SignatureKernel

Time series signature kernel, including high-order and low-rank variants.

Quickstart

from sktime.dists_kernels.signature_kernel import SignatureKernel

estimator = SignatureKernel(kernel=None, level=2, degree=1, theta=1, normalize=False, lowrank=False, rankbound=inf)

Parameters(7)

kernelsktime pairwise (tabular) transformer, callable, or None

inner (tabular) kernel used in the signature sequence kernel if callable: function (2D np.ndarray x 2D np.ndarray) -> 2D np.ndarray pairwise kernel function, matrix sizes (n, d) x (m, d) -> (n x m) optional, default = None = Euclidean (linear) kernel with scale parameter 1

levelint, optional, default = 2

an integer >= 1, representing the level of truncation of the sequential kernel

degreeint, optional, default = 1

an integer >= 1, representing the order of approximation of sequential kernel can be set only if lowrank = False, otherwise ignored (always = 1)

thetafloat, optional, default=1.0

a positive scaling factor for the levels, i-th level is scaled by theta^i

normalizebool, optional, default = False

whether the output kernel matrix is normalized if True, sums and cumsums are divided by prod(K.shape)

lowrankbool, optional, default = False

whether to use low rank approximation in computing the kernel

rankboundint, optional, default = infinity

a hard threshold for the rank of the level matrices used only if lowrank = True

References

1. [1 ] F. Kiraly, H. Oberhauser. 2016. “Kernels for sequentially ordered data.”, arXiv: 1601.08169. [2 ] F. Kiraly, H. Oberhauser. 2019. “Kernels for sequentially ordered data.”, Journal of Machine Learning Research.