Iskanje podobnih primerov v večrazsežnih prostorih : magistrsko delo

Kariž, Primož (author), Robnik Šikonja, Marko (mentor)

Iskanje najbližjih objektov se uporablja na različnih področjih in pomembno je, da jih lahko hitro poiščemo. Pri iskanju v visokodimenzionalnih prostorih ne znamo hitro poiskati eksaktnih sosedov, zato se zadovoljimo s približnimi. V magistrski nalogi opišemo najbolj uporabljane eksaktne in približne metode za iskanje najbližjih sosedov. Med eksaktnimi so to R, R*, KD, M, PM in ball-drevo, med približnimi pa RKD-drevo, LSH, hierarhično razvrščanje z voditelji in gozd robov. Nekatere smo implementirali sami, druge smo uporabili iz že obstoječih knjižnic. Predstavimo in analiziramo rezultate testiranj hitrosti iskanja najbližjih sosedov, točnosti in porabe pomnilnika. V programskem jeziku python smo razvili knjižnico, ki vsebuje opisane metode in omogoča njihovo preprosto in enotno uporabo preko programskega vmesnika. Knjižnica omogoča tudi avtomatsko izbiro najprimernejšega algoritma za dano podatkovno množico. Algoritem izberemo na podlagi dveh odločitvenih dreves, ki smo ju sestavili s pomočjo analize rezultatov testiranj.

• Language: Slovenian
• Keywords: algoritmi, podatkovne strukture, iskanje najbližjih sosedov, približni najbližji sosedi, visokodimenzionalni prostor, R-drevo, R*-drevo, M-drevo, PM-drevo, ball-drevo, KD-drevo, RKD-drevo, LSH, hierarhično razvrščanje z voditelji, računalništvo, računalništvo in informatika, magisteriji
• Work type: Master's thesis/paper
• Typology: 2.09 - Master's Thesis
• Organization: FRI - Faculty of Computer and Information Science
• Publisher: [P. Kariž]
• Year: 2015
• Number of pages: 126 str.
• PID: 20.500.12556/RUL-70240
• UDC: 004.42(043.2)
• COBISS.SI-ID: 1536276675
• Publication date in RUL: 10.07.2015

Licences

• License: CC BY-SA 2.5 SI, Creative Commons Attribution-ShareAlike 2.5 Slovenia
• Link: https://creativecommons.org/licenses/by-sa/2.5/si/deed.en
• Description: You are free to reproduce and redistribute the material in any medium or format. You are free to remix, transform, and build upon the material for any purpose, even commercially. You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. If you remix, transform, or build upon the material, you must distribute your contributions under the same license as the original. You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.

Secondary language

• Language: English
• Title: Searching nearest neighbours in high dimensional spaces

Abstract

Nearest neighbours search is used in different problems, therefore it is important that we are able to find nearest neighbours fast. When searching in high-dimensional spaces we have to be satisfied with approximate nearest neighbours, because fast methods do not exist. In this master thesis we describe some well-known exact and approximate methods for searching nearest neighbours. The described exact ones are R, R*, KD, M, PM and ball-tree, while the approximate are RKD-tree, LSH, hierarchical k-means and boundary-forest. Some of them we implemented, while others were taken from existing libraries. We present and analyze the search results in terms of speed, precision and memory requirements of methods. We developed a library in python programming language, which includes the described methods and provides a simple and consistent API. The library also allows automatic selection of the most suitable algorithm for a given dataset based on two decision trees, which were created through analysis of the results.

• Keywords: algorithms, data structures, nearest neighbours search, approximate nearest neighbours, high-dimensional space, R-tree, R*-tree, M-tree, PM-tree, ball-tree, KD-tree, RKD-tree, LSH, hierarchical k-means, computer science, computer and information science, master's degree