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 Set0:

1. Set0:
   • Energy fraction in 3x3 cluster within a r=0.7 radius:
     E_3x3/E_0.7
   • Photon-jet pt balance:
     [pt_gamma-pt_jet]/pt_gamma
   • Number of charge tracks within r=0.7 around gamma candidate:
     Ncharge
   • Number of Endcap towersL fired within r=0.7 around gamma candidate:
     NtowBarrel
   • Number of Barrel towers fired within r=0.7 around gamma candidate
     NtowEndcap
2. Set1:
   • All from Set0
   • Shower shape analysis: distance to 80% cut line:
     distance to cut line
3. Set2:
   • All from Set1
   • Energy fraction in E_2x1 and E_2x2 witin E_3x3:
     E_2x1/E_2x2 and E_2x2/E_3x3
4. Set3:
   • All from Set2
   • Energy in post-shower layer under 3x3 tower patch:
     E_post^3x3

The number of strips in SMD u or v planes is required to be greater than 3

Pre-shower sorting (energy in tiles under 3x3 tower patch):

1. pre1=0, pre2=0
2. pre1=0, pre2>0
3. 0 < pre1 < 0.004
4. 0.004 < pre1 < 0.01
5. pre1 < 0.01
6. pre1 >= 0.01

Photon pt and rapidity cuts:

1. pt>7GeV
2. pt>8GeV
3. pt>9GeV
4. pt>10GeV
5. detector eta <1.4 (pt>7GeV)
6. detector eta > 1.4 (pt>7GeV)

Figure 0: photon pt distribution for pre-shower1<0.01
Colour coding:
black pp2006 data, red gamma-jet MC, green QCD MC, blue gamma-jet+QCD

LDA Set0

Figure 1: LDA discriminant with Set0: Data to Monte-Carlo comparison (pt>7GeV cut)

Right plot for each pre-shower condition shows the ratio of pp2006 data to sum of the Monte-Carlo samples
Colour coding:
black pp2006 data, red gamma-jet MC, green QCD MC, blue gamma-jet+QCD

Figure 2: efficiency, purity, rejection vs. LDA discriminant (pt>7GeV cut)

Figure 3: rejection vs. efficiency

Figure 4: purity vs. efficiency

Figure 5: purity vs. rejection

LDA Set1

Figure 6: LDA discriminant with Set1: Data to Monte-Carlo comparison

Figure 7: rejection vs. efficiency

Figure 8: purity vs. efficiency

Figure 9: purity vs. rejection (click link to see the figure)

LDA Set2

Figure 10: rejection vs. efficiency (click link to see the figure)

Figure 11: purity vs. efficiency

Figure 12: purity vs. rejection (click link to see the figure)

LDA Set3

Figure 13: rejection vs. efficiency (click link to see the figure)

Figure 14: purity vs. efficiency

Figure 15: purity vs. rejection (click link to see the figure)