed in a classic 1977 paper that was demonstrated by Arthur Dempster, Nan laird and Donald Rubin in the early stages.  They generalized this EM algorithm method and also sketched an analysis for convergence that would provide solutions for a wider class of problems that is analyzed  This algorithm is a iterative approach and is sub- optimal where we try to find the probability distribution which has the maximum likelihood from incomplete data via the EM algorithm on its attributes that are evaluated
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  EM algorithm Clustering EM algorithm Clustering methods are grouped in the form of classes and one of the most widely clustering is the hierarchical clustering which is a popular one. These techniques are more useful in the field of data mining and in discovery of knowledge which is more complex and a powerful method  Clustering method is based on the probability models and is more helpful in finding the missing values in the given set of data. It provides a powerful insight within the data set and in analysis of the each and individual entity  It is based on the principle of the maximum likelihood method that is enriched in the analysis EM algorithm
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  Clustering
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  Properties  As thereis no increase in the observed data, there is no assurance for the maximum convergence of the likelihood estimator. If it is multimodal distribution, then it may converge to the local maximum depending upon the starting value as it is a fixed one  When the likelihood belongs to the exponential family, this algorithm is more useful and the M-step includes the maximization of the linear function  There are various methods like conjugate gradient, gradient descent for finding the likelihood estimates but, these methods also require the second derivative evaluation of the function  For the smoothing and filtering purpose of the EM algorithm, kalman filter is used for solving the joint state and other estimation problems. It is also used in two-steps such as E-step where the current parameter is used to obtain the state estimates. This step is followed by the M-step where the maximum-likelihood calculations are done
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  Applications  EM algorithmis mainly used in data clustering that helps in data mining and finite mixture model. Many EM Algorithm tutorials have come into existence for the better understanding of this process  It also helps in the computer vision and machine learning.  In the field of psychometrics, it is used in the estimation of the item parameter and abilities using the item-response theory as it is indispensable  EM arises as a useful tool in managing risk of portfolio and in price as it helps in the management of missing data and in the observation of the variables  EM algorithm is mostly used in medical filed in the reconstruction of the medical image and in the emission of single photon computed tomography  In case of structural engineering, EM algorithm is used in the identification of vibration properties of structural system using the data outcome of sensor
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  Hey Friends, This wasjust a summary on EM Algorithm. For more detailed information on this topic, please type the link given below or copy it from the description of this PPT and open it in a new browser window. http://www.transtutors.com/homework- help/statistics/em-algorithm.aspx