Multilayer perceptron (MLP) is feedforward neural networks

trained with the standard backpropagation algorithm.

They are supervised networks so they require a desired response to be trained.

They learn how to transform input data into a desired response,

so they are widely used for pattern classification.

With one or two hidden layers, they can approximate virtually any input-output map.

They have been shown to approximate the performance of optimal statistical classifiers in difficult problems.

TMultiLayerPerceptron class in ROOT

mlpHiggs.C example

Netwrok structure:

r3x3, (pt_gamma-pt_jet)/pt_gamma, nCharge, bBtow, eTow2x1: 10 hidden layers: one output later

**Figure 1:**

- Upper left: Learning curve (error vs. number of training)

Learing method is: Steepest descent with fixed step size (batch learning) - Upper right: Differences (how important are initial variableles for signal/background separation)
- Lower left: Network structure (ling thinkness corresponds to relative weight value)
- Lower right: Network output. Red - MC gamma-jets, blue QCD background, black pp2006 data

**Figure 2:** Input parameters vs. network output

Row: 1: MC QCD, 2: gamma-jet, 3 pp2006 data

Vertical axis: r3x3, (pt_gamma-pt_jet)/pt_gamma, nCharge, bBtow, eTow2x1

Horisontal axis: network output

ROOT implementation for LDA and MLP:

- Fisher's Linear Discriminant Analysis (LDA)
- Multi-Layer Perceptron (MLP) [feed-forward neural network]

LDA configuration: default

MLP configuration:

- 2 hidden layers [N+1:N neural network configuration, N is number of input parameters]
- Learning method: stochastic minimization (1000 learning cycles)

Input parameters (same for both LDA and MLP):

- 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

**Figure 1:** Signal efficiency and purity, background rejection (left),

and significance: Sig/sqrt[Sig+Bg] (right) vs. LDA (upper plots) and MLP (lower plots) classifier discriminants

**Figure 2:**

- Upper left: Rejection vs. efficiency
- Upper right: Purity vs. efficiency
- Lower left: Purity vs. Rejection
- Lower right: Significance vs. efficiency

**Figure 3:** Data to Monte-Carlo comparison for LDA (upper plots) and MLP (lower plots)

Good (within ~ 10%) match between data nad Monte-Carlo

a) up to 0.8 for LDA discriminant, and b) up to -0.7 for MLP.

**Figure 4:** Data to Monte-Carlo comparison for input parameters

from left to right

1) pt_gamma 2) pt_jet 3) r3x3 4) gamma-jet pt balance 5) N_ch[gamma] 6) N_eTow[gamma] 7) N_bTow[gamma]

Colour coding: black pp2006 data, red gamma-jet MC, green QCD MC, blue gamma-jet+QCD

**Figure 5:** Data to Monte-Carlo comparison:

correlations between input variables (in the same order as in Fig. 4)

and LDA classifier discriminant (horizontal axis).

1st raw: QCD MC; 2nd: gamma-jet MC; 3rd: pp2006 data; 4th: QCD+gamma-jet MC

Endcap photon-jet update at the STAR Collaboration meeting