Supplementary Figure 1: Illustrative example of support vector regression

A simple two-dimensional dataset analyzed with linear ν-SVR, with results shown for two values of ν (note that both panels show the same data points). As detailed in Online Methods, linear SVR identifies a hyperplane (which, in this two-dimensional example, is a line) that fits as many data points as possible (given its objective function) within a constant distance, ɛ (open circles). Data points lying outside of this ‘ɛ-tube’ are termed ‘support vectors’ (red circles), and are penalized according to their distance from the ɛ-tube by linear slack variables (ξ_i). Importantly, the support vectors alone are sufficient to completely specify the linear function, and provide a sparse solution to the regression that reduces the chance of overfitting. In ν-SVR, the ν parameter determines both the lower bound of support vectors and upper bound of training errors. As such, higher values of ν result in a smaller ɛ-tube and a greater number of support vectors (right panel). For CIBERSORT, the support vectors represent genes selected from the signature matrix for analysis of a given mixture sample, and the orientation of the regression hyperplane determines the estimated cell type proportions in the mixture. For further details, including the key technical advantages of ν-SVR for GEP deconvolution, see Online Methods.

Reference (Main Text)

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