  The high dynamic range between contaminating foreground emission and the
fluctuating 21cm brightness temperature field is one of the most problematic
characteristics of 21cm intensity mapping data. While these components would
ordinarily have distinctive frequency spectra, making it relatively easy to
separate them, instrumental effects and calibration errors further complicate
matters by modulating and mixing them together. A popular class of foreground
cleaning method are unsupervised techniques related to Principal Component
Analysis (PCA), which exploit the different shapes and amplitudes of each
component's contribution to the covariance of the data in order to segregate
the signals. These methods have been shown to be effective at removing
foregrounds, while also unavoidably filtering out some of the 21cm signal too.
In this paper we examine, for the first time in the context of 21cm intensity
mapping, a generalised method called Kernel PCA, which instead operates on the
covariance of non-linear transformations of the data. This allows more flexible
functional bases to be constructed, in principle allowing a cleaner separation
between foregrounds and the 21cm signal to be found. We show that Kernel PCA is
effective when applied to simulated single-dish (autocorrelation) 21cm data
under a variety of assumptions about foregrounds models, instrumental effects
etc. It presents a different set of behaviours to PCA, e.g. in terms of
sensitivity to the data resolution and smoothing scale, outperforming it on
intermediate to large scales in most scenarios.
