Цензурирование ошибочно классифицированных объектов

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.
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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.
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Ââåäåíèå
Ðàçëè÷íûå àëãîðèòìû ðàñïîçíàâàíèÿ ïðè íàëè÷èè øóìîâûõ
îáúåêòîâ è âûáðîñîâ â îáó÷àþùåé âûáîðêå îáðàáàòûâàþò èõ
ïî-ðàçíîìó. Â 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) Â
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.
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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.
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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)
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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