[Paper Review] REPPlab: An R package for detecting clusters and outliers using exploratory projection pursuit

Daniel Fischer, Alain Berro+2 more|Toulouse Capitole Publications (University Toulouse 1 Capitole)|Dec 20, 2016

Advanced Statistical Methods and Models24 references4 citations

TL;DR

REPPlab is an R package that provides access to exploratory projection pursuit (EPP) tools for detecting clusters and outliers in multivariate data using four projection indices and three bio-inspired optimization algorithms (genetic algorithm, particle swarm optimization, and Tribe). It enables thorough visualization and analysis of low-dimensional projections, with novel outlier detection tools that combine results across multiple indices and algorithms, significantly enhancing detection reliability and interpretability in real-world datasets.

ABSTRACT

The R-package REPPlab is designed to explore multivariate data sets using one-dimensional unsupervised projection pursuit. It is useful in practice as a preprocessing step to find clusters or as an outlier detection tool for multivariate numerical data. Except from the package tourr that implements smooth sequences of projection matrices and rggobi that provides an interface to a dynamic graphics package called GGobi, there is no implementation of exploratory projection pursuit tools available in R especially in the context of outlier detection. REPPlab is an R interface for the Java program EPPlab that implements four projection indices and three biologically inspired optimization algorithms. The implemented indices are either adapted to cluster or to outlier detection and the optimization algorithms have at most one parameter to tune. Following the original software EPPlab, the exploration strategy in REPPlab is divided into two steps. Many potentially interesting projections are calculated at the first step and examined at the second step. For this second step, different tools for plotting and combining the results are proposed with specific tools for outlier detection. Compared to EPPlab, some of these tools are new and their performance is illustrated through some simulations and using some real data sets in a clustering context. The functionalities of the package are also illustrated for outlier detection on a new data set that is provided with the package.

Motivation & Objective

• To address the lack of accessible, static exploratory projection pursuit (EPP) tools in R for unsupervised data analysis.
• To bridge the gap between the standalone Java tool EPP-lab and R users by providing a comprehensive R interface.
• To enhance outlier detection by combining results across multiple projection indices and optimization algorithms.
• To offer advanced visualization and summary tools for interpreting EPP results, especially for identifying extreme observations.
• To demonstrate the effectiveness of REPPlab on real datasets and simulations, showing improved robustness and detection accuracy.

Proposed method

• The package interfaces with the Java-based EPP-lab software to leverage its four projection indices: Friedman-Tukey, Friedman, discriminant, and kurtosis (maximized/minimized).
• It implements three optimization algorithms—genetic algorithm, particle swarm optimization (PSO), and Tribe—each with minimal tuning requirements.
• The exploration strategy follows a two-step process: first, many projections are computed using different indices and algorithms; second, results are visualized and analyzed using R-based tools.
• Outlier detection is performed by identifying observations consistently extreme across multiple projections, using both classical (mean, sd) and robust (median, mad) location and scale measures.
• The package provides functions to compute and visualize projection index values, cosine matrices between directions, and outlier frequency across multiple runs.
• It supports combining results from different indices and algorithms, with tools like `apply(outlier_matrix, 1, sum)` to identify observations detected in multiple directions.

Experimental results

Research questions

• RQ1 How can exploratory projection pursuit be effectively integrated into R for unsupervised multivariate data analysis?
• RQ2 To what extent can combining multiple projection indices and optimization algorithms improve outlier detection reliability?
• RQ3 How do robust measures (median, mad) compare to classical measures (mean, sd) in identifying outliers using EPP?
• RQ4 What is the performance of REPPlab’s visualization and summary tools in detecting clusters and extreme observations in real datasets?
• RQ5 Can the Tribe algorithm, a specialized PSO variant, outperform standard optimization methods in identifying non-gaussian structures in multivariate data?

Key findings

• Using robust measures (median and median absolute deviation) instead of classical ones (mean and standard deviation) led to the detection of 32 outliers, compared to 11 with classical measures.
• Observation 512 was detected as an outlier in 81 out of 100 projections when using robust measures, indicating extreme deviation in multiple directions.
• Observation 414 was detected in 74 projections with robust measures, confirming its status as a highly extreme outlier.
• The combination of multiple indices and algorithms identified four key outlier candidates—57, 367, 414, and 512—whose extreme positions were confirmed in scatter plots of the first two projections.
• The Tribe algorithm proved effective in identifying local optima, contributing to the detection of non-gaussian structures such as clusters and outliers.
• Visualization tools, including cosine matrices and multi-directional outlier frequency plots, enabled clear identification of the most extreme observations and their consistency across projections.