Locally fitting hyperplanes to high-dimensional data

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 distances points. Its effectiveness versatility are illustrated through approximation nonlinear manifolds Möbius strip Swiss roll, handwritten digit recognition, dimensionality reduction cosmological application, inter/extrapolation for social economic set, prediction recidivism criminal defendants. Based on two essential concepts hyperplane fitting spatial segmentation, this general unsupervised learning rigorously derived. The requires no assumptions underlying its Also, it has only parameters, namely size segmenting hypercubes number user choose. These make considerably accessible when applied solving various problems real applications.