Topological Machine Learning (TML) is a newly-emerging branch of data science at the interface of Topological Data Analysis (TDA) and Machine Learning (ML). The last decade saw an enormous boost in the field of Computational Topology. Methods and concepts from Algebraic Topology, formerly confined to the realm of pure mathematics, have demonstrated their usefulness in numerous areas e.g. biology, neuroscience, dynamical systems and material science, to name a few. In addition to the applications of TDA, it has also proven to be effective in supporting, enhancing, and augmenting both classical ML and Deep Learning (DL) models such as deep neural networks.
In the TML project we construct efficient pipelines based on TDA and ML/DL methods. Our pipelines deal with various types of data sets (time series, point cloud, image/field, network/graph), therefore they contain other well-defined tools for converting data sets of different types to each other, such as Time Delay Embedding (TDE), Correlation Network (CN), Visibility Graph (VG), Recurrence Plot (RP), Recurrence Network (RN), k-Nearest Neighbor (kNN) methods and so on.
- H. Masoomy, B. Askari, M.N. Najaﬁ, S.M.S. Movahed, “Persistent Homology of Fractional Gaussian Noise”, Physical Review E, (2021).
Conference Papers and Posters
- H. Masoomy, S.M.S. Movahed, “Application of Persistent Homology Method for Random Field Analysis (Case Study: Schizophrenia)”. The 5th Iranian Computational Physics Conference, Imam Khomeini International University, (2022).
- H. Masoomy, M. Mozaﬀarilegha, B. Askari, S.M.S. Movahed, “Computational Topology for Better Understanding Functional Brain Networks in Schizophrenia”. The 11th Conference on Statistical Physics, Soft Condensed Matters, and Complex Systems, Shahid Beheshti University, (2021).
- H. Masoomy, B. Askari, S.M.S. Movahed, “Computational Topology-based Analysis of Data Sets Correlation Function”. The 4th Iranian National Conference on Computational Physics, University of Tehran, (2020).