Robust multivariate analysis for mixed-type data: Novel algorithm and its practical application in socio-economic research

Sow-Barry

2021

Mathematics

Self Cite

This work provides a procedure with which to construct and visualize profiles, i.e., groups of individuals with similar characteristics, for weighted and mixed data by combining two classical multivariate techniques, multidimensional scaling (MDS) and the k-prototypes clustering algorithm. The well-known drawback of classical MDS in large datasets is circumvented by selecting a small random sample of the dataset, whose individuals are clustered by means of an adapted version of the k-prototypes algorithm and mapped via classical MDS. Gower’s interpolation formula is used to project remaining individuals onto the previous configuration. In all the process, Gower’s distance is used to measure the proximity between individuals. The methodology is illustrated on a real dataset, obtained from the Survey of Health, Ageing and Retirement in Europe (SHARE), which was carried out in 19 countries and represents over 124 million aged individuals in Europe. The performance of the method was evaluated through a simulation study, whose results point out that the new proposal solves the high computational cost of the classical MDS with low error.

Section: Discussionmentioning

confidence: 99%

Visualizing Profiles of Large Datasets of Weighted and Mixed Data

Sow-Barry

2021

Mathematics

Self Cite

“…The FS-DB algorithm was introduced by [8] for the analysis and clustering of mixed data. In particular, the FS-DB algorithm combines the forward search method [9,10] with a distance-based tool, used in [5], to detect outliers in mixed-type datasets.…”

Section: Fs-db Algorithmmentioning

confidence: 99%

“…Two possible distance measures are available in the FS-DB algorithm: a distance measure based on Gower's classical similarity coefficient and a metric obtained via related metric scaling, which satisfies several axioms related to the property of identifying and discarding redundant information. See [8] for details.…”

Section: Fs-db Algorithmmentioning

confidence: 99%

“…They also proposed a novel statistic for outlier detection in mixed data. Grané et al [8] proposed a method to hierarchically cluster mixed data using an approach based on the Forward Search algorithm [9]. Their proposal was to build an algorithm (called Forward Search Distance-Based (FS-DB)), which was a combination of the distance function proposed by Grané and Romera and a forward search algorithm in order to improve the robustness of the results and to visualize and identify outliers, even if they were masked in the bulk of the data.…”

Section: Introductionmentioning

confidence: 99%

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Smart Visualization of Mixed Data

Manzi

Salini

2021

Stats

Self Cite

In this work, we propose a new protocol that integrates robust classification and visualization techniques to analyze mixed data. This protocol is based on the combination of the Forward Search Distance-Based (FS-DB) algorithm (Grané, Salini, and Verdolini 2020) and robust clustering. The resulting groups are visualized via MDS maps and characterized through an analysis of several graphical outputs. The methodology is illustrated on a real dataset related to European COVID-19 numerical health data, as well as the policy and restriction measurements of the 2020–2021 COVID-19 pandemic across the EU Member States. The results show similarities among countries in terms of incidence and the management of the emergency across several waves of the disease. With the proposed methodology, new smart visualization tools for analyzing mixed data are provided.

“…Gower's distance is defined as δ 2 (z i , z j ) = 1 − s ij . There are other possible, more robust, metrics that can be used with mixed data (see, e.g., [20]), but, for simplicity, we use Gower's distance, as it is implemented in the R cluster package and supported in the dblm and dbglm functions of the dbstats package that we employed in the analysis of the real data sets and in the simulations.…”

Section: The Choice Of the Distancementioning

confidence: 99%

Subsampling and Aggregation: A Solution to the Scalability Problem in Distance-Based Prediction for Mixed-Type Data

Baı́llo

2021

Mathematics

Self Cite

The distance-based linear model (DB-LM) extends the classical linear regression to the framework of mixed-type predictors or when the only available information is a distance matrix between regressors (as it sometimes happens with big data). The main drawback of these DB methods is their computational cost, particularly due to the eigendecomposition of the Gram matrix. In this context, ensemble regression techniques provide a useful alternative to fitting the model to the whole sample. This work analyzes the performance of three subsampling and aggregation techniques in DB regression on two specific large, real datasets. We also analyze, via simulations, the performance of bagging and DB logistic regression in the classification problem with mixed-type features and large sample sizes.