title: Ð ÐµÐ³ÑÐ»ÑÑÐ¸Ð·Ð°ÑÐ¸Ñ Ð·Ð°Ð´Ð°Ñ Ð² Ð°Ð½Ð°Ð»Ð¸Ð·Ðµ Ð´Ð°Ð½Ð½ÑÑ Ñ Ð¸Ð½ÑÐµÑÐ²Ð°Ð»ÑÐ½Ð¾Ð¹ Ð½ÐµÐ¾Ð¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð½Ð¾ÑÑÑÑ
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¼Ð°Ð³Ð¸ÑÑÑÐ°
titleType: Subtitle
title: Regularization problems in data analysis with interval uncertainty
Creators: name: ÐÐµÑÑÑÑÐºÐ¾Ð², ÐÐ°Ð½Ð¸Ð»
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2023
Subjects: ÐÐ°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¸Ð¹ Ð°Ð½Ð°Ð»Ð¸Ð·
Ð¼Ð¾Ð´ÐµÐ»Ñ Ð»Ð¸Ð½ÐµÐ¹Ð½Ð¾Ð¹ Ð¸Ð½ÑÐµÑÐ²Ð°Ð»ÑÐ½Ð¾Ð¹ ÑÐµÐ³ÑÐµÑÑÐ¸Ð¸
Ð¼ÐµÑÐ¾Ð´ Ð²Ð°ÑÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ð½ÐµÐ¾Ð¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð½Ð¾ÑÑÐ¸
Ð¼ÐµÑÐ¾Ð´ Ð¼Ð°ÐºÑÐ¸Ð¼ÑÐ¼Ð° ÑÐ¾Ð²Ð¼ÐµÑÑÐ½Ð¾ÑÑÐ¸
ÑÐ¿ÑÐ°Ð²Ð»ÑÐµÐ¼Ð¾Ðµ Ð¼Ð½Ð¾Ð¶ÐµÑÑÐ²Ð¾ ÑÐµÑÐµÐ½Ð¸Ð¹
ÑÐµÐ³ÑÐ»ÑÑÐ¸Ð·Ð°ÑÐ¸Ñ Ð·Ð°Ð´Ð°Ñ
linear interval regression model
uncertainty variation method
maximum compatibility method
control solution set
problem regularization

description: Ð¢ÐµÐ¼Ð° Ð²ÑÐ¿ÑÑÐºÐ½Ð¾Ð¹ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð¾Ð¹ ÑÐ°Ð±Ð¾ÑÑ: Â«Ð ÐµÐ³ÑÐ»ÑÑÐ¸Ð·Ð°ÑÐ¸Ñ Ð·Ð°Ð´Ð°Ñ Ð² Ð°Ð½Ð°Ð»Ð¸Ð·Ðµ Ð´Ð°Ð½Ð½ÑÑ Ñ Ð¸Ð½ÑÐµÑÐ²Ð°Ð»ÑÐ½Ð¾Ð¹ Ð½ÐµÐ¾Ð¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð½Ð¾ÑÑÑÑÂ». ÐÐ°Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° Ð¼ÐµÑÐ¾Ð´Ð°Ð¼ ÑÐµÐ³ÑÐ»ÑÑÐ¸Ð·Ð°ÑÐ¸Ð¸ Ð² Ð°Ð½Ð°Ð»Ð¸Ð·Ðµ Ð´Ð°Ð½Ð½ÑÑ Ñ Ð¸Ð½ÑÐµÑÐ²Ð°Ð»ÑÐ½Ð¾Ð¹ Ð½ÐµÐ¾Ð¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð½Ð¾ÑÑÑÑ Ð²Ð¾ Ð²ÑÐ¾Ð´Ð½Ð¾Ð¼ Ð°ÑÐ³ÑÐ¼ÐµÐ½ÑÐµ. Ð Ð°ÑÑÐ¼Ð¾ÑÑÐµÐ½Ñ ÑÑÑÐµÑÑÐ²ÑÑÑÐ¸Ðµ Ð¼ÐµÑÐ¾Ð´Ñ ÑÐµÑÐµÐ½Ð¸Ñ Ð·Ð°Ð´Ð°ÑÐ¸ Ð»Ð¸Ð½ÐµÐ¹Ð½Ð¾Ð¹ Ð¸Ð½ÑÐµÑÐ²Ð°Ð»ÑÐ½Ð¾Ð¹ ÑÐµÐ³ÑÐµÑÑÐ¸Ð¸ Ð¸ Ð¿Ð¾Ð´ÑÐ¾Ð´Ñ Ðº ÐµÐµ ÑÐµÐ³ÑÐ»ÑÑÐ¸Ð·Ð°ÑÐ¸Ð¸ Ð½Ð° ÑÐ»ÑÑÐ°Ð¹, ÐµÑÐ»Ð¸ Ð¸Ð½ÑÐµÑÐ²Ð°Ð»ÑÐ½Ð°Ñ Ð²ÑÐ±Ð¾ÑÐºÐ° ÑÐ²Ð»ÑÐµÑÑÑ Ð½ÐµÐ½Ð°ÐºÑÑÐ²Ð°ÑÑÐµÐ¹ Ð¸ Ð½ÐµÑÐ¾Ð²Ð¼ÐµÑÑÐ½Ð¾Ð¹. Ð Ð°Ð±Ð¾ÑÐ° Ð²ÑÐ¿Ð¾Ð»Ð½ÐµÐ½Ð° Ð½Ð° ÑÐ·ÑÐºÐµ Matlab Ð² ÑÑÐµÐ´Ðµ Octave Ñ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸ÐµÐ¼ Ð±Ð¸Ð±Ð»Ð¸Ð¾ÑÐµÐºÐ¸ kinterval. ÐÐµÑÐ²Ð°Ñ ÑÐ°ÑÑÑ ÑÐ°Ð±Ð¾ÑÑ Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° Ð¸Ð·ÑÑÐµÐ½Ð¸Ñ Ð¸ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ Ð¼ÐµÑÐ¾Ð´Ð¾Ð² ÑÐµÐ³ÑÐ»ÑÑÐ¸Ð·Ð°ÑÐ¸Ð¸ Ð·Ð°Ð´Ð°ÑÐ¸ Ð¿Ð¾ÑÑÑÐ¾ÐµÐ½Ð¸Ñ Ð»Ð¸Ð½ÐµÐ¹Ð½Ð¾Ð¹ Ð·Ð°Ð²Ð¸ÑÐ¸Ð¼Ð¾ÑÑÐ¸ ÑÐ¸Ð»ÑÐ½Ð¾ ÑÐ¾Ð²Ð¼ÐµÑÑÐ½Ð¾Ð¹ Ñ Ð´Ð°Ð½Ð½ÑÐ¼Ð¸. ÐÑÐ¾ÑÐ°Ñ ÑÐ°ÑÑÑ ÑÐ°Ð±Ð¾ÑÑ Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ Ð¼ÐµÑÐ¾Ð´Ð° Ð¼Ð°ÐºÑÐ¸Ð¼ÑÐ¼Ð° ÑÐ¾Ð²Ð¼ÐµÑÑÐ½Ð¾ÑÑÐ¸ Ð´Ð»Ñ ÑÐ¿ÑÐ°Ð²Ð»ÑÐµÐ¼Ð¾Ð³Ð¾ Ð¼Ð½Ð¾Ð¶ÐµÑÑÐ²Ð° Ð·Ð°Ð´Ð°ÑÐ¸ Ð»Ð¸Ð½ÐµÐ¹Ð½Ð¾Ð¹ Ð¸Ð½ÑÐµÑÐ²Ð°Ð»ÑÐ½Ð¾Ð¹ ÑÐµÐ³ÑÐµÑÑÐ¸Ð¸. Ð ÑÐ¾Ð´Ðµ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ Ð±ÑÐ»Ð° ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐ°Ð½Ð° Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð½Ð°Ñ ÑÐµÐ°Ð»Ð¸Ð·Ð°ÑÐ¸Ñ ÑÐ°ÑÐ¿Ð¾Ð·Ð½Ð°ÑÑÐµÐ³Ð¾ ÑÑÐ½ÐºÑÐ¸Ð¾Ð½Ð°Ð»Ð° Ð´Ð»Ñ ÑÐ¿ÑÐ°Ð²Ð»ÑÐµÐ¼Ð¾Ð³Ð¾ Ð¼Ð½Ð¾Ð¶ÐµÑÑÐ²Ð° Ð·Ð°Ð´Ð°ÑÐ¸ Ð»Ð¸Ð½ÐµÐ¹Ð½Ð¾Ð¹ Ð¸Ð½ÑÐµÑÐ²Ð°Ð»ÑÐ½Ð¾Ð¹ ÑÐµÐ³ÑÐµÑÑÐ¸Ð¸. Ð ÑÐ°ÐºÐ¶Ðµ ÑÐµÐ°Ð»Ð¸Ð·Ð¾Ð²Ð°Ð½Ñ Ð²Ð¸Ð·ÑÐ°Ð»Ð¸Ð·Ð°ÑÐ¾Ñ ÑÐ¿ÑÐ°Ð²Ð»ÑÐµÐ¼Ð¾Ð³Ð¾ Ð¼Ð½Ð¾Ð¶ÐµÑÑÐ²Ð° Ð´Ð»Ñ Ð´Ð²ÑÐ¼ÐµÑÐ½Ð¾Ð¹ Ð·Ð°Ð´Ð°ÑÐ¸ Ð¸ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð½ÑÐ¹ Ð¼Ð¾Ð´ÑÐ»Ñ Ð´Ð»Ñ ÑÐµÐ³ÑÐ»ÑÑÐ¸Ð·Ð°ÑÐ¸Ð¸ Ð¸ÑÑÐ¾Ð´Ð½Ð¾Ð¹ Ð·Ð°Ð´Ð°ÑÐ¸. ÐÐ»Ñ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ Ð¿ÑÐµÐ´Ð»Ð°Ð³Ð°ÐµÐ¼ÑÑ Ð² ÑÐ°Ð±Ð¾ÑÐµ Ð¼ÐµÑÐ¾Ð´Ð¾Ð² Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ñ ÑÐµÐ°Ð»ÑÐ½ÑÐµ Ð´Ð°Ð½Ð½ÑÐµ. Ð ÑÐ°ÑÑÐ½Ð¾ÑÑÐ¸ ÑÐµÑÐ°ÐµÑÑÑ Ð·Ð°Ð´Ð°ÑÐ° Ð¿Ð¾ÑÑÑÐ¾ÐµÐ½Ð¸Ñ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð»Ð¸Ð½ÐµÐ¹Ð½Ð¾Ð¹ ÑÐµÐ³ÑÐµÑÑÐ¸Ð¸, Ð¾Ð¿Ð¸ÑÑÐ²Ð°ÑÑÐµÐ¹ ÑÐ°Ð±Ð¾ÑÑ ÑÐ°Ð³Ð¾Ð²Ð¾Ð³Ð¾ Ð´Ð²Ð¸Ð³Ð°ÑÐµÐ»Ñ, Ð° Ð¸Ð¼ÐµÐ½Ð½Ð¾ Ð·Ð°Ð²Ð¸ÑÐ¸Ð¼Ð¾ÑÑÑ Ð¿Ð¾Ð»Ð¾Ð¶ÐµÐ½Ð¸Ñ Ð²Ð°Ð»Ð° Ð¾Ñ Ð²ÑÐµÐ¼ÐµÐ½Ð¸. Ð¡ Ð¿Ð¾Ð¼Ð¾ÑÑÑ Ð´Ð°Ð½Ð½Ð¾Ð¹ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð¼Ð¾Ð¶Ð½Ð¾ Ð¸Ð·ÑÑÐ°ÑÑ Ð¿Ð¾Ð²ÐµÐ´ÐµÐ½Ð¸Ðµ ÑÐ°Ð³Ð¾Ð²Ð¾Ð³Ð¾ Ð´Ð²Ð¸Ð³Ð°ÑÐµÐ»Ñ Ð² ÑÐ¾ÑÐºÐ°Ñ Ð½ÐµÐ¿Ð¾Ð»Ð½Ð¾Ð³Ð¾ ÑÐ°Ð³Ð°.
description: The subject of the graduate qualification work is Â«Regularization problems in data analysis with interval uncertaintyÂ». This work is devoted to methods of regularization in the analysis of data with interval uncertainty in the input argument. The existing methods of solving the problem of linear interval regression and approaches to its regularization in case the interval sample is non-closing and incompatible are considered. The work was done in Matlab in Octave environment using the kinterval library. The first part of the work is devoted to the study and comparison of regularization methods of the problem of linear dependence strongly joint with data. The second part of the work is devoted to the study of the maximum compatibility method for the controlled set of the linear interval regression problem. In the course of the study, a software implementation of the recognition functional for the controlled set of the linear interval regression problem was developed. A visualizer of the controlled set for the two-dimensional problem and a software module for regularization of the original problem were also implemented. Real data were used to study the methods proposed in the work. In particular, the problem of constructing a linear regression model describing the operation of a stepper motor, namely the dependence of the shaft position on time, is solved. Using this model, it is possible to study the behaviour of a stepper motor at points of incomplete step.