Alternatives to algebraic modeling for complex data: topological modeling via Gunnar Carlsson

For many, mathematical modeling is exclusively about algebraic models, based on one form or another of regression or on differential equation modeling in the case of dynamical systems. However, this is too restrictive a point of view. For example, a clustering algorithm can be regarded as a modeling mechanism applicable to data where linear regression simply isn't applicable. Hierarchical clustering can also be regarded as a modeling mechanism, where the output is a dendrogram and contains information about the behavior of clusters at different levels of resolution. Kohonen self-organizing maps can similarly be regarded in this way.