G. V. Kondratiev – Dr.Sc. (Phys.-Math.), Professor, Nizhniy Novgorod State Technical University n.a. R.E. Alekseev, E-mail: email@example.com
Regression and Statistics methods of the value prediction give a good approximation only for the average cases. Marginal cases, lacking local data, are being predicted with very big errors in hundreds of percent. In the article a new approach to the value prediction problem, based on an invariant information contained in the data, is proposed. Namely, a set of metrics, such that its set of automorphisms transforms the original data in the multimetric space to the different ones, but essentially representing the same information, is being selected. For example, Euclidean motions will preserve the density and, consequently, visual identity of the data. Repetition of some columns in the data table will place the data in a higher dimensional space, but this will not change the information contained in them.
Depending on the problem there can be acceptable more complicated transformations. For many problems an appropriate metric from the point of preserving the density is the standard Euclidean one. Once the class of metrics is selected the joint invariants of the sets of data, constraints and metrics automatically appear.
There exists a joint invariant, an extension of data, which is the most adequate prediction, based on the data and the invariance property with respect to the class of acceptable transformations. In the real estate area this approach has shown better results than the other known ones.
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