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Figure 2 | BMC Bioinformatics

Figure 2

From: Knowledge driven decomposition of tumor expression profiles

Figure 2

Visualization of the Lasso shrinkage. Example showing how the shrinkage of weights by the Lasso regularization is visualized. Let's assume we have a hypothetical case with four components, labeled C1 to C4. In subplot a on the left, we show an example of the weights in w as a function of λ (in analogy to [20]). In the top row of plot a we indicate the total number of non-zero weights. Then, subplot b on the right shows the table that is used to depict the order in which the weights, w, turn non-zero under Lasso regularization. The two rows at the top and the two columns to the left indicate whether a particular weight is non-zero (1, yellow cell shading), or zero (0, white cell shading). Numbers in the table (gray shaded area) indicate the combined number of non-zero weights in w, that is, all 16 (i.e. 24) states are shown (possible combinations with 0 up to 4 weights being non-zero). There are 24 (i.e. 4!) possible unique paths to go from 0 to 4 non-zero weights. These paths can be traced in the plot assuming the left/right edges and top/bottom edges of the table are connected. We start with λ = inf, and slowly decrease λ. For an infinite λ the resulting w vector will be all-zero (bottom right in the table shown in subplot b). At a slightly lower λ one of the four weights will be the first to become non-zero. By lowering λ to zero, up to four weights will be non-zero. In subplot a on the left, the weights turn non-zero in the following order: C4, C1, C3 and lastly C2. The corresponding trajectory is depicted in subplot b on the right using the red line.

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