  Recent years have witnessed an increased interest in the application of
persistent homology, a topological tool for data analysis, to machine learning
problems. Persistent homology is known for its ability to numerically
characterize the shapes of spaces induced by features or functions. On the
other hand, deep neural networks have been shown effective in various tasks. To
our best knowledge, however, existing neural network models seldom exploit
shape information. In this paper, we investigate a way to use persistent
homology in the framework of deep neural networks. Specifically, we propose to
embed the so-called "persistence landscape," a rather new topological summary
for data, into a convolutional neural network (CNN) for dealing with audio
signals. Our evaluation on automatic music tagging, a multi-label
classification task, shows that the resulting persistent convolutional neural
network (PCNN) model can perform significantly better than state-of-the-art
models in prediction accuracy. We also discuss the intuition behind the design
of the proposed model, and offer insights into the features that it learns.

Neural and Evolutionary Computing;Computational Geometry;Multimedia;Sound