Many classi®cation tasks can be viewed as ordinal. Use of numeric information usually provides possibilities for more powerful analysis than ordinal data. On the other hand, ordinal data allows more powerful analysis when compared to nominal data. It is therefore important not to overlook knowledge about ordinal dependencies in data sets used in data mining. This paper investigates data mining ...

The performance of medical image classification has been enhanced by deep convolutional neural networks (CNNs), which are typically trained with cross-entropy (CE) loss. However, when the label presents an intrinsic ordinal property in nature, e.g., development from benign to malignant tumor, CE loss cannot take into account such information allow for better generalization. To improve model gen...

Combinatorics coding is a new data coding method based on combinatorics. Ordinal computing is the core technology of in the combinatorics coding. Ordinal properties of combinatorics coding is studied in this paper. Firstly, the combinatorics coding theory and the correlative basic concepts are described. Then, the properties of the ordinal are revealed. The study indicates that the value of ord...

Recently, Schlicht and Stephan lifted the notion of automatic-structures to the notion of (finite-word) ordinal-automatic structures. These are structures whose domain and relations can be represented by automata reading finite words whose shape is some fixed ordinal α. We lift Delhommé’s relative-growth-technique from the automatic and tree-automatic setting to the ordinal-automatic setting. T...

In order to extract and to visualize qualitative information from a highdimensional time series, we apply ideas from symbolic dynamics. Counting certain ordinal patterns in the given series, we obtain a series of matrices whose entries are symbol frequencies. This matrix series is explored by simple methods from nominal statistics and information theory. The method is applied to detect and to v...

Several real-life complex systems, like human societies or economic networks, are formed by interacting units characterized by patterns of relationships that may generate a group-based social hierarchy. In this paper, we address the problem of how to rank the individuals with respect to their ability to “influence” the relative strength of groups in a society. We also analyse the effect of basi...

How do we compare the complexities of various classes of structures? The Turing ordinal of a class of structures, introduced by Jockusch and Soare, is defined in terms of the number of jumps required for coding to be possible. The back-and-forth ordinal, introduced by Montalbán, is defined in terms of Σα-types. The back-and-forth ordinal is (roughly) bounded by the Turing ordinal. In this paper...

Network datasets typically exhibit certain types of statistical patterns, such as within-dyad correlation, degree heterogeneity, and triadic patterns transitivity clustering. The first two these can be well represented with a social relations model, type additive effects model originally developed for continuous dyadic data. Higher-order multiplicative models, which are related to matrix decomp...