Encyclopedia

Andrews plot

Type of data visualization

Wikipedia contributorsAdapted for Fathomly · View authors

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Source updated June 24, 2025

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In data visualization, an Andrews plot or Andrews curve is a way to visualize structure in high-dimensional data. It is basically a rolled-down, non-integer version of the Kent-Kiviat radar m chart, or a smoothed version of a parallel coordinate plot. It is named after the statistician David F. Andrews.

A value $x$ is a high-dimensional datapoint if it is an element of $\mathbb {R} ^{d}$ . We can represent high-dimensional data with a number for each of their dimensions, $x=\left\{x_{1},x_{2},\ldots ,x_{d}\right\}$ . To visualize them, the Andrews plot defines a finite Fourier series:

$f_{x}(t)={\frac {x_{1}}{\sqrt {2}}}+x_{2}\sin(t)+x_{3}\cos(t)+x_{4}\sin(2t)+x_{5}\cos(2t)+\cdots$

This function is then plotted for $-\pi <t<\pi$ . Thus each data point may be viewed as a line between $-\pi$ and $\pi$ . This formula can be thought of as the projection of the data point onto the vector:

$\left({\frac {1}{\sqrt {2}}},\sin(t),\cos(t),\sin(2t),\cos(2t),\ldots \right)$

If there is structure in the data, it may be visible in the Andrews curves of the data.

These curves have been utilized in fields as different as biology, neurology, sociology and semiconductor manufacturing. Some of their uses include the quality control of products, the detection of period and outliers in time series, the visualization of learning in artificial neural networks, and correspondence analysis.

Theoretically, it is possible to project them onto an n-sphere. The projection onto the circle results in the aforementioned radar chart.

Watch videos about Andrews plotExplainers and documentaries on YouTube (opens in a new tab)

Sources and credits

This article is adapted from the Wikipedia article “Andrews plot”, written by its contributors and licensed under CC BY-SA 4.0. Fathomly has changed the layout, removed citation markers, navigation and maintenance notices, and adjusted punctuation. This adapted version is shared under the same license. For references, see the original article.

Images, from Wikimedia Commons:

Andrews curve for Iris data set.png by Fatdragon2, CC BY-SA 4.0

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