Dimensiju samazināšanas algoritmi
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Latvijas Universitāte
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Abstract
Šīs darbs apskata datu dimensiju samazināšanas nepieciešamību un metodes. Tas pēta vienu no pieejām - galveno komponenšu analīzi. Darba mērķis ir izpētīt to teorētisko pamatojumu, darbības principus un pielietošanas iespējas; salīdzināt eksistējošas implementācijas, noskaidrot to pielietošanas robežas, un izpētīt iteratīvo tuvināto algoritmu veidošanas iespējas.
Algoritmu darbība tiek pārbaudīta uz lielām datu kopām, lai salīdzināt veiktspēju un patērētus resursus un ieraudzīt uzlabošanas iespējas. Papildus tiek savākta datu kopa par tīmekļa lappušu struktūru lai paradīt algoritmu pielietošanu reāliem pasaules datiem.
Darbā tiek apskatītas dimensiju samazināšanas pieejas programmēšanas un mašīnmacīšanas ietvarā. Matemātiskie pamatojumi tiek doti tikai lai nodrošināt saprašanu, pilnie pierādījumi ir pieejami avotos, norādītos atsaucēs.
This work examines data dimensionality reduction reasons and methods. It explores the approach called principal component analysis. The purpose of this work is to research algorithm principles and applications, to compare different algorithm implementations and determine their limitations, as well as to explore iterative approximation algorithm development opportunities. Algorithms are tested using large data sets to compare the performance and resource consumption and to see improvement possibilities. In addition, a data set describing web pages structure is collected and used to show the algorithm usage on the real-world data. The paper examines dimension reduction in scope of programming and machine learning. Mathematical foundations are given only to ensure comprehension, full proofs are available in sources listed in the references.
This work examines data dimensionality reduction reasons and methods. It explores the approach called principal component analysis. The purpose of this work is to research algorithm principles and applications, to compare different algorithm implementations and determine their limitations, as well as to explore iterative approximation algorithm development opportunities. Algorithms are tested using large data sets to compare the performance and resource consumption and to see improvement possibilities. In addition, a data set describing web pages structure is collected and used to show the algorithm usage on the real-world data. The paper examines dimension reduction in scope of programming and machine learning. Mathematical foundations are given only to ensure comprehension, full proofs are available in sources listed in the references.