B1099
Title: A clustering model for asymmetric data: A within-cluster approach
Authors: Cinzia Di Nuzzo - University of Catania (Italy) [presenting]
Donatella Vicari - Sapienza University (Italy)
Abstract: A new clustering model for skew-symmetric matrices is introduced to analyse asymmetric data, by definition, a $(N\times N)$ skew-symmetric matrix $K=(k_{ij})$ for $i, j=1,\ldots$, $N$ is such that $k_{ij}=-k_{ji}$, where $k_{ij}$ represents the imbalance between flows of the objects $i$ and $j$. The model aims to find clusters of objects that have a considerable amount of exchange between them. The model analyses the within-clusters effects between objects and the directions of the exchanges within clusters. Formally, it is based on the decomposition of the skew-symmetric matrix into within-cluster components, i.e. the skew-symmetric matrix is decomposed into a sum of diagonal block skew-symmetric matrices. The model is estimated in the least-squares sense through the SVD of the skew-symmetric matrices. Furthermore, the model allows for a graphical interpretation of the results in terms of the amounts and directions of the imbalances within clusters. Finally, an illustrative application is presented to show the potentiality of the model and the features of the resulting clusters.
