  Dimensionality reduction methods are very common in the field of high
dimensional data analysis. Typically, algorithms for dimensionality reduction
are computationally expensive. Therefore, their applications for the analysis
of massive amounts of data are impractical. For example, repeated computations
due to accumulated data are computationally prohibitive. In this paper, an
out-of-sample extension scheme, which is used as a complementary method for
dimensionality reduction, is presented. We describe an algorithm which performs
an out-of-sample extension to newly-arrived data points. Unlike other extension
algorithms such as Nystr\"om algorithm, the proposed algorithm uses the
intrinsic geometry of the data and properties for dimensionality reduction map.
We prove that the error of the proposed algorithm is bounded. Additionally to
the out-of-sample extension, the algorithm provides a degree of the abnormality
of any newly-arrived data point.
