Abstract Problems such as data compression, pattern recognition and artificial intelligence often deal with a large sample observations of an unknown object. An effective method is proposed to fit hyperplanes points in each hypercubic subregion the original sample. Corresponding set affine linear manifolds, locally fitted optimally approximate object sense least squares their perpendicular dist...

Multidimensional Scaling (MDS) is a classical technique for embedding data in low dimensions, still widespread use today. In this paper we study MDS modern setting - specifically, high dimensions and ambient measurement noise. We show that as the noise level increases, suffers sharp breakdown depends on dimension level, derive an explicit formula point case of white then introduce MDS+, simple ...