Email this article Cross-entropy optimal dimensionality reduction with condition on information capacity
- Authors: Popkov Y.S.1,2, Popkov A.Y.1
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Affiliations:
- Federal Research Center Computer Science and Control of the Russian Academy of Sciences
- ORT Braude College
- Issue: Vol 488, No 1 (2019)
- Pages: 21-23
- Section: Mathematics
- URL: https://journals.eco-vector.com/0869-5652/article/view/16159
- DOI: https://doi.org/10.31857/S0869-5652488121-23
- ID: 16159
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Abstract
Using a data leads to a problem of its sufficiency to solve specific task. Proposed paper is devoted to a modification of direct-inverse projection method (DIP-method) based on an idea of information capacity. DIP-method is updated with a condition on maintaining the information capacity in given ranges. Modified dimensionality reduction method (mDIP) based on the problem of minimization cross-entropy function on a set defined by linear inequality. Minimization of the function is suggested to perform by the first-order multiplicative algorithm. There obtained conditions of local convergence.
About the authors
Yu. S. Popkov
Federal Research Center Computer Science and Control of the Russian Academy of Sciences; ORT Braude College
Author for correspondence.
Email: popkov@isa.ru
Academician of the Russian Academy of Sciences
Russian Federation, 44/2, Vavilova street, Moscow, 119333; 51, Snunit str., Karmiel, Israel, 210100A. Yu. Popkov
Federal Research Center Computer Science and Control of the Russian Academy of Sciences
Email: popkov@isa.ru
Russian Federation, 44/2, Vavilova street, Moscow, 119333
References
- Bingham E., Manilla H. Random projection in dimensionality reduction: Application to image and next data // Proc. of the Seventh ACM SICKDD Intern. Conf. on Knowledge Discovery and Data Mining. N.Y.: Association for Computing Machinery. P. 245-250.
- Achlioptas D. Database-friendly random projection // Proceeding PODS’01, Proc. of the twentith ACM SIGMOD-SIGACT-SIGART symposium on principles of data base systems. 2001. P. 274-281.
- Попков Ю.С., Дубнов Ю.А., Попков А.Ю. Энтропийная редукция размерности в задачах рандомизированного машинного обучения // АиТ. 2018. № 11. С. 106-123.
- Кендал М.Дж., Стюарт А. Статистические выводы и связи // Пер. с англ. М.: Наука, 1973.
- Jollife I.T. Principle Component Analysis // N.Y.: Springer-Verlag, 2002.
- Айвазян С.А., Бухштабер И.М., Енюков И.С., Мешалкин Л.Д. Прикладная статистика: Классификация и снижение размерности // М.: Финансы и статистика, 1989.
- Fisher R.A. The Use of Multiple Measurements in Taxonomic Problems // Annals of Eugenics. 1936. V. 7. P. 179-188.
- Comon P., Jutten C. Handbook of Blind Source Separation, Independent Component Analysis and Applications. Oxford: Acag. Press, 2010.
- Michael W., et all. Algorithms and Application for Approximate Nonnegative Matrix Factorization // Computational Statistics and Data Analysis. 2007. V. 52. P. 150-173.
- Поляк Б.Т., Хлебников М.В. Метод главных компонент: робастные версии //АиТ. 2017. № 3. С. 130-148.
- Попков Ю.С. Мультипликативные схемы итерационных алгоритмов II: выпуклое программирование // Техническая кибернетика. 1993. № 2. С. 31-45.
- Попков Ю.С. Теория макросистем: равновесные модели. М.: УРСС, 1999. 317 с.
- Kullback S., Leibler R.A. On information and Sufficiency. Ann. of Math. Statistics. 1951. V. 22(1). P. 79-86.
- Magnus J., Neudecker H. Matrix Differential Calculus with Applications in Statistics and Econometrics. John Willey and Sons. 1999.
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