  In this era of data deluge, many signal processing and machine learning tasks
are faced with high-dimensional datasets, including images, videos, as well as
time series generated from social, commercial and brain network interactions.
Their efficient processing calls for dimensionality reduction techniques
capable of properly compressing the data while preserving task-related
characteristics, going beyond pairwise data correlations. The present paper
puts forth a nonlinear dimensionality reduction framework that accounts for
data lying on known graphs. The novel framework encompasses most of the
existing dimensionality reduction methods, but it is also capable of capturing
and preserving possibly nonlinear correlations that are ignored by linear
methods. Furthermore, it can take into account information from multiple
graphs. The proposed algorithms were tested on synthetic as well as real
datasets to corroborate their effectiveness.
