TITLE:
Classification Based on Invariants of the Data Matrix
AUTHORS:
Vladimir N. Shats
KEYWORDS:
Artificial Intelligence, Classification Algorithms, Granular Computing
JOURNAL NAME:
Journal of Intelligent Learning Systems and Applications,
Vol.9 No.3,
August
24,
2017
ABSTRACT: The paper proposes a solution to the problem classification by calculating the
sequence of matrices of feature indices that approximate invariants of the data
matrix. Here the feature index is the index of interval for feature values, and
the number of intervals is a parameter. Objects with the equal indices form
granules, including information granules, which correspond to the objects of
the training sample of a certain class. From the ratios of the information granules
lengths, we obtain the frequency intervals of any feature that are the
same for the appropriate objects of the control sample. Then, for an arbitrary
object, we find object probability estimation in each class and then the class of
object that corresponds to the maximum probability. For a sequence of the
parameter values, we find a converging sequence of error rates. An additional
effect is created by the parameters aimed at increasing the data variety and
compressing rare data. The high accuracy and stability of the results obtained
using this method have been confirmed for nine data set from the UCI repository.
The proposed method has obvious advantages over existing ones due
to the algorithm’s simplicity and universality, as well as the accuracy of the
solutions.