Question

Which dimension reduction method (Network multidimensional scaling, Multidimensional scaling or Optimized multidimensional scaling) should be chosen to study outliers in the lower dimensional embedding? Why?

Answer 1

Solution: The dimension reduction method is often used to address problems by decreasing the number of variables in the data and looking for shorter representations. Dimension reduction method is often aimed at normal daily data, and applying it to events deviating from this daily data (so-called outliers) can affect such events negatively. It can indeed have a large impact on outliers.

Multidimensional scaling is used to study outliers in the lower dimensional embedding. Multidimensional Scaling is the name for a family of dimensionality reduction techniques based on preserving distances in the data set. The classical version of Multidimensional Scaling finds points in a low dimensional space that minimizes

Here   are the high-dimensional points, and is the Euclidean distance in the respective space. The classical version of MDS is equivalent to PCA. Other members of the MDS family use a different distance measure or a different quantity to optimize than Eq.(1).