Multidimensional scaling for Big Data

We present a set of algorithms for Multidimensional Scaling (MDS) to be used with large datasets. MDS is a statistic tool for reduction of dimensionality, using as input a distance matrix of dimensions n x n. When n is large, classical algorithms suffer from computational problems and MDS configurat...

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Detalles Bibliográficos
Autor: Pachón García, Cristian|||0000-0001-9518-4874
Tipo de recurso: tesis de maestría
Fecha de publicación:2019
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/127318
Acceso en línea:https://hdl.handle.net/2117/127318
Access Level:acceso abierto
Palabra clave:Multivariate analysis
Multidimensional Scaling
Big Data
Recursive Programming
Simulation
Anàlisi multivariable
Classificació AMS::62 Statistics::62H Multivariate analysis
Àrees temàtiques de la UPC::Matemàtiques i estadística::Estadística matemàtica::Anàlisi multivariant
Descripción
Sumario:We present a set of algorithms for Multidimensional Scaling (MDS) to be used with large datasets. MDS is a statistic tool for reduction of dimensionality, using as input a distance matrix of dimensions n x n. When n is large, classical algorithms suffer from computational problems and MDS configuration can not be obtained. In this thesis we address these problems by means of three algorithms: Divide and Conquer MDS, Fast MDS and MDS based on Gower interpolation. The main idea of these methods is based on partitioning the dataset into small pieces, where classical methods can work. In order to check the performance of the algorithms as well as to compare them, we do a simulation study. This study points out that Fast MDS and MDS based on Gower interpolation are appropriated to use when n is large and Divide and Conquer MDS is the best method that captures the variance of the original data.