Applications of the generalized norm solver

Results of the line-fitting problem

The results of solving this problem with the least-squares, hybrid, and Huber norms are shown in Figure 1. We can see that the fitted line in the L2 norm deviates from the true line due to the presence of spiked data, whereas for the Huber solver and the hybrid solver, the fitted line correctly overlaps the true line. We conclude that our trivial line-fitting example functions properly when using the $L_1$-type hybrid and Huber norms.

fit-l2,fit-hybrid,fit-huber
Figure 1. Line fitting using the generalized norm solver: (a)$L_2$ fitting, (b) hybrid norm fitting, (c) Huber norm fitting. Notice that the $L_2$ fit-line does not match the actual data trend - this illustrates the susceptibility of least-squares minimization to strong outliers (spikes), while the other norms are totally unaffected by these data points. [ER]

Applications of the generalized norm solver