Detection of elliptical shapes via cross-entropy clustering

The problem of finding elliptical shapes in an image will be considered. We discuss the solution which uses cross-entropy clustering. The proposed method allows the search for ellipses with predefined sizes and position in the space. Moreover, it works well for search of ellipsoids in higher dimensions

Fuzzy cluster validation using the partition negentropy criterion

The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-642-04277-5_24Proceedings of the 19th International Conference, Limassol, Cyprus, September 14-17, 2009We introduce the Partition Negentropy Criterion (PNC) for cluster validation. It is a cluster validity index that rewards the average normality of the clusters, measured by means of the negentropy, and penalizes the overlap, measured by the partition entropy. The PNC is aimed at finding well separated clusters whose shape is approximately Gaussian. We use the new index to validate fuzzy partitions in a set of synthetic clustering problems, and compare the results to those obtained by the AIC, BIC and ICL criteria. The partitions are obtained by fitting a Gaussian Mixture Model to the data using the EM algorithm. We show that, when the real clusters are normally distributed, all the criteria are able to correctly assess the number of components, with AIC and BIC allowing a higher cluster overlap. However, when the real cluster distributions are not Gaussian (i.e. the distribution assumed by the mixture model) the PNC outperforms the other indices, being able to correctly evaluate the number of clusters while the other criteria (specially AIC and BIC) tend to overestimate it.This work has been partially supported with funds from MEC BFU2006-07902/BFI, CAM S-SEM-0255-2006 and CAM/UAM project CCG08-UAM/TIC-442

Understanding methods for internal and external preference mapping and clustering in sensory analysis

Doctor of PhilosophyDepartment of Human NutritionEdgar Chambers IVPreference mapping is a method that provides product development directions for developers to see a whole picture of products, liking and relevant descriptors in a target market. Many statistical methods and commercial statistical software programs offering preference mapping analyses are available to researchers. Because of numerous available options, there are two questions addressed in this research that most scientists must answer before choosing a method of analysis: 1) are the different methods providing the same interpretation, co-ordinate values and object orientation; and 2) which method and program should be used with the data provided? This research used data from paint, milk and fragrance studies, representing complexity from lesser to higher. The techniques used are principal component analysis, multidimensional preference map (MDPREF), modified preference map (PREFMAP), canonical variate analysis, generalized procrustes analysis and partial least square regression utilizing statistical software programs of SAS, Unscrambler, Senstools and XLSTAT. Moreover, the homogeneousness of consumer data were investigated through hierarchical cluster analysis (McQuitty’s similarity analysis, median, single linkage, complete linkage, average linkage, and Ward’s method), partitional algorithm (k-means method), nonparametric method versus four manual clustering groups (strict, strict-liking-only, loose, loose-liking-only segments). The manual clusters were extracted according to the most frequently rated highest for best liked and least liked products on hedonic ratings. Furthermore, impacts of plotting preference maps for individual clusters were explored with and without the use of an overall mean liking vector. Results illustrated various statistical software programs were not similar in their oriented and co-ordinate values, even when using the same preference method. Also, if data were not highly homogenous, interpretation could be different. Most computer cluster analyses did not segment consumers relevant to their preferences and did not yield as homogenous clusters as manual clustering. The interpretation of preference maps created by the highest homogeneous clusters had little improvement when applied to complicated data. Researchers should look at key findings from univariate data in descriptive sensory studies to obtain accurate interpretations and suggestions from the maps, especially for external preference mapping. When researchers make recommendations based on an external map alone for complicated data, preference maps may be overused