Luigi Caputi

Luigi Caputi, Nicholas Meadows

In this work we evaluate the performance of three classes of methods for detecting financial anomalies: topological data analysis (TDA), principal component analyis (PCA), and Neural Network-based approaches. We apply these methods to the TSX-60 data to identify major financial stress events in the Canadian stock market. We show how neural network-based methods (such as GlocalKD and One-Shot GIN(E)) and TDA methods achieve the strongest performance. The effectiveness of TDA in detecting financial anomalies suggests that global topological properties are meaningful in distinguishing financial stress events.

Luigi Caputi, Nicholas Meadows, Henri Riihimäki

We explore the recently introduced persistent reachability homology (PRH) of digraph data, i.e. data in the form of directed graphs. In particular, we study the effectiveness of PRH in network classification task in a key neuroscience problem: epilepsy detection. PRH is a variation of the persistent homology of digraphs, more traditionally based on the directed flag complex (DPH). A main advantage of PRH is that it considers the condensations of the digraphs appearing in the persistent filtration and thus is computed from smaller digraphs. We compare the effectiveness of PRH to that of DPH and we show that PRH outperforms DPH in the classification task. We use the Betti curves and their integrals as topological features and implement our pipeline on support vector machine.