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 (includes SMD inromation of the distance from max sided residual plot):

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
6. Distance to 80% cut line (see this link for more details)

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

Figure 1: SMD energy in 25 central strips sorted by pre-shower energy

1. Upper left: pre1=0, pre2=0
2. Upper right: pre1=0, pre2>0
3. Lower left: 0<4MeV
4. Lower right: 4<10MeV

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
(combined plot for all pre-shoer bins can be found here)

Figure 2: SMD energy in 5 central strips sorted by pre-shower energy
(combined plot can be found here)

Figure 3: Maximum residual sorted by pre-shower energy
(combined plot can be found here)

Figure 4: LDA discriminant. Note: LDA algo trained for each pre-shower condition independently

Figure 5: LDA: Efficiency, rejection, purity vs. discriminant, sorted by pre-shower energy

Figure 6: LDA: Efficiency, rejection, purity plots sorted by pre-shower energy
For each pre-shower condition each plot has 4 figures:

1. u-left: rejection vs. efficiency
2. u-right: purity vs. efficiency
3. l-left: purity vs. rejection
4. l-right: significance (signal/sqrt{signal+background}) vs. efficiency