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Poster
PLLay: Efficient Topological Layer based on Persistent Landscapes
Kwangho Kim · Jisu Kim · Manzil Zaheer · Joon Kim · Frederic Chazal · Larry Wasserman

Thu Dec 10 09:00 AM -- 11:00 AM (PST) @ Poster Session 5 #1582

We propose PLLay, a novel topological layer for general deep learning models based on persistence landscapes, in which we can efficiently exploit the underlying topological features of the input data structure. In this work, we show differentiability with respect to layer inputs, for a general persistent homology with arbitrary filtration. Thus, our proposed layer can be placed anywhere in the network and feed critical information on the topological features of input data into subsequent layers to improve the learnability of the networks toward a given task. A task-optimal structure of PLLay is learned during training via backpropagation, without requiring any input featurization or data preprocessing. We provide a novel adaptation for the DTM function-based filtration, and show that the proposed layer is robust against noise and outliers through a stability analysis. We demonstrate the effectiveness of our approach by classification experiments on various datasets.

Author Information

Kwangho Kim (Carnegie Mellon University)
Jisu Kim (Inria Saclay)
Manzil Zaheer (Google)
Joon Kim (Carnegie Mellon University)
Frederic Chazal (INRIA)
Larry Wasserman (Carnegie Mellon University)

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