A methodology to compare Dimensionality Reduction algorithms in terms of loss of quality

Abstract

Dimensionality Reduction (DR) is attracting more attention these days as a result of the increasing need to handle huge amounts of data effectively. DR methods allow the number of initial features to be reduced considerably until a set of them is found that allows the original properties of the data to be kept. However, their use entails an inherent loss of quality that is likely to affect the understanding of the data, in terms of data analysis. This loss of quality could be determinant when selecting a DR method, because of the nature of each method.In this paper, we propose a methodology that allows different DR methods to be analyzed and compared as regards the loss of quality produced by them. This methodology makes use of the concept of preservation of geometry (quality assessment criteria) to assess the loss of quality. Experiments have been carried out by using the most well-known DR algorithms and quality assessment criteria, based on the literature. These experiments have been applied on 12 real-world datasets.Results obtained so far show that it is possible to establish a method to select the most appropriate DR method, in terms of minimum loss of quality. Experiments have also highlighted some interesting relationships between the quality assessment criteria. Finally, the methodology allows the appropriate choice of dimensionality for reducing data to be established, whilst giving rise to a minimum loss of quality.

Projection-Based Clustering through Self-Organization and Swarm Intelligence

“…Recently, [Gracia et al] conducted a study on a number of QMs based on 12 real-world data sets. The research team's analysis of the QMs concentrated on the correlations between them [Gracia et al, 2014]. This study illustrates the other common evaluation approach: the use of various natural high-dimensional data sets for which prior classifications are available.…”

“…This type of error is often used to compare projection methods when a prior classification is given [Bunte et al, 2012;Gracia et al, 2014;Venna et al, 2010]. Each point ∈ in the output space is classified by a majority vote among its k nearest neighbors in the visualization [Venna et al, 2010], although sometimes simply the cluster of the nearest neighbor is chosen.…”

“…Because the correlation between these two measures is very high [Gracia et al, 2014]), only the LCMC is introduced here. The LCMC is defined as the average size of the overlap between neighborhoods consisting of k nearest neighbors in I and O [Chen/Buja, 2009].…”

MedVir: An Interactive Representation System of Multidimensional Medical Data Applied to Traumatic Brain Injury’s Rehabilitation Prediction

“…For DV, one of the main applications of DR is to map a set of observations into a 2 or 3 dimensional space that preserves the intrinsic geometric structure of the data as much as possible [21]. More related work about DR is presented in [22].…”

“…For example, for clustering tasks, one might be interested in using PCA, since due to its great ability to obtain the directions of maximum variance of data, it produces minimum loss of quality of data [22], thus making more reliable the visualization of the real structure of data. Instead, LDA could be useful for supervised tasks, because even if the effectiveness in the preservation of the original geometry data is drastically reduced [22], the spatial directions of maximum discrimination between classes are easily obtained. This will facilitate the separation of different classes when the data are displayed.…”