  Large high-dimensional datasets are becoming more and more popular in an
increasing number of research areas. Processing the high dimensional data
incurs a high computational cost and is inherently inefficient since many of
the values that describe a data object are redundant due to noise and inner
correlations. Consequently, the dimensionality, i.e. the number of values that
are used to describe a data object, needs to be reduced prior to any other
processing of the data. The dimensionality reduction removes, in most cases,
noise from the data and reduces substantially the computational cost of
algorithms that are applied to the data.
  In this thesis, a novel coherent integrated methodology is introduced
(theory, algorithm and applications) to reduce the dimensionality of
high-dimensional datasets. The method constructs a diffusion process among the
data coordinates via a random walk. The dimensionality reduction is obtained
based on the eigen-decomposition of the Markov matrix that is associated with
the random walk. The proposed method is utilized for: (a) segmentation and
detection of anomalies in hyper-spectral images; (b) segmentation of
multi-contrast MRI images; and (c) segmentation of video sequences.
  We also present algorithms for: (a) the characterization of materials using
their spectral signatures to enable their identification; (b) detection of
vehicles according to their acoustic signatures; and (c) classification of
vascular vessels recordings to detect hyper-tension and cardio-vascular
diseases.
  The proposed methodology and algorithms produce excellent results that
successfully compete with current state-of-the-art algorithms.
