Michael Wodny

Data Mining and Metrics on Data Sets

One needs suitable metrics for topologically based methods of the data analysis. Examples of distances and metrics are given. A general method for the generation of metrics is developed. Its usefulness is demonstrated in support of classification methods for mixed type data

Cluster- and Discriminant Analysis With Both Metric and Categorial Data

Questions in medicine and biological sciences which require a cluster or discriminant analysis frequently appear. If there isn’t clarity concerning a probability theoretical data model, topologically based methods should be preferred. In this paper, a topological data model is defined for both metric and categorial variables. Every categorial character can be transformed into dichotomous characters. Therefore, we restrict the description to continuous and binary variables. A cluster analysis regarding this data space topology is illustrated on hand of a data set from forensic medicine.

Splines and compartment models : an introduction

Interpolating Splines of Degree n Interpolating Cubic Splines Interpolating Cubic Splines with Several Extreme Characteristics Smoothing Cubic Splines Estimation of Smoothing Parameters Interpolating Quadratic Splines Smoothing Quadratic Splines Splines and Average Functions Compartment Models Calculability and Identifiability Compartment Models and Associated Residence Time Distributions Calculation Methods Related to Compartment Models Varied Minimum Chi-square Parameter Estimation Pharmacokinetics for Multiple Applications Mathematica(R) Programs for Selected Problems.

How Exactly Do We Know Inheritance Parameters

There are different concepts to quantify the information contained in a data set. The classic result is from R.A.Fisher: Regarding a sample over a random variable. The Fisher-Information is defined under certain assumptions as the inverse of the Rao-Cramer barrier in the well known inequality of the same name. The Fisher-Informations are considered for the simplest genetic models of intheritance. This applies to medically relevant ranges of the inheritance model parameter and large data sets. The results are compared with exact calculations.