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Two-parameter sums signatures and corresponding quasisymmetric functions
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Quasisymmetric functions have recently been used in time series analysis as polynomial features that are invariant under, so-called, dynamic time warping. We extend this notion to data indexed by two parameters and thus provide warping invariants for images. We show that two-parameter quasisymmetric functions are complete in a certain sense, and provide a two-parameter quasi-shuffle identity. A compatible coproduct is based on diagonal concatenation of the input data, leading to a (weak) form of Chen's identity.
Forward citations
Cited by 2 Pith papers
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Thin homotopy and the signature of piecewise linear surfaces
The piecewise linear surface signature is injective: it characterizes surfaces up to translation and thin homotopy, generalizing Chen's path signature theorem.
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Tensor-to-Tensor Models with Fast Iterated Sum Features
A corner-tree algorithm computes a large class of two-parameter iterated sums in linear time, enabling a cheap tensor-to-tensor neural layer that matches larger ResNets on CIFAR and works for texture anomaly detection.
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