Classification with Ordinal Circular Data

In the context of ordinal circular data, the categories are arranged in a cyclical manner, denoted as $$C_1 \prec C_2 \prec \cdots \prec C_k \prec C_1$$ C 1 ≺ C 2 ≺ ⋯ ≺ C k ≺ C 1 , where categories $$C_1$$ C 1 and $$C_k$$ C k are adjacent to each other. Consequently, conventional multilabel classification techniques are ineffective in this scenario. This paper addresses this challenge by constructing a loss function tailored for circular data, enabling the calculation of fitted and predictive probability distributions of observations belonging to different categories. Furthermore, we propose a new approach called Circular Ordistic Barycenter Method (COBM) to analyze ordinal circular data, leveraging the concept of barycenter of probability distributions. This method is found to be effective in classifying circular ordinal data. The algorithm’s efficacy is assessed through simulations and applications to real-life datasets, like Brain-Computer Interference (BCI) data and wind direction data.