{"id":279,"date":"2021-08-02T02:02:57","date_gmt":"2021-08-02T02:02:57","guid":{"rendered":"http:\/\/summergeometry.org\/sgi2021\/?p=279"},"modified":"2021-08-02T02:02:57","modified_gmt":"2021-08-02T02:02:57","slug":"embedding-hierarchical-data-in-hyperbolic-geometry","status":"publish","type":"post","link":"https:\/\/summergeometry.org\/sgi2021\/embedding-hierarchical-data-in-hyperbolic-geometry\/","title":{"rendered":"Embedding Hierarchical Data in Hyperbolic Geometry"},"content":{"rendered":"\n

By: Zeltzyn Montes and Sneha Sambandam<\/em><\/p>\n\n\n\n

Many of the datasets we would like to perform machine learning on have an intrinsic hierarchical structure. This includes social networks, taxonomies, NLP sentence structure, and anything that can be represented as a tree. While the most common machine learning tools work in the Euclidean space, this space is not optimal for representing hierarchical data.<\/p>\n\n\n\n

When representing hierarchical data in the 2D space, we have two main objectives: to preserve the hierarchical relationships between parent and child nodes; and to ensure distances between nodes are somewhat proportional to the number of links in between. However, when representing this structure in the 2D Euclidean space, we run into a few limitations.<\/p>\n\n\n\n

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Fig 1. A tree with branching factor of 2 drawn in the Euclidean space. (Courtesy of Alison Pouplin)<\/figcaption><\/figure><\/div>\n\n\n\n

For example, let’s first draw a tree, with a branching factor of 2 (Fig 1<\/em>). When our tree is very deep, placing nodes equidistantly causes us to run out of space rather quickly, like in our example above at only a depth of 5. The second problem we run into is with untrue distance relationships among nodes. To help visualize this phenomenon, refer to Fig 2a<\/em>. Here, arc refers to the shortest path between two nodes.<\/p>\n\n\n\n