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In [[data visualization]], an '''Andrews plot''' or '''Andrews curve''' is a way to visualize structure in high-dimensional data.
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Each data point <math>x = \left \{ x_1, x_2, \ldots x_d \right \}</math> defines a finite [[Fourier series]]:
 
<math>f_x(t) = \frac{x_1}{\sqrt 2} + x_2 \sin(t) + x_3 \cos(t) + x_4 \sin(2t) + x_5 \cos(2t) + \ldots</math>
 
This function is then plotted for <math>-\pi < t < \pi</math>. Thus each data point may be viewed as a line between <math>-\pi</math> and <math>\pi</math>. This formula can be thought of as the projection of the data point onto the vector:
 
<math>\left ( \frac{1}{\sqrt 2}, \sin(t), \cos(t), \sin(2t), \cos(2t), \ldots \right )</math>
 
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 [[outlier]]s in [[time series]], the visualization of learning in [[artificial neural network]]s, and correspondence analysis.
 
==References==
* {{cite journal |first=David F. |last=Andrews |title=Plots of High-Dimensional Data |journal=International Biometric Society |volume=18 |issue=1 |pages=125–136 |year=1972 |jstor=2528964 }}
* {{cite journal |title=Visualization of High-Dimensional Data via Orthogonal Curves |first1=César |last1=García-Osorio |first2=Colin |last2=Fyfe |journal=Journal of Universal Computer Science |volume=11 |issue=11 |year=2005 |pages=1806–1819 |url=http://www.jucs.org/jucs_11_11/visualization_of_high_dimensional/jucs_11_11_1806_1819_garc_a_osorio.pdf }}
* {{cite web |work=Rip’s Applied Mathematics Blog |title=Andrews Curves |date=3 October 2011 |url=http://rip94550.wordpress.com/2011/10/03/andrews-curves/ }}
 
==See also==
* [[Wegman's curve]]
 
[[Category:Visualization (graphic)]]

Revision as of 05:33, 26 February 2014

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