# Optimal Data Reduction of Training Data in Machine Learning-Based Modelling: A Multidimensional Bin Packing Approach

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## Abstract

**:**

## 1. Introduction

## 2. Related Work

## 3. Methodology

#### 3.1. Multidimensional Bin Reduction

#### 3.2. Data Set Test

## 4. Numerical Study

#### 4.1. Data Set

#### 4.2. Feasibility Test

#### 4.3. Neural Network

#### 4.4. Training Set Generation Using MdBR

#### 4.5. Training Results

#### 4.6. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Plotted results of the feasibility test using the data of May 2017. The MdBs are sorted by prevalence.

**Figure 4.**Size of the reduced training sets with a different number of bins per feature. The number of different MdBs per data set is equal to the number of samples in the training set.

**Figure 5.**Distribution of the normalized output power in the training set after reducing with the respective number of bins per feature.

**Figure 6.**Comparison of the model average accuracy (

**a**) and training time (

**b**) using 10 to 80 bins per feature for reducing the training data set. Each model has been trained 20 times.

**Figure 7.**Comparison of the model average accuracy using 3 to 20 bins per feature for reducing the training data set. The number of different MdBs per data set is equal to the samples. Each model has been trained 20 times.

Features/Channels | Abbreviation |
---|---|

AC real power | PwrMtrP_kW |

Outdoor ambient temperature | SEWSAmbientTemp_C |

Module Temperature | SEWSModuleTemp_C |

Plane of array irradiance | SEWSPOAIrrad_Wm2 |

Inverter heatsink temperature | InvTempHeatsink_C |

Inverter operating status | InvOpState |

Artifact | Value |
---|---|

Period | May 2017 |

Number of samples | 2,671,113 |

Number of bins per feature | 50 |

Number of possible MdB | $1.56\times {10}^{10}$ |

Number of found MdB | 108,733 |

Max. sample in one MdB | 13,545 |

Artifact | Value |
---|---|

Number of training samples | 83,508,520 |

NRMSE | $3.63\pm 0.12\%$ |

Training Time | 4 h:24 m ± 1 h:42 m |

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**MDPI and ACS Style**

Wibbeke, J.; Teimourzadeh Baboli, P.; Rohjans, S.
Optimal Data Reduction of Training Data in Machine Learning-Based Modelling: A Multidimensional Bin Packing Approach. *Energies* **2022**, *15*, 3092.
https://doi.org/10.3390/en15093092

**AMA Style**

Wibbeke J, Teimourzadeh Baboli P, Rohjans S.
Optimal Data Reduction of Training Data in Machine Learning-Based Modelling: A Multidimensional Bin Packing Approach. *Energies*. 2022; 15(9):3092.
https://doi.org/10.3390/en15093092

**Chicago/Turabian Style**

Wibbeke, Jelke, Payam Teimourzadeh Baboli, and Sebastian Rohjans.
2022. "Optimal Data Reduction of Training Data in Machine Learning-Based Modelling: A Multidimensional Bin Packing Approach" *Energies* 15, no. 9: 3092.
https://doi.org/10.3390/en15093092