Document Type : Applied Article


1 Department of math and computer Sciences, Kharazmi University, Tehran, Iran.

2 Department of Engineering, Kharazmi University, Tehran, Iran.


In this paper, we use the topological data analysis (TDA) mapper algorithm alongside a deep convolutional neural network in order to classify some medical images.
Deep learning models and convolutional neural networks can capture the Euclidean relation of a data point with its neighbor data points like the pixels of an image and they are particularly good at modeling data structures that live in the Euclidean space and not effective at modeling data structures that live in the non-Euclidean spaces. Topological data analysis-based methods have the ability to not only extract the Euclidean, but also topological features of data.
For the first time in this paper, we apply a neural network as one of the filter steps of the Kepler mapper algorithm to classify skin cancer images. The major advantage of this method is that Kepler Mapper visualizes the classification result by a simplicial complex, where neural network increases the accuracy of classification. Furthermore, we apply TDA mapper and persistent homology algorithms to analyze the layers of Xception network in different training epochs. Also, we use persistent diagrams to visualize the results of the analysis of layers of the Xception network and then compare them by Wasserstein distances.


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