Cut optimization with Fisher's LDA classifier

ROOT implementation for LDA:

• Fisher's Linear Discriminant Analysis (LDA)

Application for cuts optimization in the gamma-jet analysis

LDA configuration: default

LDA input parameters:

1. Energy fraction in 3x3 cluster within a r=0.7 radius: r3x3
2. Photon-jet pt balance: [pt_gamma-pt_jet]/pt_gamma
3. Number of charge tracks within r=0.7 around gamma candidate
4. Number of Endcap towers fired within r=0.7 around gamma candidate
5. Number of Barrel towers fired within r=0.7 around gamma candidate

Figure 1: LDA discriminant (no SMD involved in training)

Figure 2: LDA (no SMD): Efficiency, rejection, purity vs. discriminant

Figure 3: SMD energy in 25 central strips (LDA-dsicriminant>0, no pre-shower1 cut)

Figure 4: SMD energy in 25 central strips (LDA-dsicriminant>0, pre-shower1 < 10MeV)

Figure 5: Maximum residual (LDA-dsicriminant>0, no pre-shower1 cut)

Figure 6: Maximum residual (LDA-dsicriminant>0, pre-shower1 < 10MeV)

LDA+ SMD analysis

SMD info added:
a) energy in 5 central srtips
b) maximum sided residual

Figure 7:LDA with SMD: Efficiency, rejection, purity vs. LDA discriminant

Figure 8: LDA discriminant with SMD

Figure 9: Maximum residual (SMD LDA-dsicriminant>0, pre-shower1 < 10MeV)

LDA with and without SMD comparison

Figure 10:LDA (no SMD): Efficiency, rejection, purity plots

Figure 11: LDA with SMD: Efficiency, rejection, purity plots