Functional Analysis of the Differences in the Dimensions of Two Types of Boiled and Steamed Rice Grains.

The study tested how the cooking process can change the dimensions of rice grains. The impact of set times of cooking or steaming process on the characteristics such as length, width, and height of two varieties of rice, namely, long-grain white and parboiled, was investigated. The measurements of the dimension characteristics obtained at different times of the cooking process were converted to functional data. Different methods of multivariate functional data analysis, namely, functional multivariate analysis of variance, functional discriminant coordinates, and cluster analysis, were applied to discover the differences between the two varieties and the two heat treatment methods.

Sustainable Development of Polish Macroregions-Study by Means of the Kernel Discriminant Coordinates Method.

The aim of this study was to investigate if the macroregions of Poland are homogeneous in terms of the observed spatio-temporal data characterizing their sustainable development. So far, works related to the sustainable development of selected territorial units have been based on data relating to a specific year rather than many years. The solution to the problem of macroregion homogeneity goes through two stages. In step one, the original spatio-temporal data space (matrix space) was transformed into a kernel discriminant coordinates space. The obtained kernel discriminant coordinates function as synthetic measures of the level of sustainable development of Polish macroregions. These measures contain complete information on the values of 27 diagnostic features examined over 15 years. In the second step, cluster analysis was used in order to identify groups of homogeneous macroregions in the space of kernel discriminant coordinates. The agglomeration method and the Ward method were chosen as commonly used methods. By means of both methods, three super macroregions composed of homogeneous macroregions were identified. Within the kernel discriminant coordinates, the differentiating power of a selected set of 27 features characterizing the sustainable development of macroregions was also assessed. To this end, five different and most commonly used methods of discriminant analysis were used to test the correctness of the classification. Depending on the method, the classification errors amounted to zero or were close to zero, which proves a well-chosen set of diagnostic features. Although the data relate only to a specific country (Poland), the presented statistical methodology is universal and can be applied to any territorial unit and spatial-temporal dynamic data.