469 lines
23 KiB
TeX
469 lines
23 KiB
TeX
\chapter{Graphical Representation of Scientific Data}
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We may count the ability of adequately presenting scientific data to
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the core competences needed to do science. We need to present data in
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a meaningful way that fosters understanding of the data and the
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results.
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\begin{figure}[hb!]
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\includegraphics[width=0.9\columnwidth]{convincing}
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\titlecaption{The consequences of bad plots may be
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severe.}{\url{www.xkcd.com}}\label{xkcdplotting}
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\end{figure}
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\section{What makes a good plot?}
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Plot should help/enable the interested reader to get a grasp of the
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data and to understand the performed analysis and to critically assess
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the presented results. The most important rule is the correct and
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complete annotation of the plots. This starts with axis labels and
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units and and extends to legends. Incomplete annotation can have
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terrible consequences (\figref{xkcdplotting}).
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The principle of \emph{ink minimization} may be used a a guiding
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principle for appealing plots. It requires that the relation of amount
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of ink spent on the data and that spent on other parts of the plot
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should be strongly in favor of the data. Ornamental of otherwise
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unnecessary gimicks should not be used in scientific contexts. An
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exception can be made if the particular figure was designed for
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didactic purposes and sometimes for presentations.
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\begin{important}[Correct labeling of plots]
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A data plot must be sufficiently labeled:
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\begin{itemize}
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\item Every axis must have a label and the correct unit, if it has
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one.\\ (e.g. \code[xlabel()]{xlabel('Speed [m/s]'}).
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\item When more than one line is plotted, they have to be labeled
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using the figure legend, or similar \matlabfun{legend()}.
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\item If using subplots that show similar information on the axes,
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they should be scaled to show the same ranges to ease comparison
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between plots. (e.g. \code[xlim()]{xlim([0 100])}.\\ If one
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chooses to ignore this rule one should explicitly state this in
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the figure caption and/or the descriptions in the text.
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\item Labels must be large enough to be readable. In particular,
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when using the figure in a presentation use large enough fonts.
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\end{itemize}
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\end{important}
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\section{Things that should be avoided.}
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When plotting scientific data we should take great care to avoid
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suggestive or misleading presentations. Unnecessary additions and
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fancy graphical effects make a plot frivolous and also violate the
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\emph{ink minimization principle}. Illustrations in comic style
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(\figref{comicexamplefig}) are not suited for scientific data in most
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instances. For presentations or didactic purposes, however, using a
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comic style may be helpful to indicate that the figure is a mere
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sketch and the exact position of the data points is of no importance.
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\begin{figure}[t]
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\includegraphics[width=0.7\columnwidth]{outlier}\vspace{-3ex}
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\titlecaption{Comic-like illustration.}{Obviously not suited to
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present scientific data. In didactic or illustrative contexts they
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can be helpful to focus on the important
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aspects.}\label{comicexamplefig}
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\end{figure}
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The following figures show examples of misleading or suggestive
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presentaions of data. Several of the effects have been axaggerated to
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make the point. A little more subtlely these methods are employed to
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nudge the viewers experience into the desired direction. You can find
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more examples on \url{https://en.wikipedia.org/wiki/Misleading_graph}.
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\begin{figure}[p]
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\includegraphics[width=0.35\textwidth]{misleading_pie}
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\hspace{0.05\textwidth}
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\includegraphics[width=0.35\textwidth]{sample_pie}
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\titlecaption{Perspective distortion influendes the perceived
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size.}{By changing the perspective of the 3-D illustration the
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highlighted segment \textbf{C} gains more weight than it should
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have. In the left graph segments \textbf{A} and \textbf{C} appear
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very similar. The 2-D plot on the right-hand side shows that this
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is an
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illusion. \url{https://en.wikipedia.org/wiki/Misleading_graph}}\label{misleadingpiefig}
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\end{figure}
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\begin{figure}[p]
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\begin{minipage}[t]{0.3\textwidth}
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\includegraphics[width=0.9\textwidth]{line_graph1}
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\end{minipage}
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\begin{minipage}[t]{0.3\textwidth}
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\includegraphics[width=0.9\textwidth]{line_graph1_3}
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\end{minipage}
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\begin{minipage}[t]{0.3\textwidth}
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\includegraphics[width=0.9\textwidth]{line_graph1_4}
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\end{minipage}
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\titlecaption{Chosing the figure format influences the erceived
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strength of a correlation.}{All three subplots show the same data.
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By choosing a certain figure size we can pronounce or to reduce
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the perceived strength of the correlation in th data. Techincally
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all three plots are correct.
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\url{https://en.wikipedia.org/wiki/Misleading_graph}}\label{misleadingscalingfig}
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\end{figure}
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\begin{figure}[p]
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\begin{minipage}[t]{0.3\textwidth}
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\includegraphics[width=0.8\textwidth]{improperly_scaled_graph}
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\end{minipage}
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\begin{minipage}[t]{0.3\textwidth}
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\includegraphics[width=0.8\textwidth]{comparison_properly_improperly_graph}
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\end{minipage}
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\begin{minipage}[t]{0.3\textwidth}
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\includegraphics[width=0.7\textwidth]{properly_scaled_graph}
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\end{minipage}
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\titlecaption{Scaling of markers and symbols.} {In these graphs
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symbols have been used to illustrate the measurements made in two
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categories. The measured value for category \textbf{B} is actually
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three times the measured value for category \textbf{A}. In the
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left graph the symbol for catergory \textbf{B} has been scaled to
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triple heigth while maintaining the porpotions. This appears jusst
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fair and correct but leads to the effect that the covered surface
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is not increased to the 3-fold but the 9-fold (center plot). The
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plot on the right shows how it could have been done correctly.
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\url{https://en.wikipedia.org/wiki/Misleading_graph}}\label{misleadingsymbolsfig}
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\end{figure}
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By using perspective effects in 3-D plot the perceived size can be
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distorted into the desired direction. While the plot is correct in a
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strict sense it is rather suggestive
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(\figref{misleadingpiefig}). Similarly the choice of figure size and
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proportions can lead to different interpretations of the
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data. Stretching the y-extent of a graph leads to a stronger
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impression of the correlation in the data. Compressing this axis will
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lead to a much weaker perceived correlation
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(\figref{misleadingscalingfig}). When using symbols to illustrate a
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quantity we have to take care not to overrate of difference due to
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symbol scaling (\figref{misleadingsymbolsfig}).
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\section{The \matlab{} plotting system}
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Plotting data in \matlab{} is rather straight forward for simple line
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plots. By calling \code[plot()]{plot(x, y)} a simple line plot will be
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created. This figure, however is missing any annotations like axis
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labeling, a legend, etc.. There are two options to edit the plot: (i)
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the graphical user interface (GUI) or the command line. Both ways have
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their right to exist associated with respective pros and cons. The UI
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way of editing plots is ideal for experimenting the command line
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approach is best suited for automation and to achieve a consistent
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layout across figures and graphs.
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\begin{figure}
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\begin{minipage}[t]{0.6\textwidth}
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\includegraphics[height=0.29\textheight]{plot_editor}
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\end{minipage}
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\begin{minipage}[t]{0.3\textwidth}
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\includegraphics[height=0.29\textheight]{property_editor}
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\end{minipage}
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\titlecaption{The graphical plot-editor.}{From the menu ``Tools
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$\rightarrow$ Edit Plot'' one can select the editor. Using the
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mouse you can select different parts of the current plot (axes,
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lines, the figure background, etc.) and the interface will change
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to allow modifying the properties. Some properties are not offered
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directly but hide behind the \emph{More Properties} button which
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will open the \emph{Property Editor}.}\label{ploteditorfig}
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\end{figure}
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\vspace{1ex} While it is very convenient to edit a figure using the
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GUI (\figref{ploteditorfig}), it is hard to re-create the exact same
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plot later on or transfer the changes done to one figure to
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another. \matlab{} figures consist of several graphical objects:
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\begin{enumerate}
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\item \enterm[figure]{Figure}: This object represents the whole
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drawing area, it holds properties like background color, the size of
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the figure/paper and the placement of the axes on the paper, etc..
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\item \enterm[axes]{Axes}: The coordinate system for plotting the
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data. Defines properties like the scaling of the axes, the labeling,
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line widths, etc..
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\item \enterm[lines]{Lines}: The drawn data lines. Holds properties
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like line width and color, the name associated with the line, marker
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size and many more.
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\item \enterm[annotations]{Annotations}: Annotations like textboxes
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and or arrows that can be used to highlight points or segments.
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\item \enterm[legends]{Legends}: Legends of the data plot. One can
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define the style of the legend, its placement in the plot, etc..
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\end{enumerate}
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Each of these objects offers a number of settings some of them can be
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directly manipulated in the plot editor others are available via the
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property editor.
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\subsection{Avoiding manual editing of figures}
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All properties that can be manipulated with the graphical interfaces
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can also be edited using command line or the respective commands can
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be included in a script or function. Creating the plot from inside a
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script or function has the advantage that one can apply the same
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settings to several figures, re-create the figure automatically when
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the data was changed or the same kind of plot has to be created for a
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number of datasets.
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\begin{important}[Why manual editing should be avoided.]
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On first glance the manual editing of a figure using common tools
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like Corel draw, Illustrator, etc.\,appears some much more
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convenient and less complex. This, however, is not entirely
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true. What if the figure has to be re-drawn or updated? Then the
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editing work starts all over again. Rather, there is a great risk
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associated with this approach. Axes are shifted, fonts have not been
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embedded into the final document, annotations have been copy pasted
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between figures and are not valid. All of these mistakes can be
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found in publications and then require an erratum, which is not
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desirable. Even if it appears more cumbersome in the beginning one
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should always try to create publication-ready figures directly from
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the data analysis tool using scripts or functions to properly
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layout the plot.
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\end{important}
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\subsection{Simple plotting}
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Creating a simple line-plot is rather easy. Assuming there exists a
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varaible \varcode{y} in the \codeterm{Workspace} that contains the
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measurement data it is enough to call \code[plot()]{plot(y)}. At the
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first call of this function a new window will be opened and the data
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will be plotted with as a line plot. If you repeatedly call this
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function the current plot will be replaced unless the the
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\code[hold]{hold on} command was issued before. If it was, the current
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plot is held and a second line will be added to it. Calling
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\code[hold]{hold off} will release the plot and any subsequent
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plotting will replace the previous plot.
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In our previous call to \varcode{plot} we have provided just a single
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variable containing the y-values of the plot. The x-axis will be
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scaled from zero to the number of elements in \varcode{y} the x-values
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are automatically substituted assuming a constant stepsize of 1. This
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automatic scaling is probably not desired and thus, we need to provide
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the missing information ourselves. The respective call will expand to
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\code[plot()]{plot(x, y)}. In axis will be scaled from the minimum in
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\varcode{x} to the maximum of \varcode{x} and by default it will be
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plotted as a line plot with a solid blue line of the with 1pt. A
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second plot that is added to the figure will be plotted in red using
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the same standard settings. The order of the used colors depends on
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the \enterm{colormap} settings which can be adjusted to personal taste
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or need. Table\,\ref{plotlinestyles} shows some predefined values
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that can be chosen for the line style, the marker, or the color. For
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additional options consult the help.
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\begin{table}[tp]
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\titlecaption{Predefined line styles (left), colors (center) and
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marker symbols (right).}{}\label{plotlinestyles}
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\begin{tabular}[t]{lc} \hline
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\textbf{line styles} & \textbf{abbreviation} \erh \\\hline solid
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& '\verb|-|' \erb \\ dashed & '\verb|--|' \\ dotted &
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'\verb|:|' \\ dash-dotted & '\verb|.-|' \\\hline
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\end{tabular}
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\hfill
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\begin{tabular}[t]{lc} \hline
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\textbf{color} & \textbf{abbreviation} \erh \\ \hline red & 'r' \erb
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\\ green & 'g' \\ blue & 'b' \\ cyan & 'c' \\ magenta & 'm'
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\\ yellow & 'y' \\ black & 'k' \\ \hline
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\end{tabular}
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\hfill
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\begin{tabular}[t]{lc} \hline
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\textbf{marker symbols} & \textbf{abbreviation} \erh \\ \hline circle &
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'o' \erb \\ star & '*' \\ plus & '+' \\ cross & 'x' \\ diamond &
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'd' \\ pentagram & 'p' \\ hexagram & 'h' \\ square & 's'
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\\ triangle & '\^{}' \\ inverted triangle & 'v' \\ triangle left
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& '$<$'\\ triangle right & '$>$'\\\hline
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\end{tabular}
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\end{table}
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\subsection{Changing properties of a line plot}
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Die properties of line plots can be changed by passing more arguments
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to the \varcode{plot} function. The command show in
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listing\,\ref{settinglineprops} creates line plot using the dotted
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line style, setting the line width to 1.5pt, a red line color is
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chosen, and star marker symbols will be used. Finally the name of the
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curve is set to 'plot 1' which will be displayed in a legend, if
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chosen.
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\begin{lstlisting}[label=settinglineprops, caption={Setting line properties when calling \varcode{plot}.}]
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x = 0:0.1:2*pi; y = sin(x); plot( x, y, 'color', 'r', 'linestyle',
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':', 'marker', '*', 'linewidth', 1.5, 'displayname', 'plot 1')
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\end{lstlisting}
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\begin{important}[Choosing the right color.]
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Choosing the perfect color goes a little bit beyond personal
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taste. When creating a colored plot you may want to consider the
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following:
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\begin{itemize}
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\item A substantial amount (about 9\%) of the male population can
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not distinguish between red and green.
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\item Can you distinguish the colors in a b/w respectively gray
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scale print?
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\item Color figures in publications often cost extra money.
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\end{itemize}
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\end{important}
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\subsection{Changing the axis properties}
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The first thing a data plot needs are axis labels with a correct
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unit. By calling the functions \code[xlabel]{xlabel('Time [ms]')} and
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\code[ylabel]{ylabel{'Voltage [mV]'}} these can be set. By default the
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axes will be scaled to show the whole data range. The extremes will be
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selected as the closest integer for small values of the next full
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multiple of tens, hundreds, thousands, etc. depending on the maximum
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value. If these defaults do not match our needs the limits of the axes
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can be explicitly set with the functions \code[xlim()]{xlim()} and
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\code[ylim()]{ylim()} functions. To do this, the functions expect a
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single argument that is a vector containing the minimum and maximum
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value. Table\,\ref{plotaxisprops} list some of the commonly adjusted
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properties of an axis. These properties can be set using the
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\code[set()]{set()} function. The \code{set} function expects as a
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first argument a \enterm{handle} of the affected axis. An axis handle
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of the current plot is returned by the \code[gca]{gca} function (gca
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stands for ``get current axis''). The following arguments passed to
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\code{set} are pairs of the property name and the desired value. It is
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possible to set any number of properties using a single call to
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\code{set}. See listing\,\ref{niceplotlisting} (lines 20 and 21) for an
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example.
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\begin{table}[tp]
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\titlecaption{Incomplete list of axis properties.}{For a complete
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list consult the help system or open the property editor when an
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axis is selected (\figref{ploteditorfig}). If there is a default
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value of a property it will be listed first.}\label{plotaxisprops}
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\begin{tabular*}{1\textwidth}{lp{5.8cm}p{5.5cm}} \hline
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\textbf{property} & \textbf{Description} & \textbf{options} \erh
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\\ \hline \code{Box} & Defines whether the axes are drawn an all
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sides. & $\{'on'|'off'\}$ \erb\\
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\code{Color} & Background color of the drawing area, not the whole figure. & Any RGB or CMYK
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values. \\
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\code{FontName} & Name of the font used for labeling. & Installed fonts. \\
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\code{FontSize} & Fontsize used for labels. & any scalar value.\\
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\code{FontUnit} & Unit in which the font size is given. & $\{'points' | 'centimeters' | 'inches',
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...\}$\\ \code{FontWeight} & Bold or normal font. & $\{'normal' | 'bold'\}$\\
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\code{TickDir} & Direction of the axis ticks. & $\{'in' | 'out'\}$\\
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\code{TickLength} & Length of the ticks. & scalar value\\
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\code{X-, Y-, ZDir} & Direction of axis scaling. Zero bottom/left, or not? & $\{'normal' | 'reversed'\}$\\
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\code{X-, Y-, ZGrid} & Defines whether grid line for the respective axes should be plotted? &
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$\{'off'|'on'\}$ \\
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\code{X-, Y-, ZScale} & Linear of logarithmic scaling? & $\{'linear' | 'log'\}$\\
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\code{X-, Y-, ZTick} & Position of the tick marks. & Vector of positions.\\
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\code{X-, Y-, ZTickLabel} & Labels that should be use to label the ticks. & Vector of numbers or a cell-array of strings.\\ \hline
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\end{tabular*}
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\end{table}
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\subsection{Changing the figure properties}
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\begin{table}[tp]
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\titlecaption{Incomple list of available figure properties.}{For a complete reference consult the \matlab{} help or select the property editor while having the figuree background selected
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(\figref{ploteditorfig}).}\label{plotfigureprops}
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\begin{tabular*}{1\textwidth}{lp{6.6cm}p{5.7cm}} \hline
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\textbf{property} & \textbf{description} & \textbf{options}
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\erh \\
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\hline \code{Color} & Background color of the figure, not the drawing area. & Any RGB, CMYK values. \erb
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\\ \code{PaperPosition} & Position of the axes on the paper. & 4-element vector containing the positions of the botom-left and top-right corners. \\
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\code{PaperSize} & Size of the paper. & 2-element vector defining width and height.\\
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\code{PaperUnits} & Unit in which size and postition are given. & $\{'inches' | 'centimeters' |
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'normalized' | 'points'\}$\\
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\code{Visible} & Defines whether the plot should actually be drawn on screen. Useful when plots should not be displayed but directly saved to file. & $\{'on' | 'off'\}$\\ \hline
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\end{tabular*}
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\end{table}
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Like axes also the whole figure has several properties that can be
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adjusted to the current needs. Most notably the paper (figure) size
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and the placement of the axes on the
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paper. Table\,\ref{plotfigureprops} lists commonly used ones. For a
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complete reference check the help. To change the properties, we again
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use the \code{set()} function. The first argument is now a handle to
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the current figure, not the current axis as before. Analogously to the
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\code{gca} command there is a \code{gcf} (``get current figure'')
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command with which the handle can be retrieved.
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The script shown in the listing\,\ref{niceplotlisting} exemplifies
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several features of the plotting system and automatically generates
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and saves figure\,\ref{spikedetectionfig}. With any execution of this
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script exactly the same plot will be created. If we decided to plot a
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different recording, the format will stay exactly the same, just the
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data changes. Of special interest are the lines 22 and 23 which set
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the size of the figure and line 26 which saves the figure in the 'pdf'
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format to file. When calling the function \code{saveas()} the first
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argument is the current figure handle a, the second the file name, and
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the last one defines the output format (box\,\ref{graphicsformatbox}).
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\begin{figure}[t]
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\includegraphics{spike_detection} \titlecaption{Automatically
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created plot.}{This plot has been created using the code in
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listing\,\ref{niceplotlisting}.}\label{spikedetectionfig}
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\end{figure}
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\begin{ibox}[t]{\label{graphicsformatbox}File formats for digital artwork.}
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There are two fundamentally different types of formats for digital artwork:
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\begin{enumerate}
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\item \enterm{Bitmaps}
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\item \enterm{Vector graphics}
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\end{enumerate}
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When using bitmaps a color is given for each pixel of the stored
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figure. Bitmaps do have a fixed resolution (e.g.\,300\,dpi --- dots
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|
per inch), they are very useful for photographs. In the contrary
|
|
vector graphics store descriptions of the graphic in terms of so
|
|
called primitives (lines, circles, polygons, etc.). The main
|
|
advantage of a vector graphic is that it can be scaled without a
|
|
loss of quality.
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|
|
|
\begin{minipage}[t]{0.38\textwidth}
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|
\mbox{}\\[-2ex]
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|
\includegraphics[width=0.85\textwidth]{VectorBitmap.pdf}
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|
\rotatebox{90}{\footnotesize by Darth Stabro at en.wikipedia.org}
|
|
\end{minipage}
|
|
\hfill
|
|
\begin{minipage}[t]{0.5\textwidth}
|
|
Formats supported by \matlab{} \footnote{more information can be
|
|
found in the documentation of \code{saveas()}}:\\[2ex]
|
|
\begin{tabular}{|l|c|l|}
|
|
\hline \textbf{format} & \textbf{type} & \code{saveas()} \textbf{argument}
|
|
\erh \\ \hline pdf & vector & \varcode{'pdf'} \erb \\ eps &
|
|
vector & \varcode{'eps'}, \varcode{'epsc'} \\ SVG & vector &
|
|
\varcode{'svg'} \\ PS & vector & \varcode{'ps'}, \varcode{'psc'}
|
|
\\ jpg & bitmap & \varcode{'jpeg'} \\ tif & bitmap &
|
|
\varcode{'tiff'}, \varcode{'tiffn'} \\ png & bitmap &
|
|
\varcode{'png'} \\ bmp & bitmap & \varcode{'bmp'} \\ \hline
|
|
\end{tabular}
|
|
\end{minipage}
|
|
|
|
It is often meaningful to store of data plots generated by \matlab{}
|
|
using a vector graphics format. When in doubt they can usually be
|
|
easily converted to a bitmap format. The way from a bitmap to a
|
|
vector graphic is not possible without a loss in quality. Storing a
|
|
plot that contains a very large set of graphical elements (e.g.\,a
|
|
raster-plot showing thousands of action potentials) may, on the
|
|
other hand, lead to very large files that can be hard to
|
|
handle. Saving such a plot using a bitmap format may be more
|
|
efficient.
|
|
\end{ibox}
|
|
|
|
\lstinputlisting[caption={Skript zur Erstellung des Plots in
|
|
\figref{spikedetectionfig}.},
|
|
label=niceplotlisting]{automatic_plot.m}
|
|
|
|
Next to the standard line plots there are many more options to display
|
|
scientific data. Mathworks shows various examples and the respective
|
|
code on their website
|
|
\url{http://www.mathworks.de/discovery/gallery.html}.
|
|
|
|
|
|
\section{Conclusion}
|
|
A good plot of scientific data displays the data completely and
|
|
seriously without too many distractions. Misleading or suggestive
|
|
plots as may result from perspective presentations, inappropriate
|
|
scaling of axes of symbols should be avoided.
|
|
|
|
\noindent When combining several line plots within the same figure one should
|
|
consider adapting color \textbf{and} line style (solid, dashed,
|
|
dotted. etc.) to make the distinguishable even in black-and-white
|
|
prints. Combinations of red and green are no good choice since they
|
|
cannot be distinguished by people with red-green blindness.
|
|
|
|
\vspace{2ex}
|
|
Key ingredients for a good data plot:
|
|
\begin{itemize}
|
|
\item Clearness.
|
|
\item Complete labeling.
|
|
\item Plotted lines and curves must be distinguishable.
|
|
\item No suggestive or misleading presentation.
|
|
\item The right balance of line width, font size and size of the figure.
|
|
\item Error bars wherever they are appropriate.
|
|
\end{itemize}
|