Learning on the symmetric group

Many data can be represented as rankings or permutations, raising the question of developing machine learning models on the symmetric group. When the number of items in the permutations gets large, manipulating permutations can quickly become computationally intractable. I will discuss two computationally efficient embeddings of the symmetric groups in Euclidean spaces leading to fast machine learning algorithms, and illustrate their relevance on biological applications and image classification.