Persistent homology: shaping the new unsupervised learning - Juanjo Madrigal - JOTB24
In the last years we have witnessed the rise of Machine Learning and a wide variety of data processing techniques. Among its many branches, Unsupervised Learning tries to extract information from lots of interrelated data. Clustering algorithms group and segment data based on closeness and similarity; however, many times grouping is not significant enough, but the shapes that the data creates. Attempts to study the shapes of point clouds have resulted in advances far beyond simple clustering, from segmenting 3D shapes to classifying cancerous tissues based on the degree of connectivity between malignant cell nuclei. The applications are promising, but the computational effort for such features turns out to be remarkably complex.
This is the scenario where persistent homology emerges, a technique that strikingly combines the best of many worlds, from the pure mathematics of the 20th century to the latest advances in matrix calculus and graph algorithms. It is truly an alignment of the planets: the language that best describes geometry and shapes turns out, decades later, to be ideal for computational treatment, and the results achieved are so good that it is capturing the attention of the data science community. We will analyze all these ingredients that make up this very special technique that is going beyond the borders of machine learning.
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