3. Electronic Theses and Dissertations (ETDs) - All submissions
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Item Evaluation of cluster analysis and latent class analysis in clustering(2019) Murisa, TatendaThe study compares the performance of latent class, K-means and hierarchical clustering on data with different degrees of cluster overlap. It also assesses how various standardisation methods affect the results of hierarchical and K-means clustering. Several distance and agglomeration methods are evaluated to observe how they perform depending on cluster overlap. Three artificial datasets were simulated whose clusters were poorly, moderately and well separated. These along with the seeds data were run through the three clustering methods. Several external validity indices were calculated for each cluster solution. The adjusted Rand index was used for comparison in the discussion because it is not affected by the number of clusters. Results showed that Ward’s method performed better compared to all other agglomeration methods and the Manhattan distance performed better across the different cluster types in hierarchical clustering. Latent class clustering performed better for poorly and well separated clusters. When the variance of the variables were comparable, K-means clustering with no standardisation performed well. Standardisation by the maximum value and z-score had the best cluster recovery when the variance of variables were large.Item Analysis of bounded distance decoding for Reed Solomon codes(2017) Babalola, Oluwaseyi PaulBounded distance decoding of Reed Solomon (RS) codes involves nding a unique codeword if there is at least one codeword within the given distance. A corrupted message having errors that is less than or equal to half the minimum distance cor- responds to a unique codeword, and therefore will decode errors correctly using the minimum distance decoder. However, increasing the decoding radius to be slightly higher than half of the minimum distance may result in multiple codewords within the Hamming sphere. The list decoding and syndrome extension methods provide a maximum error correcting capability whereby the radius of the Hamming ball can be extended for low rate RS codes. In this research, we study the probability of having unique codewords for (7; k) RS codes when the decoding radius is increased from the error correcting capability t to t + 1. Simulation results show a signi cant e ect of the code rates on the probability of having unique codewords. It also shows that the probability of having unique codeword for low rate codes is close to one.