Multidimensional Data using Parallel Coordinate Plots

    Last week I stumbled upon one of my research assignments using Parallel coordinate plots(PCP) which I did last year. When the data has two dimensions it can be easily plotted using a bar chat or a scattered plot. But as the dimensions increase it is difficult to plot them as the chart gets distorted. I found this tool called Tibco spotfire which readily allows to explore PCP data and many more options. Lets see them below.

    For example: there are 5 cars and each car has 5 features to be compared then we can use Bar charts. Radar charts can also be used to plot the spatial area between these dimensions. 

    Now consider that there are 1000's of car and each car has many attributes. Radar charts cannot be used here as the visualization would be difficult. We can use parallel coordinate plots. Parallel coordinate plots are used for plotting multi variate numerical data. Here each feature is represented by a line between two axis instead of a dot. 

    Mapping Scattered plot on to a PCP line. The plot below shows how a 2 dimensional attribute can be replicated onto a PCP line.

    Thus, 2 dimensional data can be represented on a parallel co-ordinate plot. As the dimensions increase the number of parallel axis can be increased. In our example as the features of the car increase an additional vertical axis can be added on the plot.

    One question which should be raised here is how can we compare data which are not similar. For example how to compare MPG and Cylinders. If we plot them normally it would be hard to notice the differences as the MPG will be always higher.  

   Normalization can be used to show each data as a percentage of the total. So, when we are comparing the MPG and Cylinders data we are comparing them as a percentage. Tibco Spotfire has all these built in and the data are already normalized when we upload data in it.

     I have used Tibco Spotfire to analyze this data. (If you have not yet tried it, its a great visualization tool).

PCP plot for Cars and the corresponding attributes

Vertical axis represents the attributes of the car
Color represents the country of the car manufacturer.
The table layout at the bottom shows all the records readily available for export in excel format.

Here the lines represent each car.

PCP  - Each car data can be selected

    Each car when selected gives the attributes of the corresponding car which can be compared. Here we see that the Triumph R7 coupe car has more MPG compared to other attributes.

    Filters can be added to limit the data set and visualize the data thereby, a single parallel coordinate plot was able to show the data set of 160000 cars.

PCP - Filtered the dataset to find out all the Coupe cars

    For example if we want to find all the Coupe type cars from the dataset and want to compare them. Just use the filter options on the right. Further, the techniques of Brushing can be applied to select a certain category of cars.

    Selection of the dataset can be done by using Probing or Area Brush techniques, Probing is simply selecting any car in the dataset. Area Brush technique is used to select a particular area on the plot and highlight a set of records to see the comparison.

PCP - Select a particular area on the plot

Here is a short video of how it works.

    Thus, parallel coordinate plots enhance the ability of visualizing multi dimensional data. And Tibco spotfire is a great tool to easily achieve this. Also for reference to the research paper on PCP and further reading, follow this link. (https://ieeexplore.ieee.org/document/7192696/)