# Multivariate Functional Data Visualization and Outlier Detection

## TL;DR

This paper introduces the magnitude-shape (MS) plot, a novel visualization tool for multivariate functional data that effectively displays outlyingness in magnitude and shape, improving outlier detection compared to existing methods.

## Contribution

The paper presents the MS-plot, a new graphical method based on functional directional outlyingness for visualizing and detecting outliers in multivariate functional data.

## Key findings

- MS-plot effectively visualizes outliers in simulated data.
- MS-plot outperforms existing tools in practical examples.
- The method clearly separates outliers from non-outliers.

## Abstract

This article proposes a new graphical tool, the magnitude-shape (MS) plot, for visualizing both the magnitude and shape outlyingness of multivariate functional data. The proposed tool builds on the recent notion of functional directional outlyingness, which measures the centrality of functional data by simultaneously considering the level and the direction of their deviation from the central region. The MS-plot intuitively presents not only levels but also directions of magnitude outlyingness on the horizontal axis or plane, and demonstrates shape outlyingness on the vertical axis. A dividing curve or surface is provided to separate non-outlying data from the outliers. Both the simulated data and the practical examples confirm that the MS-plot is superior to existing tools for visualizing centrality and detecting outliers for functional data.