Fig. 2
From: A cost-sensitive online learning method for peptide identification
Distribution of identified PSMs by Percolator and OLCS-Ranker. The blue and yellow dots represent target and decoy PSMs, respectively, the cyan dots represent the target PSMs identified by Percolator (98.8% of them have also been identified by OLCS-Ranker), and the red dots represent the target PSMs identified by OLCS-Ranker only. The dotted line represents the linear classifier given by Percolator, and its margin region is defined by the region bounded by the two solid lines. The two-step projection is given as follows. Step 1. Rotate the sample space. Let 〈b,u〉+b0=0 be the discriminant hyperplane trained by Percolator, with feature coefficients b=[b1,⋯,bq], intercept b0, and number of features q. Let P∈Rq×q be orthogonal rotation matrix with w=[1,1,0,⋯,0]∈Rq such that Pw=b. Then the hyperplane after rotation is \(\langle P w,u \rangle + b_{0} = 0 \quad \Leftrightarrow \quad \langle w,P_{}^{T} u \rangle + b_{0} = 0 \quad \Leftrightarrow \quad \langle [1,\ 1], [x_{1},x_{2}] \rangle + b_{0} = 0 \), with \( P_{}^{T} u = [x_{1},\cdots, x_{q}]\). PSM u in sample space Rq is rotated as \( P_{}^{T} u = [x_{1},\cdots, x_{q}]\). Step 2. Project the rotated PSMs to a plane with the first two rotated coordinates x1 and x2 (two axes in the figure). The dotted line 〈[1, 1],[x1,x2]〉+b0=0 is the linear classifier. 〈[1, 1],[x1,x2]〉+b0=+1 and 〈[1, 1],[x1,x2]〉+b0=−1 are the boundaries of the margin of the linear classifier