Persistent topology for natural data analysis - A survey

Natural data offer a hard challenge to data analysis. One set of tools is being developed by several teams to face this difficult task: Persistent topology. After a brief introduction to this theory, some applications to the analysis and classification of cells, lesions, music pieces, gait, oil and gas reservoirs, cyclones, galaxies, bones, brain connections, languages, handwritten and gestured letters are shown

Geometry Helps to Compare Persistence Diagrams

Exploiting geometric structure to improve the asymptotic complexity of discrete assignment problems is a well-studied subject. In contrast, the practical advantages of using geometry for such problems have not been explored. We implement geometric variants of the Hopcroft--Karp algorithm for bottleneck matching (based on previous work by Efrat el al.) and of the auction algorithm by Bertsekas for Wasserstein distance computation. Both implementations use k-d trees to replace a linear scan with a geometric proximity query. Our interest in this problem stems from the desire to compute distances between persistence diagrams, a problem that comes up frequently in topological data analysis. We show that our geometric matching algorithms lead to a substantial performance gain, both in running time and in memory consumption, over their purely combinatorial counterparts. Moreover, our implementation significantly outperforms the only other implementation available for comparing persistence diagrams.Comment: 20 pages, 10 figures; extended version of paper published in ALENEX 201

PREDICTION OF 1P/19Q CODELETION STATUS IN DIFFUSE GLIOMA PATIENTS USING PREOPERATIVE MULTIPARAMETRIC MAGNETIC RESONANCE IMAGING

A complete codeletion of chromosome 1p/19q is strongly correlated with better overall survival of diffuse glioma patients, hence determining the codeletion status early in the course of a patient’s disease would be valuable in that patient’s care. The current practice requires a surgical biopsy in order to assess the codeletion status, which exposes patients to risks and is limited in its accuracy by sampling variations. To overcome such limitations, we utilized four conventional magnetic resonance imaging sequences to predict the 1p/19q status. We extracted three sets of image-derived features, namely texture-based, topology-based, and convolutional neural network (CNN)-based, and analyzed each feature’s prediction performance. The topology-based model (AUC = 0.855 +/- 0.079) performed significantly better compared to the texture-based model (AUC = 0.707 +/- 0.118) while comparably against the CNN-based model (0.787 +/- 0.195). However, none of the models performed better than the baseline model that is built with only clinical variables, namely, age, gender, and Karnofsky Performance Score (AUC = 0.703 +/- 0.256). In summary, predicting 1p/19q chromosome codeletion status via MRI scan analysis can be a viable non-invasive assessment tool at an early stage of gliomas and in follow-ups although further investigation is needed to improve the model performance