  This paper explores the extension of dimension reduction (DR) techniques to
the multi-dimension case by using the Einstein product. Our focus lies on
graph-based methods, encompassing both linear and nonlinear approaches, within
both supervised and unsupervised learning paradigms. Additionally, we
investigate variants such as repulsion graphs and kernel methods for linear
approaches. Furthermore, we present two generalizations for each method, based
on single or multiple weights. We demonstrate the straightforward nature of
these generalizations and provide theoretical insights. Numerical experiments
are conducted, and results are compared with original methods, highlighting the
efficiency of our proposed methods, particularly in handling high-dimensional
data such as color images.
