@CONFERENCE\{IMM2009-05908,
    author       = "T. J. Abrahamsen and L. K. Hansen",
    title        = "Input Space Regularization Stabilizes Pre-images for Kernel {PCA} De-noising",
    year         = "2009",
    keywords     = "Kernel {PCA,} Pre-image, De-noising",
    booktitle    = "{IEEE} Workshop on Machine Learning for Signal Processing (MLSP)",
    volume       = "",
    series       = "",
    editor       = "",
    publisher    = "",
    organization = "",
    address      = "",
    url          = "http://www2.compute.dtu.dk/pubdb/pubs/5908-full.html",
    abstract     = "Solution of the pre-image problem is key to efficient nonlinear de-noising using kernel Principal Component Analysis. Pre-image estimation is inherently ill-posed for typical kernels used in applications and consequently the most widely used estimation schemes lack stability. For de-noising applications we propose input space distance regularization as a stabilizer for pre-image estimation. We perform extensive experiments on the {USPS} digit modeling problem to evaluate the stability of three widely used pre-image estimators. We show that the previous methods lack stability when the feature mapping is non-linear, however, by applying a simple input space distance regularizer we can reduce variability with very limited sacrifice in terms of de-noising efficiency."
}