# Bagging Machine Learning Algorithms: A Generic Computing Framework Based on Machine-Learning Methods for Regional Rainfall Forecasting in Upstate New York

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## Abstract

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## 1. Introduction

## 2. Related Work

## 3. Methods

#### 3.1. A Generic Framework

**Data Preprocessing:**In the first step of data preprocessing, a rainfall data acquiring and generating process is conducted. We have developed an automatic data acquiring tool to acquire and generate data from the online data source. After data acquiring and generating, raw data are fed further to three parts: cleaning, interpolating, and splitting. There are some empty items and some duplicates existing in the raw datasets. We delete those empty and duplicated items. Data interpolating is used to handle many empty values spread around the entire dataset. We calculate the average value from its chronicle neighbors and interpolate it as the estimated value. As a necessary step for training and testing in machine learning models, we adopt 70/30 ratio in dataset splitting to meet the need. The detailed process is described in Section 3.2.

**Data Normalization:**Two important normalization methods, Z-score and Minmax, are used to evaluate the impact of normalization and non-normalization in the framework. The Z-score value ${z}_{i}$ is calculated in terms of Equation (1):

**Forecasting Engines:**The computing framework provides the options of machine learning models and algorithms for either classification or regression. The technical details of models and algorithms are described in Section 3.3.

**Result Assessment:**Different assessment metrics are used for evaluating classification and regression respectively. In classification, accuracy is the most used to measure the classifier’s performance, which can greatly manifest the capability of predictive models. In regression, the coefficient of determination (${R}^{2}$), Mean Square Error (MSE), Root Mean Square Error (RMSE), and Pearson Correlation Coefficient (Pcc) are adopted to measure the fitness of a regression model to the dataset. After the experimental results are obtained and saved in the local storage, a comparison based on these assessment metrics will be conducted.

#### 3.2. Data Preprocessing

#### 3.3. Models and Algorithms

#### 3.3.1. K-Nearest Neighbors

#### 3.3.2. Support Vector Machine

#### 3.3.3. Deep Neural Network

#### 3.3.4. Wide Neural Network

#### 3.3.5. Wide and Deep Neural Network

#### 3.3.6. Reservoir Computing

#### 3.3.7. Long Short Term Memory

## 4. Results Assessment

#### 4.1. Running and Tuning

#### 4.2. Classification

**KNN:**Six datasets were crossed with the 3 different random seeds for a total of 18 forms of data. These 18 forms were iterated through a KNN Classifier 25 times to find the best n_neighbor value. After 450 iterations the best accuracy was 96.09% which was obtained from the Rochester, Buffalo, Syracuse, and Albany dataset, normalized by Z-score, a random state of 0, and 9 n_neighbors.

**SVM:**There were 72 unique Support Vector Machine Classifiers by training against the cross of 6 premade datasets, 4 kernels, and the same 3 random states as before. The best accuracy for SVM, and ultimately the best accuracy for all classifiers, was 96.22% obtained from the ROC + BUF + SYR + ALB, normalized with Z-score, using 0 as random state and the rbf kernel.

**DNN:**126 DNN Classifiers were tested and used by training against the cross of the 6 premade datasets, 7 different amounts of hidden layers, and the 3 random states used from before. The 7 different hidden layers were: 2, 3, 4, 5, 10, 20, and 30 layers. Each of the hidden layers had the number of inputs equal to the number of features which for the ROC datasets was 9 and for the ROC + BUF + SYR + ALB there were 36 inputs at each hidden layer. The best accuracy for DNN was 94.81% obtained from the ROC dataset only, normalized with Z-score, using 42 as random state and with 10 hidden layers.

**WNN:**There were 18 unique WNN Classifiers by training against the cross of the 6 premade datasets and the 3 random states used from before. The best accuracy for WNN was 95.91% obtained from the ROC + BUF + SYR + ALB, normalized with Z-score, using 0 as random state.

**DWNN:**There were 126 unique DWNN Classifiers by training against the cross of the 6 premade datasets, 7 different amounts of hidden layers for the deep aspect, and the 3 random states used from before. The 7 different hidden layers were: 2, 3, 4, 5, 10, 20, and 30 layers. Each of the hidden layers had the number of inputs equal to the number of features which for the ROC datasets was 9 and for the ROC + BUF + SYR + ALB there were 36 inputs at each hidden layer. The best accuracy for DWNN was 95.74% obtained from the ROC + BUF + SYR + ALB, normalized with Z-score, using None as random state and with 10 hidden layers.

**RCC:**Reservoir Computing Classifier was investigated because, in a previous investigation of daily values, RCC had the highest accuracy. For RCC, six datasets were crossed with the same 3 random states as before and crossed again with 6 different sizes of the reservoir; 50, 100, 200, 400, 600, 1000. The result of these crosses was 108 unique data forms to train with. The best accuracy was 95.81% which was obtained from the Rochester only dataset, normalized by Z-score, a random state of 42, and a reservoir size of 1000.

**LSTM:**There were 12 unique LSTM Classifiers by training against the cross of the 6 premade datasets, and 2 different sequence lengths. Random states were not used for LSTM as it depends on chronologically consecutive rows of data. The two sequence lengths considered were 3 previous rows of data and 7 previous rows of data. The best accuracy for LSTM was 94.82% obtained from the ROC + BUF + SYR + ALB, normalized with Minmax, using a sequence length of 3.

**Overall:**Both SVM and KNN classifiers performed the best. Figure 9A,D show all of the best accuracies for each of the classification methods used in the mixed and ROC datasets. The plotting for this ranking was zoomed into the accuracy range of 94.5–96.5% to better show the differences between the methods. A further examination of the ranking with the normalization data is shown in Figure 9C,F. In almost every case except for LSTM, the best normalization method was Z-score. It can also be seen that in many cases the non-normalized version of the data performed measurably worse than its Z-score counterpart. The groups of (B,E) and (C,F) are derived from the same results. However, Figure 9B,E show another way to highlight the performance in regards to normalization.

#### 4.3. Regression

#### 4.3.1. KNN Regressor

#### 4.3.2. Linear Regressor

#### 4.3.3. SVM Regressor

#### 4.3.4. DNN Regressor

#### 4.3.5. WNN Regressor

#### 4.3.6. DWNN Regressor

#### 4.3.7. LSTM Regressor

#### 4.3.8. LSTM Bi-Direction

#### 4.3.9. GRU Regressor

#### 4.3.10. Overall Regression Results

#### 4.4. Running Time

## 5. Discussion and Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Weather stations in Upstate New York. The blue circle indicates that ROC dataset is from Rochester station and the red circles are Buffalo’s two stations, Syracuse’s two stations, and Albany’s two stations. Both the blue and red circles contribute to the mixed dataset.

**Figure 3.**The feature matrix in ROC dataset. Notation: tmpf, air temperature in Fahrenheit typically at 2 m; dwpf, dew point temperature in Fahrenheit typically at 2 m; relh, relative humidity in %; drct, wind direction in degrees from north; sknt, wind speed in knots; alti, pressure altimeter in inches; mslp, sea level pressure in millibar; vsby, visibility in miles.

**Figure 6.**An illustration of reservoir computing [63].

**Figure 9.**Classification performance. (

**A**–

**C**): Classification ranking in the Mixed dataset. (

**D**–

**F**): Classification ranking in the ROC dataset. (

**A**,

**D**): The best performance ranking mixing the normalization. (

**B**,

**E**): Accuracy in regard to normalization. (

**C**,

**F**): An overall ranking among models and normalizations.

**Figure 11.**The number of indexed articles for KNN and Neural Network used in rainfall forecasting from Google Scholar as of 20 Junuary 2021.

Dataset | Norm. | Random | Neighbor | ${\mathit{R}}^{2}$ | MSE | RMSE | Pcc |
---|---|---|---|---|---|---|---|

Mixed | Z-score | None | 57 | 0.181718 | 0.005819 | 0.076282 | 0.428720 |

Mixed | Z-score | 42 | 37 | 0.179490 | 0.009653 | 0.098247 | 0.445571 |

ROC | Z-score | None | 53 | 0.151876 | 0.006031 | 0.077660 | 0.392005 |

ROC | Z-score | 42 | 44 | 0.136763 | 0.010155 | 0.100773 | 0.376142 |

Dataset | Norm. | Random | ${\mathit{R}}^{2}$ | MSE | RMSE | Pcc |
---|---|---|---|---|---|---|

Mixed | None | None | 0.173853 | 0.005875 | 0.076648 | 0.418374 |

Mixed | Z-score | None | 0.173853 | 0.005875 | 0.076648 | 0.418374 |

ROC | Z-score | None | 0.152275 | 0.006028 | 0.077642 | 0.390999 |

ROC | None | None | 0.152275 | 0.006028 | 0.077642 | 0.390999 |

Dataset | Norm. | Kernel | Random | ${\mathit{R}}^{2}$ | MSE | RMSE | Pcc |
---|---|---|---|---|---|---|---|

Mixed | Z-score | rbf | 42 | 0.036320 | 0.011337 | 0.106474 | 0.380177 |

Mixed | Minmax | linear | None | invalid | 0.009003 | 0.094882 | 0.408546 |

ROC | None | sigmoid | 42 | invalid | 0.012855 | 0.113380 | 0.168737 |

ROC | Minmax | poly | None | invalid | 0.009645 | 0.098208 | 0.407548 |

Dataset | Norm. | Layers | Random | ${\mathit{R}}^{2}$ | MSE | RMSE | Pcc |
---|---|---|---|---|---|---|---|

Mixed | Minmax | 3 | None | 0.021768 | 0.006956 | 0.083405 | 0.215921 |

Mixed | Z-score | 30 | 42 | Invalid | 0.011765 | 0.108465 | 0.290540 |

ROC | Minmax | 4 | 42 | 0.036257 | 0.011338 | 0.106478 | 0.240040 |

ROC | Minmax | 2 | None | 0.033795 | 0.006871 | 0.082891 | 0.214836 |

Dataset | Norm. | Random | ${\mathit{R}}^{2}$ | MSE | RMSE | Pcc |
---|---|---|---|---|---|---|

Mixed | Minmax | 0 | 0.121694 | 0.008829 | 0.093963 | 0.354666 |

Mixed | Minmax | None | 0.099783 | 0.006402 | 0.080010 | 0.415068 |

ROC | Z-score | None | 0.148975 | 0.006052 | 0.077793 | 0.387437 |

ROC | Minmax | None | 0.139087 | 0.006122 | 0.078244 | 0.376594 |

Dataset | Norm. | Layers | Random | ${\mathit{R}}^{2}$ | MSE | RMSE | Pcc |
---|---|---|---|---|---|---|---|

Mixed | Z-score | 20 | 42 | 0.181974 | 0.009623 | 0.098098 | 0.426754 |

Mixed | Z-score | 30 | 42 | 0.181682 | 0.009627 | 0.098116 | 0.428402 |

ROC | Z-score | 20 | None | 0.156510 | 0.005998 | 0.077448 | 0.396452 |

ROC | Z-score | 10 | None | 0.155902 | 0.006003 | 0.077476 | 0.395922 |

Dataset | Norm. | Sequence | ${\mathit{R}}^{2}$ | MSE | RMSE | Pcc |
---|---|---|---|---|---|---|

Mixed | Minmax | 12 | 0.093923 | 0.006489 | 0.080555 | 0.310783 |

Mixed | None | 12 | 0.072728 | 0.006641 | 0.081492 | 0.272889 |

ROC | None | 5 | 0.099439 | 0.006424 | 0.080149 | 0.318826 |

ROC | None | 48 | 0.089427 | 0.006539 | 0.080865 | 0.307474 |

Dataset | Norm. | Sequence | ${\mathit{R}}^{2}$ | MSE | RMSE | Pcc |
---|---|---|---|---|---|---|

Mixed | Minmax | 3 | 0.067292 | 0.006645 | 0.081519 | 0.295810 |

Mixed | Minmax | 7 | 0.061097 | 0.006706 | 0.081889 | 0.285112 |

ROC | Minmax | 12 | 0.092928 | 0.006496 | 0.080599 | 0.320603 |

ROC | None | 12 | 0.085119 | 0.006552 | 0.080945 | 0.311874 |

Dataset | Norm. | Sequence | ${\mathit{R}}^{2}$ | MSE | RMSE | Pcc |
---|---|---|---|---|---|---|

Mixed | Minmax | 36 | 0.073474 | 0.006608 | 0.081291 | 0.287391 |

Mixed | Minmax | 9 | 0.073345 | 0.006626 | 0.081400 | 0.293189 |

ROC | Z-score | 48 | 0.091028 | 0.006528 | 0.080794 | 0.310435 |

ROC | Z-score | 3 | 0.088520 | 0.006494 | 0.080586 | 0.323445 |

Model | Norm. | Random | Param. | ${\mathit{R}}^{2}$ | MSE | RMSE | Pcc |
---|---|---|---|---|---|---|---|

DWNNr | Z-score | 42 | 20 layers | 0.181974 | 0.009623 | 0.098098 | 0.426754 |

KNN | Z-score | None | 57 nodes | 0.181718 | 0.005819 | 0.076282 | 0.428720 |

Linear | None | None | N/A | 0.173853 | 0.005875 | 0.076648 | 0.418374 |

WNNr | Minmax | 0 | N/A | 0.121694 | 0.008829 | 0.093963 | 0.354666 |

LSTM | Minmax | N/A | 12 units | 0.093923 | 0.006489 | 0.080555 | 0.310783 |

GRU | Minmax | N/A | 36 units | 0.073474 | 0.006608 | 0.081291 | 0.287391 |

Bidirect | Minmax | N/A | 3 units | 0.067292 | 0.006645 | 0.081519 | 0.29581 |

SVR | Z-score | 42 | Rbf | 0.03632 | 0.011337 | 0.106474 | 0.380177 |

DNNr | Minmax | None | 3 layers | 0.021768 | 0.006956 | 0.083405 | 0.215921 |

Model | Norm. | Random | Param. | ${\mathit{R}}^{2}$ | MSE | RMSE | Pcc |
---|---|---|---|---|---|---|---|

DWNNr | Z-score | None | 20 layers | 0.156510 | 0.005998 | 0.077448 | 0.396452 |

Linear | None | None | N/A | 0.152275 | 0.006028 | 0.077642 | 0.390999 |

KNN | Z-score | None | 53 nodes | 0.151876 | 0.006031 | 0.077661 | 0.392005 |

WNNr | Z-score | None | N/A | 0.148975 | 0.006052 | 0.077793 | 0.387437 |

LSTM | None | N/A | 5 units | 0.099439 | 0.006424 | 0.080149 | 0.318826 |

Bidirect | Minmax | N/A | 12 units | 0.092928 | 0.006496 | 0.080599 | 0.320603 |

GRU | Z-score | N/A | 48 units | 0.091028 | 0.006528 | 0.080794 | 0.310435 |

DNNr | Minmax | 42 | 4 layers | 0.036257 | 0.011338 | 0.106478 | 0.24004 |

SVR | None | 42 | Sigmoid | invalid | 0.012855 | 0.11338 | 0.168737 |

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**MDPI and ACS Style**

Yu, N.; Haskins, T. Bagging Machine Learning Algorithms: A Generic Computing Framework Based on Machine-Learning Methods for Regional Rainfall Forecasting in Upstate New York. *Informatics* **2021**, *8*, 47.
https://doi.org/10.3390/informatics8030047

**AMA Style**

Yu N, Haskins T. Bagging Machine Learning Algorithms: A Generic Computing Framework Based on Machine-Learning Methods for Regional Rainfall Forecasting in Upstate New York. *Informatics*. 2021; 8(3):47.
https://doi.org/10.3390/informatics8030047

**Chicago/Turabian Style**

Yu, Ning, and Timothy Haskins. 2021. "Bagging Machine Learning Algorithms: A Generic Computing Framework Based on Machine-Learning Methods for Regional Rainfall Forecasting in Upstate New York" *Informatics* 8, no. 3: 47.
https://doi.org/10.3390/informatics8030047