Öåíçóðèðîâàíèå îøèáî÷íî êëàññèôèöèðîâàííûõ îáúåêòîâ âûáîðêè Áîðèñîâà È. À. 1 Èíñòèòóò 1,2 , Êóòíåíêî Î. À. 1,2 ìàòåìàòèêè èì. Ñ.Ë. Ñîáîëåâà ÑÎ ÐÀÍ, Íîâîñèáèðñê; 2 Íîâîñèáèðñêèé ãîñóäàðñòâåííûé óíèâåðñèòåò, Íîâîñèáèðñê 17-ÿ Âñåðîññèéñêàÿ êîíôåðåíöèÿ ¾Ìàòåìàòè÷åñêèå ìåòîäû ðàñïîçíàâàíèÿ îáðàçîâ 2015¿ 1925 ñåíòÿáðÿ, 2015, Ðîññèÿ, ã. Ñâåòëîãîðñê Áîðèñîâà È.À., Êóòíåíêî Î.À. Óäàëåíèå îøèáî÷íî êëàññèôèöèðîâàííûõ îáúåêòîâ 1 / 21 Ââåäåíèå Ïðåäìåò èññëåäîâàíèÿ öåíçóðèðîâàíèå âûáîðîê, ñîäåðæàùèõ çíà÷èòåëüíîå ÷èñëî íåâåðíî êëàññèôèöèðîâàííûõ îáúåêòîâ. Öåëü èññëåäîâàíèÿ ïîñòðîåíèå àëãîðèòìà, ïîñëåäîâàòåëüíî óäàëÿþùåãî îáúåêòû, ìàêñèìàëüíî óõóäøàþùèõ êà÷åñòâî îïèñàíèÿ âûáîðêè, è àâòîìàòè÷åñêè îáíàðóæèâàþùåãî ìîìåíò îêîí÷àíèÿ öåíçóðèðîâàíèÿ äàííûõ. Ìîòèâàöèÿ èññëåäîâàíèÿ àíàëèç âîçìîæíîñòè èñïîëüçîâàíèÿ FRiS-ôóíêöèè äëÿ ðåøåíèÿ çàäà÷è âîññòàíîâëåíèÿ ñòðóêòóðû äàííûõ, èçíà÷àëüíî ñîäåðæàùèõ çíà÷èòåëüíîå ÷èñëî íåâåðíî êëàññèôèöèðîâàííûõ îáúåêòîâ. . Îáëàñòè ïðèëîæåíèé: Àíàëèç äàííûõ è ðàñïîçíàâàíèå îáðàçîâ. Áîðèñîâà È.À., Êóòíåíêî Î.À. Óäàëåíèå îøèáî÷íî êëàññèôèöèðîâàííûõ îáúåêòîâ 2 / 21 Ââåäåíèå Ðàçëè÷íûå àëãîðèòìû ðàñïîçíàâàíèÿ ïðè íàëè÷èè øóìîâûõ îáúåêòîâ è âûáðîñîâ â îáó÷àþùåé âûáîðêå îáðàáàòûâàþò èõ ïî-ðàçíîìó.  àëãîðèòìàõ ïîñòðîåíèÿ ðåøàþùèõ äåðåâüåâ äëÿ óìåíüøåíèÿ âëèÿíèÿ òàêèõ îáúåêòîâ ïðåäóñìîòðåíà ïðîöåäóðà ðåäóêöèè (pruning)- óäàëåíèå ïîääåðåâüåâ, èìåþùèõ íèçêóþ ñòàòèñòè÷åñêóþ íàäåæíîñòü èç-çà òîãî, ÷òî äëÿ èõ ïîñòðîåíèÿ èñïîëüçîâàëèñü îáúåêòû-âûáðîñû. (Teng, 2001; Quinlan, 1986)  äðóãèõ àëãîðèòìàõ ïðåäóñìîòðåíà ïðåäîáðàáîòêà äàííûõ, â ïðîöåññå êîòîðîé øóìîâûå îáúåêòû ñ ïîìîùüþ íåêîòîðîãî êðèòåðèÿ âûÿâëÿþòñÿ è îòôèëüòðîâûâàþòñÿ. (Frinay and Verleysen, 2014; Segata and Blanzieri, 2010; Massie et al.,2007; Son and Kim, 2006; Delany et al., 2012),  íåêîòîðûõ ñëó÷àÿõ äàæå ïðåäïðèíèìàåòñÿ ïîïûòêà êîððåêòèðîâêè îòäåëüíûõ ïðèçíàêîâ îáúåêòà-âûáðîñà ñ öåëüþ ïðåîáðàçîâàòü åãî â òèïè÷íûé îáúåêò, õîòÿ ýòî ðèñêîâàííûé ïðîöåññ, êîòîðûé ìîæåò çàìåíèòü îäèí øóì äðóãèì. (Yang et al., 2004; Teng, 2001;Brodley and Friedl, 1999). Áîëüøèíñòâî ïðîöåäóð âûÿâëåíèÿ øóìîâûõ îáúåêòîâ îñíîâàíî íà èñïîëüçîâàíèè ïðàâèëà áëèæàéøåãî ñîñåäà. (Wilson and Martinez, 2000; Jankowski and Grochowski, 2004; Brighton and Mellish, 2002). Áîðèñîâà È.À., Êóòíåíêî Î.À. Óäàëåíèå îøèáî÷íî êëàññèôèöèðîâàííûõ îáúåêòîâ 3 / 21 Ââåäåíèå Ëèòåðàòóðà 1. Teng, Choh Man. 2001. "A Comparison of Noise Handling Techniques."Proceedings of the Fourteenth International Florida Articial Intelligence Research Society Conference: 269-273. 2. Quinlan, J R. 1986. "Induction of Decision Trees."Machine Learning: 81-106. 3. Frenay, Benoit, and Michel Verleysen. 2014. "Classication in the Presence of Label Noise: a Survey."IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 25 (5): 845-869. 4. Segata, N, and E Blanzieri. 2010. "Noise Reduction for Instance-Based Learning with a Local Maximal Margin Approach."Journal of Intelligent Information Systems 35 (October). 5. Massie, Stewart, Susan Craw, and Nirmalie Wiratunga. 2007."When Similar Problems Don't Have Similar Solutions."In: Proceedings of the 7th International Conference on Case-Based Reasoning (ICCBR 07), Springer-Verlag, Berlin, Heidelberg: 92-106. 6. Son, Seung-hyun, and Jae-yearn Kim. 2006. "Data Reduction for Instance-Based Learning Using Entropy-Based Partitioning."iN Proceedings of the International Conference on Computational Science and Its Applications: 590-599. 7. Delany, Sarah Jane, Nicola Segata, and Brian Mac Namee. 2012. "Proling Instances in Noise Reduction."Knowledge-Based Systems 31 (July): 28-40. 8. Yang, Ying, Xindong Wu, and Xingquan Zhu. 2004. "Dealing with Predictive-but-Unpredictable Attributes in Noisy Data Sources."In: Proceedings of 8th European Conference on Principles and Practice of Knowledge Discovery in Databases, Pisa, Italy. 9. Brodley, Carla E, and Mark A Friedl. 1999. "Identifying Mislabeled Training Data."Journal of Articial Intelligence Research 11: 131-167. 10. Wilson, D.R., and T.R. Martinez. 2000. "Reduction Techniques for Instance-Based Learning Algorithms."Machine Learning 38 (3): 257-286. 11. Jankowski, Norbert, and Marek Grochowski. 2004. "Comparison of Instances Seletion Algorithms I. Algorithms Survey."Articial Intelligence and Soft Computing: 1-6. 12. Brighton, Henry, and Chris Mellish. 2002. "Advances in Instance Selection for Instance-Based Learning Algorithms *."Data Mining and Knowledge Discovery 6: 153-172. Áîðèñîâà È.À., Êóòíåíêî Î.À. Óäàëåíèå îøèáî÷íî êëàññèôèöèðîâàííûõ îáúåêòîâ 4 / 21 Ôóíêöèÿ êîíêóðåíòíîãî ñõîäñòâà (FRiS-ôóíêöèÿ) (Function of Rival Similarity) Ðèñ. 1. Èëëþñòðàöèÿ îòíîñèòåëüíîñòè ñõîäñòâà îáúåêòîâ a è z . Zagoruiko N. G., Borisova I. A., Dyubanov V. V., Kutnenko O. A. Methods of recognition based on the function of rival similarity // Pattern Recognition and Image Analisys. V. 18, 1. 16. F (z, a|b) = 1 1, r (z, b) − r (z, a) r (z, b) − r (z, a) F (z, a|b) ∈ [− , ] r (z, a) = r (z, b) F (z, a|b) = −F (z, b|a). åñëè , òî F (z, a|b) = 0, F (z, A|B) = Áîðèñîâà È.À., Êóòíåíêî Î.À. r (z, B) − r (z, A) r (z, B) − r (z, A) (1) Óäàëåíèå îøèáî÷íî êëàññèôèöèðîâàííûõ îáúåêòîâ 5 / 21 FRiS-êîìïàêòíîñòü è êà÷åñòâî îïèñàíèÿ âûáîðêè Zagoruiko N. G., Borisova I. A., Dyubanov V. V., Kutnenko O. A. A construction of a compressed description of data using a function of rival similarity // Journal of Applied and Industrial Mathematics. 2013. V. 7, 2, Ð. 275286. Êîìïàêòíîñòü îáðàçîâ óñðåäíåííîå çíà÷åíèå FRiS-ôóíêöèè ïî âñåì îáúåêòàì îáðàçîâ A è B : P P a∈A F (a, A|B) + b∈B F (b, B|A) (2) FAB = |A| + |B| Áîðèñîâà È.À., Êóòíåíêî Î.À. Óäàëåíèå îøèáî÷íî êëàññèôèöèðîâàííûõ îáúåêòîâ 6 / 21 FRiS-êîìïàêòíîñòü è êà÷åñòâî îïèñàíèÿ âûáîðêè Zagoruiko N. G., Borisova I. A., Dyubanov V. V., Kutnenko O. A. A construction of a compressed description of data using a function of rival similarity // Journal of Applied and Industrial Mathematics. 2013. V. 7, 2, Ð. 275286. Zagoruiko N. G., Borisova I. A., Dyubanov V. V., Kutnenko O. A. Methods of recognition based on the function of rival similarity // Pattern Recognition and Image Analisys. 2008. V. 18, 1. P. 16. FRiS-êîìïàêòíîñòü îáðàçà A ïî ìíîæåñòâó ñòîëïîâ SA è SB îáðàçîâ A è B : P F (a, SA |SB ) − |SA | , (3) CA|B = a∈A |SA ||A| S ãäå SA SB - äîñòàòî÷íûé äëÿ îïèñàíèÿ âûáîðêè íàáîð ñòîëïîâ. Àíàëîãè÷íî âû÷èñëÿåòñÿ âåëè÷èíà CB|A FRiS-êîìïàêòíîñòè îáðàçà B â êîíêóðåíöèè ñ A. Êîìïàêòíîñòü îáðàçîâ A è B : q CAB = CA|B CB|A (4) Áîðèñîâà È.À., Êóòíåíêî Î.À. Óäàëåíèå îøèáî÷íî êëàññèôèöèðîâàííûõ îáúåêòîâ 7 / 21 FRiS-êîìïàêòíîñòü è êà÷åñòâî îïèñàíèÿ âûáîðêè Zagoruiko N. G., Êóòíåíêî Î. À., Çûðÿíîâ À. Î., Ëåâàíîâ Ä. À. Îáó÷åíèå ðàñïîçíàâàíèþ áåç ïåðåîáó÷åíèÿ //Ìàøèííîå îáó÷åíèå è àíàëèç äàííûõ. 2014. Ò. 1, 7. Ñ. 891901. Êà÷åñòâî îïèñàíèÿ âûáîðêè íàáîðîì ñòîëïîâ SA è SB îáðàçîâ P H(SA , SB ) = a∈A P F (a, SA |B) + b∈B F (b, SB |A) |SA ∪ SB ||A ∪ B| A è B: (5) Ïðè èçìåíåíèè íàáîðà ñòîëïîâ ìåíÿåòñÿ êà÷åñòâî îïèñàíèÿ H îáó÷àþùåé âûáîðêè è îøèáêà ðàñïîçíàâàíèÿ E íåçàâèñèìîé òåñòîâîé âûáîðêè. Ðèñ. 2. Ãðàôèêè êà÷åñòâà îïèñàíèÿ îáó÷àþùåé âûáîðêè (H ) è ãðàôèêè îøèáêè ðàñïîçíàâàíèÿ (E ) â çàâèñèìîñòè îò ÷èñëà âûáðàííûõ ýòàëîíîâ. Áîðèñîâà È.À., Êóòíåíêî Î.À. Óäàëåíèå îøèáî÷íî êëàññèôèöèðîâàííûõ îáúåêòîâ 8 / 21 Öåíçóðèðîâàíèå âûáîðêè áåç ïîñòðîåíèÿ ñòîëïîâ Áîðèñîâà È. À., Êóòíåíêî Î. À. Öåíçóðèðîâàíèå îøèáî÷íî êëàññèôèöèðîâàííûõ îáúåêòîâ âûáîðêè //Ìàøèííîå îáó÷åíèå è àíàëèç äàííûõ. 2015. Ò. 1, 11. Ñ. 1632-1641. âûáîðêà ñîäåðæèò íåâåðíî êëàññèôèöèðîâàííûå îáúåêòû (èëè øóìîâûå îáúåêòû). Äàíî: Òðåáóåòñÿ: èñêëþ÷èòü øóìîâûå îáúåêòû. Ñëîæíîñòü: ìàëûé îáúåì âûáîðêè; áîëüøàÿ äîëÿ øóìîâ. Äëÿ öåíçóðèðîâàíèÿ îøèáî÷íî êëàññèôèöèðîâàííûõ îáúåêòîâ ðàçðàáîòàí àëãîðèòì, êîòîðûé îðèåíòèðóåòñÿ òîëüêî íà ëîêàëüíûå õàðàêòåðèñòèêè îáúåêòîâ âûáîðêè. Áîðèñîâà È.À., Êóòíåíêî Î.À. Óäàëåíèå îøèáî÷íî êëàññèôèöèðîâàííûõ îáúåêòîâ 9 / 21 Öåíçóðèðîâàíèå âûáîðêè áåç ïîñòðîåíèÿ ñòîëïîâ Êîëè÷åñòâåííûå õàðàêòåðèñòèêè ëîêàëüíîé êîìïàêòíîñòè îáúåêòîâ â òîé èëè èíîé ÷àñòè âûáîðêè îöåíèâàþòñÿ ñ ïîìîùüþ FRiS-ôóíêöèè. Ëîêàëüíàÿ êîìïàêòíîñòü âûáîðêè: FAB = P a∈A P F (a,A|B)+ b∈B F (b,B|A) , |A|+|B| ãäå â êà÷åñòâå ðàññòîÿíèÿ îò îáúåêòà äî îáðàçà èñïîëüçóåòñÿ ñðåäíåå ðàññòîÿíèå äî k áëèæàéøèõ îáúåêòîâ ýòîãî îáðàçà. Ëîêàëüíàÿ ðàçäåëèìîñòü îáó÷àþùåé âûáîðêè: M∗ FAB , (6) M M ∗ /M øòðàô, ðåãóëèðóþùèé êîëè÷åñòâî èñêëþ÷åííûõ îáúåêòîâ. GAB = Áîðèñîâà È.À., Êóòíåíêî Î.À. Óäàëåíèå îøèáî÷íî êëàññèôèöèðîâàííûõ îáúåêòîâ 10 / 21 Öåíçóðèðîâàíèå âûáîðêè áåç ïîñòðîåíèÿ ñòîëïîâ Àëãîðèòì öåíçóðèðîâàíèÿ: 1. Âû÷èñëÿåòñÿ ðàçäåëèìîñòü äëÿ âñåé âûáîðêè. 2. Îòûñêèâàåòñÿ îáúåêò, óäàëåíèå êîòîðîãî èç âûáîðêè ìàêñèìàëüíî ïîâûøàåò åå ðàçäåëèìîñòü. Ýòîò îáúåêò ïðèçíàåòñÿ âûáðîñîì è èñêëþ÷àåòñÿ èç âûáîðêè. 3. Ïðîöåäóðà ïîâòîðÿåòñÿ äî ìîìåíòà, êîãäà èñêëþ÷åíèå ëþáîãî îáúåêòà èç îáó÷àþùåé âûáîðêè òîëüêî óõóäøàåò åå ðàçäåëèìîñòü, ò.å. ïðîöåññ öåíçóðèðîâàíèÿ ïðîäîëæàåòñÿ äî äîñòèæåíèÿ òî÷êè ïåðåãèáà ôóíêöèè ðàçäåëèìîñòè. Áîðèñîâà È.À., Êóòíåíêî Î.À. Óäàëåíèå îøèáî÷íî êëàññèôèöèðîâàííûõ îáúåêòîâ 11 / 21 Òåñòèðîâàíèå àëãîðèòìà. Ðåçóëüòàòû ýêñïåðèìåíòîâ ×óâñòâèòåëüíîñòü è ñïåöèôè÷íîñòü àëãîðèòìà ×óâñòâèòåëüíîñòü (Sensitivi) - ñïîñîáíîñòü ìåòîäà äàâàòü ïðàâèëüíûé ðåçóëüòàò: TP × 100%, TP + FN TP - êîëè÷åñòâî èñòèíî ïîëîæèòåëüíûõ ðåçóëüòàòîâ, FN - êîëè÷åñòâî ëîæíîîòðèöàòåëüíûõ ðåçóëüòàòîâ. Se = ×óâñòâèòåëüíîñòü àëãîðèòìà õàðàêòåðèçóåòñÿ åãî âåðîÿòíîñòüþ îïðåäåëÿòü øóìîâûå îáúåêòû. Áîðèñîâà È.À., Êóòíåíêî Î.À. Óäàëåíèå îøèáî÷íî êëàññèôèöèðîâàííûõ îáúåêòîâ 12 / 21 Òåñòèðîâàíèå àëãîðèòìà. Ðåçóëüòàòû ýêñïåðèìåíòîâ ×óâñòâèòåëüíîñòü è ñïåöèôè÷íîñòü àëãîðèòìà Ñïåöèôè÷íîñòü (Specicity) - ñïîñîáíîñòü ìåòîäà íå äàâàòü ëîæíîïîëîæèòåëüíûõ ðåçóëüòàòîâ: TN × 100%, TN + FP TN - êîëè÷åñòâî èñòèíî îòðèöàòåëüíûõ ðåçóëüòàòîâ, FP - êîëè÷åñòâî ëîæíîïîëîæèòåëüíûõ ðåçóëüòàòîâ. Sp = Ñïåöèôè÷íîñòü àëãîðèòìà õàðàêòåðèçóåòñÿ îòñóòñòâèåì îøèáî÷íûõ ðåçóëüòàòîâ äëÿ íåøóìîâûõ îáúåêòîâ. Áîðèñîâà È.À., Êóòíåíêî Î.À. Óäàëåíèå îøèáî÷íî êëàññèôèöèðîâàííûõ îáúåêòîâ 13 / 21 Òåñòèðîâàíèå àëãîðèòìà. Ðåçóëüòàòû ýêñïåðèìåíòîâ Àëãîðèòì òåñòèðîâàëñÿ íà ñåðèè èç 10 ìîäåëüíûõ çàäà÷, îòëè÷àþùèõñÿ ñëîæíîñòüþ è ñòðóêòóðîé, êàæäàÿ èç êîòîðûõ ðåøàëàñü 100 ðàç íà ðàçíûõ îáó÷àþùèõ âûáîðêàõ, ò. å. îáùåå êîëè÷åñòâî ýêñïåðèìåíòîâ ïðè ðàçëè÷íûõ ÷èñëåííûõ ðåàëèçàöèÿõ äàííûõ áûëî ðàâíî 1000. Îáúåì îáó÷àþùèõ âûáîðîê áûë 100 îáúåêòîâ. Óðîâåíü øóìà (α) ñîñòàâëÿë 15%. Ðåøàþùåå ïðàâèëî ïðàâèëî k áëèæàéøèõ ñîñåäåé, k = 3. Áîðèñîâà È.À., Êóòíåíêî Î.À. Óäàëåíèå îøèáî÷íî êëàññèôèöèðîâàííûõ îáúåêòîâ 14 / 21 Òåñòèðîâàíèå àëãîðèòìà. Ðåçóëüòàòû ýêñïåðèìåíòîâ G0 = FAB ∗ G1 = MM FAB ∗ G2 = ( MM )2 FAB ×óâñòâèòåëüíîñòü (Se) 98.28 97.48 96.16 Ñïåöèôè÷íîñòü (Sp) 50.72 96.31 98.94 Ðèñ. 3. Ñâÿçü ÷óâñòâèòåëüíîñòè (Se) è ñïåöèôè÷íîñòè (Sp) àëãîðèòìà: 0 - êðèòåðèé G0 , 1 - êðèòåðèé G1 , 2 - êðèòåðèé G2 . Áîðèñîâà È.À., Êóòíåíêî Î.À. Óäàëåíèå îøèáî÷íî êëàññèôèöèðîâàííûõ îáúåêòîâ 15 / 21 Òåñòèðîâàíèå àëãîðèòìà. Ðåçóëüòàòû ýêñïåðèìåíòîâ Ðèñ. 4. Çàâèñèìîñòü äîëè ëîæíîïîëîæèòåëüíûõ ðåçóëüòàòîâ (FP) îò òî÷êè îñòàíîâà àëãîðèòìà: 1 - êðèòåðèé G1 , 2 - êðèòåðèé G2 . G0 : n = 56.55; G1 : n = 17.69; G2 : n = 15.17. Áîðèñîâà È.À., Êóòíåíêî Î.À. Óäàëåíèå îøèáî÷íî êëàññèôèöèðîâàííûõ îáúåêòîâ 16 / 21 Òåñòèðîâàíèå àëãîðèòìà. Ðåçóëüòàòû ýêñïåðèìåíòîâ Èëëþñòðàöèÿ ðàáîòû àëãîðèòìà Ðèñ. 5. a) èñõîäíàÿ âûáîðêà, b) çàøóìëåííàÿ âûáîðêà (α = 15%), ñ) î÷èùåííàÿ âûáîðêà, d) ãðàôèê ëîêàëüíîé ðàçäåëèìîñòè îïèñàíèÿ îáó÷àþùåé âûáîðêè (GAB ). Áîðèñîâà È.À., Êóòíåíêî Î.À. Óäàëåíèå îøèáî÷íî êëàññèôèöèðîâàííûõ îáúåêòîâ 17 / 21 Òåñòèðîâàíèå àëãîðèòìà. Ðåçóëüòàòû ýêñïåðèìåíòîâ Ñðàâíåíèå ðåçóëüòàòîâ ðàñïîçíàâàíèÿ òåñòîâîé âûáîðêè äî è ïîñëå öåíçóðèðîâàíèÿ. Ïóíêòèðíàÿ äèàãîíàëü çàäàåò ïîðîã, ïðè êîòîðîì E0 = E . Ðèñ. 6. Ñâÿçü îøèáêè ðàñïîçíàâàíèÿ äî (E0 ) è ïîñëå öåíçóðèðîâàíèÿ (E ): 0 - êðèòåðèé G0 , 1 - êðèòåðèé G1 , 2 - êðèòåðèé G2 . Áîðèñîâà È.À., Êóòíåíêî Î.À. Óäàëåíèå îøèáî÷íî êëàññèôèöèðîâàííûõ îáúåêòîâ 18 / 21 Òåñòèðîâàíèå àëãîðèòìà. Ðåçóëüòàòû ýêñïåðèìåíòîâ  êà÷åñòâå îöåíêè ýôôåêòèâíîñòè àëãîðèòìà èñïîëüçîâàëîñü ðàçíèöà â âåëè÷èíàõ îæèäàåìîé îøèáêè ðàñïîçíàâàíèÿ äî è ïîñëå öåíçóðèðîâàíèÿ îáó÷àþùåé âûáîðêè. Îæèäàåìàÿ îøèáêà ðàñïîçíàâàíèÿ îöåíèâàëàñü ìåòîäîì Cross Validation. α äîëÿ îáúåêòîâ, äëÿ êîòîðûõ èçìåíÿëàñü öåëåâàÿ õàðàêòåðèñòèêà. Ñåðèÿ 100 âûáîðîê. Îáúåì îáó÷àþùåé âûáîðêè 100 îáúåêòîâ. Ðèñ. 7. Çàâèñèìîñòü îøèáêè ðàñïîçíàâàíèÿ îò α äîëè íåâåðíî êëàññèôèöèðîâàííûõ îáúåêòîâ âûáîðêè äî (1) è ïîñëå (2) öåíçóðèðîâàíèÿ. Áîðèñîâà È.À., Êóòíåíêî Î.À. Óäàëåíèå îøèáî÷íî êëàññèôèöèðîâàííûõ îáúåêòîâ 19 / 21 Çàêëþ÷åíèå Èññëåäîâàëàñü âîçìîæíîñòü öåíçóðèðîâàíèÿ îøèáî÷íî êëàññèôèöèðîâàííûõ îáúåêòîâ îáó÷àþùåé âûáîðêè äëÿ ñëó÷àÿ, êîãäà äîëÿ òàêèõ îáúåêòîâ äîñòàòî÷íî âåëèêà, à îáúåì âûáîðêè îãðàíè÷åí.  ýòîì ñëó÷àå öåíçóðèðîâàíèå îñóùåñòâëÿåòñÿ ïóòåì ñíèæåíèÿ ñëîæíîñòè âûáîðêè. Ñëîæíîñòü ïðè ýòîì îöåíèâàåòñÿ âåëè÷èíîé ëîêàëüíîé ðàçäåëèìîñòè êëàññîâ, êîòîðàÿ âû÷èñëÿåòñÿ ñ ïîìîùüþ ôóíêöèè êîíêóðåíòíîãî ñõîäñòâà. Ïðîâåäåííûå ýêñïåðèìåíòû íà øèðîêîì ñïåêòðå ìîäåëüíûõ çàäà÷ ïîäòâåðæäàþò ðàáîòîñïîñîáíîñòü ïðåäëîæåííîãî àëãîðèòìà öåíçóðèðîâàíèÿ. Áîðèñîâà È.À., Êóòíåíêî Î.À. Óäàëåíèå îøèáî÷íî êëàññèôèöèðîâàííûõ îáúåêòîâ 20 / 21 Ñïàñèáî çà âíèìàíèå! Áîðèñîâà È.À., Êóòíåíêî Î.À. Óäàëåíèå îøèáî÷íî êëàññèôèöèðîâàííûõ îáúåêòîâ 21 / 21