Convex Optimization and Structural Clustering
One of the main examples, which illustrate the meaning of the Structural Clustering, gives investigations of the global financial market. One of the first problems there is to construct its segmentation and to develop the local Market performance indexes, one for each segment. Convex Optimization approach to Structural Clustering is considered as the problem of optimization of a criterion, which measures the quality of a clustering. The form of optimal Clustering for convex criterion is investigated.
The optimization algorithms for different convex criteria are presented and discussed.
We consider different types of Structural Clustering: deterministic clustering, classic fuzzy clustering, clustering with fuzzy boundaries, overlapping clustering and clustering with outliers. In this talk we take a special attention to overlapping clustering and clustering with outliers.
Clustering with outliers allows us to avoid influence of exotic objects to form clusters. Overlapping clustering allows us to determine objects, which belong to only one of the clusters, and objects, which belong to many clusters simultaneously. Then, we can construct a graph of a neighborhood of clusters. Suggested approach is illustrated by Investigation of Global Market of Equities.