A new algorithm of non-Gaussian component analysis with radial kernel functions
Motoaki Kawanabe, Gilles Blanchard, Masahi Sugiyama and Klaus-Robert Müller
Annals of the Institute of Statistical Mathematics
We consider high-dimensional data which
contains a linear low-dimensional non-Gaussian structure contaminated
with Gaussian noise, and discuss a method to identify
this non-Gaussian subspace.
For this problem, we provided in our previous work
a very general semi-parametric framework
called Non-Gaussian Component Analysis (NGCA).
NGCA has a uniform probabilistic bound on the error
of finding the non-Gaussian components
and within this framework,
we presented an efficient NGCA algorithm called Multi-index
The algorithm is justified as an extension of
the ordinary projection pursuit (PP) methods and is shown to outperform PP
particularly when the data has complicated non-Gaussian structure.
However, it turns out that multi-index PP is not optimal in the context
In this article,
we therefore develop an alternative algorithm called
Iterative Metric Adaptation for
radial Kernel functions (IMAK),
which is theoretically better justifiable within the NGCA framework.
We demonstrate that
the new algorithm tends to outperform existing methods
through numerical examples.