title: ÐÐµÑÑÐ¾Ð»Ð¾Ð³Ð¸ÑÐµÑÐºÐ¾Ðµ ÑÐ¾Ð¿ÑÐ¾Ð²Ð¾Ð¶Ð´ÐµÐ½Ð¸Ðµ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð° TwoStep Ð´Ð»Ñ ÐºÐ»Ð°ÑÑÐµÑÐ¸Ð·Ð°ÑÐ¸Ð¸ Ð½ÐµÑÐ¾ÑÐ½ÑÑ Ð´Ð°Ð½Ð½ÑÑ
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: Metrological support of the TwoStep algorithm for clustering inexact data
Creators: name: ÐÐ½Ð´ÑÐ¸ÐµÐ½ÐºÐ¾, ÐÐ½Ð´ÑÐµÐ¹
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: 2022
Subjects: Ð¾Ð±ÑÐ°Ð±Ð¾ÑÐºÐ° Ð½ÐµÑÐ¾ÑÐ½ÑÑ Ð´Ð°Ð½Ð½ÑÑ
Ð¿Ð¾Ð³ÑÐµÑÐ½Ð¾ÑÑÑ Ð½ÐµÑÐ¾ÑÐ½ÑÑ Ð´Ð°Ð½Ð½ÑÑ
ÐºÐ»Ð°ÑÑÐµÑÐ¸Ð·Ð°ÑÐ¸Ñ
inaccurate data processing
raw data error
clustering

description: Ð¢ÐµÐ¼Ð° Ð²ÑÐ¿ÑÑÐºÐ½Ð¾Ð¹ ÑÐ°Ð±Ð¾ÑÑ: âÐÐµÑÑÐ¾Ð»Ð¾Ð³Ð¸ÑÐµÑÐºÐ¾Ðµ ÑÐ¾Ð¿ÑÐ¾Ð²Ð¾Ð¶Ð´ÐµÐ½Ð¸Ðµ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð° TwoStep Ð´Ð»Ñ ÐºÐ»Ð°ÑÑÐµÑÐ¸Ð·Ð°ÑÐ¸Ð¸ Ð½ÐµÑÐ¾ÑÐ½ÑÑ Ð´Ð°Ð½Ð½ÑÑâ. Ð Ð´Ð°Ð½Ð½Ð¾Ð¹ Ð²ÑÐ¿ÑÑÐºÐ½Ð¾Ð¹ ÑÐ°Ð±Ð¾ÑÐµ Ð¿ÑÐ¾Ð²Ð¾Ð´Ð¸ÑÑÑ Ð¼ÐµÑÑÐ¾Ð»Ð¾Ð³Ð¸ÑÐµÑÐºÐ¾Ðµ ÑÐ¾Ð¿ÑÐ¾Ð²Ð¾Ð¶Ð´ÐµÐ½Ð¸Ðµ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð° Two-Step, Ð°Ð½Ð°Ð»Ð¸Ð·Ð¸ÑÑÐµÑÑÑ Ð²Ð»Ð¸ÑÐ½Ð¸Ðµ Ð¿Ð¾Ð³ÑÐµÑÐ½Ð¾ÑÑÐ¸ Ð¸ÑÑÐ¾Ð´Ð½ÑÑ Ð´Ð°Ð½Ð½ÑÑ Ð½Ð° Ð´Ð¾ÑÑÐ¾Ð²ÐµÑÐ½Ð¾ÑÑÑ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ¾Ð², Ð¿Ð¾Ð»ÑÑÐµÐ½Ð½ÑÑ Ð¿ÑÐ¸ Ð¸Ñ Ð¾Ð±ÑÐ°Ð±Ð¾ÑÐºÐµ. Ð ÑÐ°Ð±Ð¾ÑÐµ Ð¿Ð¾ÐºÐ°Ð·Ð°Ð½ Ð¿Ð¾ÑÑÐ°Ð¿Ð½ÑÐ¹ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼ Ð´ÐµÐ¹ÑÑÐ²Ð¸Ñ ÐºÐ»Ð°ÑÑÐµÑÐ¸Ð·Ð°ÑÐ¸Ð¸, Ð¿ÑÐ°Ð²Ð¸Ð»Ð° Ð¿ÑÐ¸Ð½ÑÑÐ¸Ñ ÑÐµÑÐµÐ½Ð¸Ñ Ð¾ ÐºÐ¾Ð»Ð¸ÑÐµÑÑÐ²Ðµ ÐºÐ»Ð°ÑÑÐµÑÐ¾Ð², Ð¿ÑÐ¾Ð²ÐµÐ´ÑÐ½ Ð°Ð½Ð°Ð»Ð¸Ð· Ð¾ ÐºÐ°ÑÐµÑÑÐ²Ðµ Ð¿Ð¾Ð»ÑÑÐµÐ½Ð½ÑÑ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ¾Ð² Ð² Ð·Ð°Ð²Ð¸ÑÐ¸Ð¼Ð¾ÑÑÐ¸ Ð¾Ñ Ð²ÐµÐ»Ð¸ÑÐ¸Ð½Ñ Ð¿ÑÐµÐ´ÐµÐ»Ð° Ð¿Ð¾Ð³ÑÐµÑÐ½Ð¾ÑÑÐ¸. Ð Ð½ÐµÐ¹ Ð¿ÑÐ¾Ð´ÐµÐ¼Ð¾Ð½ÑÑÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð¾, ÑÑÐ¾ Ð¸Ð½ÑÑÑÑÐ¼ÐµÐ½ÑÐ°Ð»ÑÐ½Ð°Ñ Ð¿Ð¾Ð³ÑÐµÑÐ½Ð¾ÑÑÑ Ð¸ÑÑÐ¾Ð´Ð½ÑÑ Ð´Ð°Ð½Ð½ÑÑ Ð² Ð·Ð½Ð°ÑÐ¸ÑÐµÐ»ÑÐ½Ð¾Ð¹ ÑÑÐµÐ¿ÐµÐ½Ð¸ Ð¾ÐºÐ°Ð·ÑÐ²Ð°ÐµÑ Ð²Ð»Ð¸ÑÐ½Ð¸Ðµ Ð½Ð° Ð´Ð¾ÑÑÐ¾Ð²ÐµÑÐ½Ð¾ÑÑÑ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ¾Ð² Ð¸ Ð½Ðµ Ð¿Ð¾Ð·Ð²Ð¾Ð»ÑÐµÑ Ñ Ð´Ð¾ÑÑÐ°ÑÐ¾ÑÐ½Ð¾Ð¹ ÑÐ¾ÑÐ½Ð¾ÑÑÑÑ Ð¾ÑÐµÐ½Ð¸ÑÑ Ð´Ð¾ÑÑÐ¾Ð²ÐµÑÐ½Ð¾ÑÑÑ Ð°Ð½Ð°Ð»Ð¸Ð·Ð¸ÑÑÐµÐ¼ÑÑ Ð´Ð°Ð½Ð½ÑÑ. ÐÐ½Ð°Ð»Ð¸Ð· Ð¿ÑÐ¾Ð²Ð¾Ð´Ð¸Ð»ÑÑ Ð½Ð° ÐÐ Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð½Ð¾Ð³Ð¾ Ð¾Ð±ÐµÑÐ¿ÐµÑÐµÐ½Ð¸Ñ IBM SPSS Statistics. ÐÐ°Ð½Ð½Ð¾Ðµ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð½Ð¾Ðµ Ð¾Ð±ÐµÑÐ¿ÐµÑÐµÐ½Ð¸Ðµ Ð¿Ð¾Ð·Ð²Ð¾Ð»ÑÐµÑ Ð¿ÑÐ¾Ð²ÐµÑÑÐ¸ ÐºÐ¾Ð¼Ð¿Ð»ÐµÐºÑÐ½ÑÐ¹ Ð°Ð½Ð°Ð»Ð¸Ð· Ð½ÐµÑÐ¾ÑÐ½ÑÑ Ð´Ð°Ð½Ð½ÑÑ, Ð¸ÑÐ¿Ð¾Ð»ÑÐ·ÑÑ Ð½Ð°Ð¸Ð±Ð¾Ð»ÐµÐµ ÑÐ°ÑÑÐ¾ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·ÑÐµÐ¼ÑÐµ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ñ ÐºÐ»Ð°ÑÑÐµÑÐ¸Ð·Ð°ÑÐ¸Ð¸, Ð² ÑÐ¾Ð¼ ÑÐ¸ÑÐ»Ðµ Two-Step. Ð ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐµ Ð²ÑÐ¿Ð¾Ð»Ð½ÐµÐ½ ÐºÐ¾Ð¼Ð¿Ð»ÐµÐºÑÐ½ÑÐ¹ Ð°Ð½Ð°Ð»Ð¸Ð· ÐºÐ»Ð°ÑÑÐµÑÐ¸Ð·Ð°ÑÐ¸Ð¸ Ð½Ð° Ð¾ÑÐ½Ð¾Ð²Ðµ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ¾Ð² Ð¸Ð·Ð¼ÐµÑÐµÐ½Ð¸Ð¹ Ð¾ Ð¿Ð¾ÑÑÐµÐ±Ð»ÐµÐ½Ð¸Ð¸ ÑÐ½ÐµÑÐ³Ð¾ÑÐ½Ð°Ð±Ð¶ÐµÐ½Ð¸Ñ Ð³Ð¾ÑÑÐ´Ð°ÑÑÑÐ²ÐµÐ½Ð½ÑÑ Ð¼ÑÐ½Ð¸ÑÐ¸Ð¿Ð°Ð»Ð¸ÑÐµÑÐ¾Ð², Ð´Ð¾ÐºÐ°Ð·ÑÐ²Ð°ÑÑÐµÐµ Ð²Ð°Ð¶Ð½Ð¾ÑÑÑ ÑÑÑÑÐ° Ð´Ð¾ÑÑÐ¾Ð²ÐµÑÐ½Ð¾ÑÑÐ¸ Ð¸ÑÑÐ¾Ð´Ð½ÑÑ Ð´Ð°Ð½Ð½ÑÑ Ð¿ÑÐ¸ ÐºÐ»Ð°ÑÑÐµÑÐ¸Ð·Ð°ÑÐ¸Ð¸. ÐÐ¾Ð»ÑÑÐµÐ½Ð½ÑÐµ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÑ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ Ð½Ð°Ð³Ð»ÑÐ´Ð½Ð¾ Ð¿Ð¾ÐºÐ°Ð·ÑÐ²Ð°ÑÑ Ð½ÐµÐ¾Ð±ÑÐ¾Ð´Ð¸Ð¼Ð¾ÑÑÑ ÑÑÐ¸ÑÑÐ²Ð°ÑÑ Ð¿Ð¾Ð³ÑÐµÑÐ½Ð¾ÑÑÑ Ð² ÐºÐ»Ð°ÑÑÐµÑÐ¸Ð·Ð°ÑÐ¸Ð¸ Ð½ÐµÑÐ¾ÑÐ½ÑÑ Ð´Ð°Ð½Ð½ÑÑ.
description: The topic of the graduate work: "Metrological support of the algorithm TwoStep for clustering of imprecise data". This final work provides metrological support for the algorithm Two-Step, analyzes the impact of the error of raw data on the reliability of the results obtained from their processing. The paper shows a step-by-step algorithm of clustering action, the rules for deciding on the number of clusters, the analysis of the quality of the results obtained depending on the error limit value.It demonstrated that the instrumental error of the initial data to a large extent affects the reliability of the results and does not allow us to accurately assess the reliability of the analyzed data. The analysis was conducted on a PC using IBM SPSS Statistics software. This software allows a comprehensive analysis of imprecise data, using the most used clustering algorithms, including Two-Step. As a result, a comprehensive clustering analysis based on the results of measurements on the energy supply consumption of state municipalities was performed, proving the importance of considering the reliability of the raw data when clustering. The results of the study clearly show the need to consider the error in clustering inaccurate data.