By Donald E. Knuth
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Additional resources for Companion to the Papers of Donald Knuth
5 OBSERVATIONS AS OBJECTS Parallel coordinate plots and Andrew’s curves represent observations as 1D curves. Chernoff faces represent observations with schematic human faces. We mention also other possibilities for visualizing data by representing the data points as objects. These methods work typically for small data sets. Also, the methods are usually sensitive for the ordering of the variables. 1 Parallel Coordinate Plots Parallel coordinate plots may be used to visualize a multivariate point cloud by looking at the one-dimensional projections of the data to the coordinate axes, which are drawn parallel to each other.
Subsetting means that one chooses subsets of the data and visualizes only one subset at a time. Subsetting is a concept that has been used particularly in earth sciences to describe the process of retrieving just the parts of large files that may arise, for example, when collecting data with earth-observing satellites. The classical subsetting techniques include the following: 1. The subset chosen randomly. 2. The subset consists only of the central data points, with outliers removed by taking all inside a box or inside a sphere.
1 shows three scatter plots of data of three different sizes, when the data is simulated from the same density. The sample sizes are n = 30, n = 300, and n = 10,000. 7. When the sample size is small, then the point cloud is too sparse to reveal the three modes of the density. When the sample size is large, then the scatter plot is mostly black, so the visuality of density of the points in different regions is obscured. When the sample size is moderate, a more accurate impression of the distribution of the probability mass is possible.