Monday, 7 March 2011

My book on biplots

Now for something scientific but which is equally "moving": visualizing data through biplots.  A biplot is simply an extension of what statisticians call a scatterplot.  A scatterplot plots two variables, often called x (the horizontal axis of the plot) and y (the vertical axis).  A biplot includes many variables at the same time, but because it is trying to show many relationships at the same time, it compromises by showing the data approximately as best it can.  Opposite you will see the cover of my book, published in 2010, on this subject.  The book was published by the BBVA Foundation in Madrid, with excellent production by Rubes Editorial in Barcelona.  The book is sold without profit and is also available online for free download at the website

Now how can one method like this fill a whole book?  It is simply because there are many different types of data in research: quantitative data, qualitative data, data on a scale of percentages, and so on, and each data type poses a different challenge for the way it is turned into a biplot.  A novel aspect of the book is that the associated website mentioned above also contains videos which illustrate the concepts in the book.  Here are two for a start:

Video showing a three-dimensional view of a set of points (countries measured on three economic indicators). At one point the country points almost line up, showing that the three-dimensional configuration is approximately two-dimensional. The rotation spreads out the configuration of points, pausing at that two-dimensional view. (Since one's eye can flip between seeing a regular cube and a distorted one, try to keep the "Purchasing power" axis at the back, away from you.

Video showing a set of points where the vertical variable (abundance of a marine species, denoted by d) is assumed to depend on the other two, pollution and depth. The so-called regression plane is shown, which best fits the points and so summarizes the functional relationship approximately. (The rotation should be seen to be counter-clockwise.)

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