Projection score gives you the best visualization yet

Visualization and especially principal component analysis (PCA) are easy to use and powerful tools to detect structure and patterns in multidimensional data such as gene expression, DNA methylation and proteomics data. These methods do not, however, provide any direct guidance regarding the statistical validity of the patterns identified.

In version 3.0 of Qlucore Omics Explorer, a new feature called Projection Score has been introduced. A brief description is that Projection Score gives the user a measurement of how plausible the detected patterns are compared to was completely random data.

The Projection Score is enormously useful when doing data exploration, as it gives you direct feedback on which variance filter settings are best for a given data set, and with which setting the PCA plot provides the most information.

To compute the projection score for a given data set, first start by computing the fraction of the total variance that is captured by the first three principal components. Then, an estimate is taken for the expected value of the same entity for completely random data. The projection score is defined as the difference between the square root of the observed quantity and the square root of the expected value for random data.
Therefore, a high value projection score means that the PCA representation of the observed representation contains much more information (variance) than the corresponding representation of a random data set of the same size, which suggests that there are non-random, potentially interesting structures present in the representation. 

The above calculation is done automatically in Qlucore Omics Explorer and the result is presented in a box next to the variance slider. The box will change color based on a rule of thumb given the user a visual feedback on how good the visualization is. The colors are green (good), yellow (medium) and red (bad).
To learn more about projection score you can read in -

BMC Bioinformatics (2011), article by Charlotte Soneson and Magnus Fontes