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Image Classification using Combination of Topological Features and Neural Networks

In this work we use the persistent homology method, a technique in topological data analysis (TDA), to extract essential topological features from the data space and combine them with deep learning features for classification tasks. In TDA, the concepts of complexes and filtration are building blocks. Firstly, a filtration is constructed from some complex. Then, persistent homology classes are computed, and their evolution along the filtration is visualized through the persistence diagram. Additionally, we applied vectorization techniques to the persistence diagram to make this topological information compatible with machine learning algorithms. This was carried out with the aim of classifying images from multiple classes in the MNIST dataset. Our approach inserts topological features into deep learning approaches composed by single and two-streams neural networks architectures based on a multi-layer perceptron (MLP) and a convolutional neral network (CNN) taylored for multi-class classification in the MNIST dataset. In our analysis, we evaluated the obtained results and compared them with the outcomes achieved through the baselines that are available in the TensorFlow library. The main conclusion is that topological information may increase neural network accuracy in multi-class classification tasks with the price of computational complexity of persistent homology calculation. Up to the best of our knowledge, it is the first work that combines deep learning features and the combination of topological features for multi-class classification tasks.

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