# 2009.04.28 LDA plus SMD analysis with pre-shower sorting

### Cut optimization with Fisher's LDA classifier

ROOT implementation for 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):

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

- Upper left: pre1=0, pre2=0
- Upper right: pre1=0, pre2>0
- Lower left: 0<4MeV
- 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:

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

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