# Composition Classification of Ultra-High Energy Cosmic Rays

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## Abstract

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## 1. Introduction

**C**Osmic

**R**ay

**SI**mulations for

**KA**scade) simulator [8,9]. Five different types of particles have been considered: Photons, Protons, Helium, Nitrogen, and Iron. Four different machine learning classifiers have been trained and analyzed under Python implementation, including XGBoost, K-NN, Deep Neural Networks and Support Vector Machines. This comparison allows comparing these alternatives, both from the performance and the computational cost point of view, allowing for us to assess the best alternative for the given problem. Moreover, a modification of the Markov Blanket Mutual Information Feature Selection (MBFS) algorithm [10,11,12] adapted for classification has been applied in order to identify the relevance of the features involved. The importance of this type of ML techniques application comparative analysis is corroborated in the extent recent literature for other problems from a wide range of fields [13,14,15,16].

## 2. Data Description

**Q**uark

**G**luon

**S**tring model with

**Jet**s) [18], SIBYLL [19], and EPOS(LHC) (

**E**nergy conserving quantum mechanical multi-scattering approach, based on

**P**artons,

**O**ff-shell remnants and

**S**plitting parton ladders) [20] are options that can be used to describe high energy collisions. At lower energies, interactions can be used the models GHEISHA (

**G**amma

**H**adron

**E**lectron

**I**nteraction

**SH**ower) [21], the FLUKA [22], or the microscopic URQMD (

**U**ltra-

**R**elativistic

**Q**uantum

**M**olecular

**D**ynamics) [23]. For electromagnetic (EM) interactions, a version of the code EGS4 (

**E**lectron

**G**amma

**S**hower) [24] or the analytical NKG (

**N**ishimura-

**K**amata-

**G**reisen) [2] formulas may be used. For this work. we are using, at higher energy, the model QGSJetII-04, combined with FLUKA2011.2c for lower energies, and EGS4 for EM interactions.

- $NALLParticlesTotal$: total number of particles generated by the event at the ground level.
- $MUTotal$: total number of muons, at the ground level.
- $ELTotal$: total number of electromagnetic particles, at the ground level.
- $Zenith$: zenith angle of the primary particle [degrees].
- $Energy$: primary particle energy [GeV].

## 3. Methods

#### 3.1. Classification Methods

#### 3.1.1. Artificial Neural Network

- Number of layers: configurations containing from 2 up to 7 hidden layers were considered. ReLu units were taken for the these [27]. For the output layer, softmax units (one per class) were used.
- Number of neurons: configurations containing from five up to 50 neurons per layer were considered for the hidden layers.
- Constant weight initialization to 0.025 (for the sake of reproducibility).
- Optimisation algorithm: Adam [28] with default parameters (after analysing the behaviour of higher and lower learning rate and beta values) and a maximum of 500 epochs. Batch size was set fixed to 256.
- Loss function: crossentropy for classification [29].

#### 3.1.2. XGBoost

#### 3.1.3. Support Vector Machines

#### 3.1.4. K-Nearest Neighbors

#### 3.1.5. Classifiers Comparison

#### 3.2. Markov Blanket Feature Selection (MBFS) Algorithm

## 4. Results

#### 4.1. Classification

- 5 features: $NALLParticles$, $MUTotal$, $ELTotal$, $Zenith$, $Energy$
- 3 features: $MUTotal$, $Zenith$, $Energy$

#### 4.2. Feature Ranking

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Confusion matrix for the first test set returned by XGBoost classification with five features.

**Figure 2.**Confusion matrix for the first test set returned by XGBoost classification with three features.

**Figure 3.**Evolution of the test performance on the problem according to the ranking returned by the Markov Blanket Mutual Information Feature Selection (MBFS) algorithm using XGBoost. Hyperparameters of XGBoost were optimized for each feature subset size combination.

**Table 1.**Classification report obtained by the classification approach with five and three features over test dataset.

5 Features | 3 Features | |||||
---|---|---|---|---|---|---|

trn. Time (s.) | Accuracy | f1-Score | trn. Time (s.) | Accuracy | f1-Score | |

ANN | 48,715 | 0.91 (0.015) | 0.92 (0.012) | 23,957 | 0.76 (0.14) | 0.77 (0.017) |

XGBoost | 909 | 0.97 (0.002) | 0.97 (0.002) | 843 | 0.87 (0.002) | 0.87 (0.002) |

SVMs | 9536 | 0.94 (0.003) | 0.94 (0.003) | 10,677 | 0.83 (0.004) | 0.83 (0.004) |

KNN | 3.59 | 0.78 (0.003) | 0.79 (0.003) | 2.75 | 0.62 (0.006) | 0.63(0.005) |

Classifier | 5 Features | 3 Features |
---|---|---|

ANN | 2 layers, $n.u.=[39,31]$ | 2 layers, $n.u.=[17,18]$ |

XGBoost | $max\phantom{\rule{4pt}{0ex}}depth=5,eta=0.85$ | $max\phantom{\rule{4pt}{0ex}}depth=5,eta=0.55$ |

SVMs | $\sigma =512,\gamma =0.5$ | $\sigma =512,\gamma =0.5$ |

KNN | $k=1$ | $k=1$ |

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**MDPI and ACS Style**

Herrera, L.J.; Todero Peixoto, C.J.; Baños, O.; Carceller, J.M.; Carrillo, F.; Guillén, A. Composition Classification of Ultra-High Energy Cosmic Rays. *Entropy* **2020**, *22*, 998.
https://doi.org/10.3390/e22090998

**AMA Style**

Herrera LJ, Todero Peixoto CJ, Baños O, Carceller JM, Carrillo F, Guillén A. Composition Classification of Ultra-High Energy Cosmic Rays. *Entropy*. 2020; 22(9):998.
https://doi.org/10.3390/e22090998

**Chicago/Turabian Style**

Herrera, Luis Javier, Carlos José Todero Peixoto, Oresti Baños, Juan Miguel Carceller, Francisco Carrillo, and Alberto Guillén. 2020. "Composition Classification of Ultra-High Energy Cosmic Rays" *Entropy* 22, no. 9: 998.
https://doi.org/10.3390/e22090998