Aloba, Aishat O. (2015) Estimating the Number of Components of a Spatial–Em Algorithm: an R Package. Undergraduate thesis, under the direction of Yixin Chen from Computer and Information Science, The University of Mississippi.

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Abstract
The Expectation Maximization algorithm also known as the EM algorithm is an algorithm used to solve the maximum likelihood parameter estimation problem. This problem arises when some of the data involved are missing or incomplete, hence it becomes diﬃcult to know the parameters of the underlying distribution. The EM algorithm mainly comprises of two steps; the E–Step, and the M–Step. In the E–Step, estimated parameter values are used as true values to calculate the maximum likelihood estimate, and in the M–Step, the maximum likelihood calculated is used to estimate the parameters. The E–Step and M–Step iterate through until a speciﬁed convergence is met. Applications of the EM algorithm include density estimation in unsupervised clustering, estimating class–conditional densities in supervised learning settings, and for outlier detection purposes. The Spatial – EM algorithm is a novel approach that utilizes median – based location and rank – based scatter estimators to replace the sample mean and sample covariance matrix in the M – Step of an EM algorithm. This helps to enhance the stability and robustness of the Spatial – EM algorithm for ﬁnite mixture models. The algorithm is especially robust to outliers. In this research, we use the trimmed Bayesian Information Criterion (BIC) to determine the optimal value of the number of components in the distribution. The algorithm is implemented as an R package, and tested on diﬀerent datasets.
Item Type:  Thesis (Undergraduate) 

Creators:  Aloba, Aishat O. 
Student's Degree Program(s):  Computer Science 
Thesis Advisor:  Yixin Chen 
Thesis Advisor's Department:  Computer and Information Science 
Institution:  The University of Mississippi 
Subjects:  Q Science > QA Mathematics > QA75 Electronic computers. Computer science Q Science > QA Mathematics > QA76 Computer software 
Depositing User:  Aishat Oluwaseun Aloba 
Date Deposited:  06 May 2015 19:10 
Last Modified:  06 May 2015 19:10 
URI:  http://thesis.honors.olemiss.edu/id/eprint/311 
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