A.A. Sirota, A.V. Tsurikov, M.A. Dryuchenko

The paper discusses the approaches to creating content-dependent digital watermarks that can be used with text data, based on the neural network technologies. It shows that the watermark creation is equal to classifying high-dimensional data and introduces a mathematical model of data distribution in high-dimensional spaces along with the classification algorithm that is based on the radial basis functions (RBF) networks. The paper also describes the ways that allow to significantly reduce the number of RBF functions in the classifying network using the k-means algorithm (data clustering). The dependencies between classification error, the number of the classified objects and the radial functions parameters are explored. The article presents the results of the system statistical modeling using the amount of randomly generated points that are distributed (uniform distribution) in the hypercube as an example. It gives the theoretical evaluation of the classification error. It is based on the assumption that the influence ranges of the different radial functions intersect in the hypercube. The paper shows the results of exploring dependencies between cluster spacings, cluster sizes, theoretical evaluation of the classification error and the space dimension size.