Parallel Coordinate Plots 

Parallel Coordinates (||-coords) were firstly studied by Maurice d'Ocagne in 1885 (mostly for 2-D use in Nomography) and were popularised by Al Inselberg. The first Multidimensional Coordinate System was developed by Al Inselberg in 1977 based on his independent rediscovery in 1959. Since then, ||-coords aim at visualizing high-dimensional geometry and analyze multivariate data. Many people contributed to the development and popularization of ||-coords. Among them, Ed Wegman (1990) applied ||-coords to data exploration, and particularly visualize correlations in datasets. The modern trends for ||-coords are to concentrate relational information in datasets into patterns without any display clutter.

There is a basic point <--> line duality for 2-D representations for lines, planes, curves, surfaces, proximities (A book on Parallel Coordinates by Al Inselberg is being released by Springer in Feb. 2009). Thus a isomorphic mapping between scatterplots and ||-coords based on the basic point-line duality. Because of such geometric property, many 2D patterns in scatterplots that are characterized for visual analytics can be found characterized in ||-coords as well (of course in different patterns). For instance, the characteristic patterns of correlation.

The main challenge for this visualization method is the visual clutter when dealing with large sample data. Many successive visualization researches have been done to tackle this problem in Information Visualization. Many methods turn out to efficiently reduce the clutter and improve the perception. Some recent research results show that complex relations can be visualized as clear patterns without any clutter.  

It has been accepted that ||-coords can support a continuous overview of multi-dimensional data. However, the exaustive combinations can only be obtained by changing the axes order interactively. At the same time, many visual misperception in scatterplots might also exist in parallel coordinates. So far, not much work has been done for the evaluation work.

In our research, we have compared the scatterplots with ||-coords for correlation analysis. A user judgment process is parameterized in a statistic model. Parameters were estimated based on the experimental data collected from 25 subjects. Finally, the judge accuracy and biases were derived from those parameter values. Our results show that with ||-coords, peoples cannot judge more than 5 levels constantly(correlation coefficient from -1 to +1) and an obvious negative bias exists because of the strong peceptual effect from intersection patterns of negative correlations. At the same time with scatterplots, a lot more levels can be distinguished constantly (up to 22 levels when sample dataset is large) and no obvious biases being found.

Even though, ||-coords may still have some merits for cluster detection, especially detecting the continuous changing of clusters among different dimensions. Therefore some medical visualization tools start to take benefit from it. However, my expectation is that we might make comparatively rough estimations or general hypotheses out from Parallel Coordinates but we should not rely on it for a higher quality (high precision) analysis or pattern detection.