6 papers
Barcoding Invariants and Their Comparison
Emerson G. Escolar, Woojin Kim
The persistence barcode, which can be obtained from the interval decomposition of a persistence module, plays a pivotal role in applications of persistent homology. For multi-param…
Interleaving Distance as a Galois-Edit Distance
Woojin Kim, Won Seong
The concept of edit distance, which dates back to the 1960s in the context of comparing word strings, has since found numerous applications with various adaptations in computer sci…
On Integer Programming for the Binarized Neural Network Verification Problem
Woojin Kim, James R. Luedtke
Binarized neural networks (BNNs) are feedforward neural networks with binary weights and activation functions. In the context of using a BNN for classification, the verification pr…
Limit Theorems for Verbose Persistence Diagrams
Jeong-hwi Joe, Woojin Kim, Cheolwoo Park
The persistence diagram is a central object in the study of persistent homology and has also been investigated in the context of random topology. The more recent notion of the verb…
Super-Polynomial Growth of the Generalized Persistence Diagram
Donghan Kim, Woojin Kim, Wonjun Lee
The Generalized Persistence Diagram (GPD) for multi-parameter persistence naturally extends the classical notion of persistence diagram for one-parameter persistence. However, unli…
Sparsification of the Generalized Persistence Diagrams for Scalability through Gradient Descent
Mathieu Carrière, Seunghyun Kim, Woojin Kim
The generalized persistence diagram (GPD) is a natural extension of the classical persistence barcode to the setting of multi-parameter persistence and beyond. The GPD is defined a…