Functional data analysis (FDA) -the analysis of data that can be considered a set of observed continuous functions -is an increasingly common class of statistical analysis. One of the most widely used FDA methods is the cluster analysis of functional data; however, little work has been done to compare the performance of clustering methods on functional data. In this paper a simulation study compares the performance of four major hierarchical methods for clustering functional data. The simulated data varied in three ways: the nature of the signal functions (periodic, non-periodic, or mixed), the amount of noise added to the signal functions, and the pattern of the true cluster sizes. The Rand index was used to compare the performance of each clustering method. As a secondary goal, clustering methods were also compared when the number of clusters has been misspecified. To illustrate the results, a real set of functional data was clustered where the true clustering structure is believed to be known. Comparing the clustering methods for the real data set confirmed the findings of the simulation. This study yields concrete suggestions to future researchers to determine the best method for clustering their functional data.

Dual purpose wheat could be a good alternative for helping overcome the need to import this cereal in Brazil. To achieve this, development of cultivars with high yield is necessary. The contribution of genetics in defining traits is very important for directing breeding programs for the development of cultivars that provide the desired agronomic ideotype. We estimated heritability for 36 characters of agronomic importance in dual-purpose wheat. The inheritable genetic patterns were examined using linear trends, a Euclidean algorithm, factor analysis and artificial neural networks. The study was carried out during the crop seasons of 2011, 2012 and 2013. The experimental design was randomized block, arranged in a factorial scheme with three growing seasons (2011, 2012 and 2013) and five dual-purpose wheat genotypes (BRS Tarumã, BRS Umbu, BRS Figueira, BRS Guatambu and BRS 277) x three cuttings (first cutting, second cutting and third cutting), with three replicates. Deviance analysis or maximum likelihood was significant for the 36 characters. The length of the head of the main plant, plant height ©FUNPEC-RP www.funpecrp.com.br Genetics and Molecular Research 18 (3): gmr18266 I.R. Carvalho et al. 2 before the first second cutting and dry mass of the seedlings showed high variability. The 36 characters expressed linear genetic dependence based on the Euclidean Algorithm; similar to what was found with the Tocher Optimized Clustering and Artificial Neural Networks K-means methods. Similar genetic trends for heritability profiles were obtained with factor analysis and Artificial Neural Networks by the Kohonem method. The use of Artificial Neural Networks through the Kohonem method gave the greatest efficacy in the definition of the genetic profiles needed to develop the recommended agronomic ideotype for the improvement of dualpurpose wheat.