  Low dimensional nonlinear structure abounds in datasets across computer
vision and machine learning. Kernelized matrix factorization techniques have
recently been proposed to learn these nonlinear structures for denoising,
classification, dictionary learning, and missing data imputation, by observing
that the image of the matrix in a sufficiently large feature space is low-rank.
However, these nonlinear methods fail in the presence of sparse noise or
outliers. In this work, we propose a new robust nonlinear factorization method
called Robust Non-Linear Matrix Factorization (RNLMF). RNLMF constructs a
dictionary for the data space by factoring a kernelized feature space; a noisy
matrix can then be decomposed as the sum of a sparse noise matrix and a clean
data matrix that lies in a low dimensional nonlinear manifold. RNLMF is robust
to sparse noise and outliers and scales to matrices with thousands of rows and
columns. Empirically, RNLMF achieves noticeable improvements over baseline
methods in denoising and clustering.
