On the finite convergence of the NN classification learning on mistakes
The paper establishes an analog of well-known Novikoff’s theorem on the perceptron learning algorithm’s finite convergence in linearly separated classes. We obtain a similar result concerning the nearest neighbor classification algorithm in the case of compact classes in a general metric space for...
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| Date: | 2022 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Видавничий дім "Академперіодика" НАН України
2022
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| Series: | Доповіді НАН України |
| Subjects: | |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/184927 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | On the finite convergence of the NN classification learning on mistakes / V.I. Norkin // Доповіді Національної академії наук України. — 2022. — № 1. — С. 34-38. — Бібліогр.: 10 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | The paper establishes an analog of well-known Novikoff’s theorem on the perceptron learning algorithm’s finite convergence
in linearly separated classes. We obtain a similar result concerning the nearest neighbor classification algorithm
in the case of compact classes in a general metric space for the case of non-intersecting classes. The learning
process consists of gradual modification of the algorithm in misclassification cases. The process is studied in the
deterministic setting. Classes are understood as compacts in complete metric space, and class separation is defined as
the non-intersection of compacts. The number of learning steps is bounded by the number of elements in some ε-net
for the considered classes. |
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