A data-driven way to compute vector summaries of persistence diagrams using functional data analysis

Music City Center 

Vectorization plays a crucial role in Topological Data Analysis (TDA), bridging topological descriptors with conventional machine learning models. While numerous vectorization techniques exist, their effectiveness varies across datasets. We propose adaptive vectorization methods that adjust to the structure of the given data, optimizing representation for downstream tasks. Our approach refines vectorization using iterative optimization tailored to classification and regression settings. Extensive simulations demonstrate that these adaptive methods can outperform existing techniques in specific cases, yielding improved predictive accuracy and robustness. These findings highlight the importance of dataset-specific vectorization strategies in TDA.

Topology Data Analysis

Functional Data Analysis

Data-Driven Optimization

Classification and Regression

Feature Engineering 

Section on Statistical Learning and Data Science