# Modeling and Forecasting Gender-Based Violence through Machine Learning Techniques

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## Abstract

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## 1. Introduction

## 2. Related Works

## 3. Feature Selection and Forecasting Time Series

#### 3.1. Feature Selection Techniques

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- Wrapper methods
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- Filter methods
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- Embedded methods

#### 3.2. Forecasting

## 4. Database, Available Features, and Target to Be Forecasted

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- Territorial: We study the time-series data for the entire country but also some provinces as examples, in order to test the validation of our purpose.
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- Date and season: We will explore the evolution of GBV within years, month by month. We will also include the quarter to evaluate the influence of the season, as indicated by previous works [59].
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- Demography and population: Considering population can offer insights into the influence of big population areas, but some changes in demography can also provide explanations of the course of couples [60]. In this manner, marriages, separations, and births are included, but also the proportion of men vs. women.
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- Specific variables related to GBV: In this sense, there are some interesting variables available, such as:
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- Calls to the special number 016. This is a phone number dedicated to providing information to survivors, but also to manage assistance (imperative or not).
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- Complaints: In particular, we will study the number of complaints presented to a court as the independent variable to be modeled and forecasted. Ultimately, we feel that complaints express the incidence of worst cases.
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- Security devices for tracking offenders: This kind of device is proposed by a judge in high-risk cases.
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- Protection orders: Also ordered by a judge in cases of high risk.
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- Level of risk of aggression for the survivor: After a police evaluation, the cases are classified as unappreciated, low, medium, high, and extremely high.
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- Fatalities: Murdered victims of GBV.

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- Wealth and employment: The level of wealth in a region can be related to the levels of crime and violence. Similarly, levels of unemployment (male and female) can give an idea of the level of economic stability [61]. We differentiate between the inactive population (retired, disabled) and also the employed and unemployed population.
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- Education level: The relationship of illiteracy (male and female) and other educational levels (primary, secondary, university) with violence will also be studied, as previous literature indicates this point [62].

## 5. Methodology

#### 5.1. Territories under Study

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- Spain: A Mediterranean country and member of the European Union. The total population consists of 47,329,981 people.
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- Madrid: locating the homonymous capital city of Spain, with a population of 6,661,949 people, is centered on the country’s map and has a dynamic economy.
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- Alicante: In the east of Spain with a population of 1,858,683 people. It has a marked open and Mediterranean character, medium-range age inhabitants, and a flourishing economy.
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- Segovia: An inland province located in the west of Spain with a population of only 153,342 people and an aging population.

#### 5.2. The Waikato Environment for Knowledge Analysis (WEKA)

#### 5.3. Computer Hardware

#### 5.4. Data Cleaning, Regularization, and Lagged Variables

#### 5.5. Features Selection

#### 5.5.1. Search Methods

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- Multi-Objective Evolutionary Search Strategy (MOES): In particular, we execute the multi-objective evolutionary algorithm known as the Evolutionary NOn-dominated Radial slots-based Algorithm (ENORA) as a selection strategy for a random search method, which minimizes the selected features and also the RMSE [66].
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- Ranker: This search strategy makes ranks of features one by one by utilizing their evaluations [67].

#### 5.5.2. Attribute Evaluators

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- Wrapper methods. The WrapperSubsetEval routine implemented in WEKA will allow us to evaluate some approaches via multivariate techniques. For univariate ones, we need to instead use the ClassifierAttributeEval procedure. We will execute the following predictors:
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- Linear Regression: This offers fast computation, fixing the coefficients for each feature.
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- Random Forest [68]: As stated earlier, this is a tree-based algorithm well-known for classification purposes.
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- Instance-Based K-nearest neighbor algorithm (IBk) [69]: A K-nearest neighbors classifier, this algorithm allows for selecting an appropriate value of K based on cross-validation but is also able to carry out distance weighting.

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- Filter Method. On the side of the univariate methods, we will use the Ranker operation according to the below predictors:
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- Relief Attribute (Rlf) [70]: Relief feature selection is based on scoring by the identification of feature value differences between the nearest neighbor instance pairs.
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- Principal Component Analysis (PCA) [71]: With this technique, a new set of orthogonal coordinate axes is introduced, and, at the same time, the sample data variance is maximized. This leads to the scenario that the other directions, in which the variance is minor, are less important and, hence, can be removed from the dataset. PCA offers a very effective way of transforming the data in a lower dimensionality, while also being able to reveal some simplified patterns that often underlie the data.

#### 5.5.3. Generated Subsets

#### 5.6. Data Modeling and Forecasting

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- Linear Regression (LR).
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- Support Vector Machines (SVM).
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- Random Forest (RF).
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- Gaussian Process (GP).

## 6. Results and Discussion: Forecasting Performance

## 7. Conclusions and Future Works

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Comparative evolution of GBV complaints’ RMSE evolution obtained via an RF predictive algorithm with different FS techniques.

**Figure 3.**Comparative evolution of GBV complaints’ RMSE evolution obtained with MOES-RF feature selection technique for different predictive algorithms.

**Figure 4.**Prediction for the months October 2019 to March 2020 and real data comparison. Feature selection: MOES-RF. Forecasting technique: RF.

**Figure 5.**Evolution of RMSE in 6-step GBV complaints’ forecast, performed by FS dataset MOES-RF and RF as predictive techniques for different territories.

Variable | Description | Units |
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PROVINCE | Spanish province under study (or the whole country) | (Categorical) |

DATE | Data collection date | Month |

QUARTER | Quarter of the year | Quarter |

YEAR | Year of data collection | Year |

POP_TOT | Total population of the province | Units |

RATIO_MvsW | Ratio Population of men/women | Adimensional |

MARRIAGES | Number of new weddings | Units/10,000 pop |

SEPARATIONS | Number of separated marriages | Units/100,000 pop |

BIRTHS | Number of newborn children | Units/1000 pop |

CALLS | Calls to special telephone number 016 (requests for information and assistance) | Units/10,000 pop |

COMPLAINTS | Complaints made to a Court | Units/10,000 pop |

DEVICES | Security devices for tracking offenders | Units/100,000 pop |

PROTECTION_ORDER | Restraining order for survivors decreed by a judge | Units/10,000 pop |

RISK_UN | Survivors with unappreciated risk after police valuation | Units/10,000 pop |

RISK_L | Survivors with low risk after police valuation | Units/10,000 pop |

RISK_M | Survivors with medium risk after police valuation | Units/10,000 pop |

RISK_H | Survivors with high risk after police valuation | Units/10,000 pop |

RISK_EH | Survivors with extremely high risk after police valuation | Units/10,000 pop |

FATALITIES | Murdered victims of GBV | Units/1,000,000 pop |

GDP | Gross Domestic Product per capita | €/10,000 pop |

EMPL_MEN | Employed men | Units/100 pop |

UNEMPL_MEN | Unemployed women | Units/100 pop |

INACT_MEN | Inactive women | Units/100 pop |

EMPL_WOM | Employed women | Units/100 pop |

UNEMPL_WOM | Unemployed women | Units/100 pop |

INACT_WOM | Inactive women | Units/100 pop |

ILLIT_MEN | Illiterate men | Units/100 pop |

ILLIT_WOM | Illiterate women | Units/100 pop |

PRIM_ED_MEN | Primary education men | Units/100 pop |

SEC_ED_MEN | Secondary education men | Units/100 pop |

HIGH_ED_MEN | Higher education men | Units/100 pop |

PRIM_ED_WOM | Primary education women | Units/100 pop |

SEC_ED_WOM | Secondary education women | Units/100 pop |

HIGH_ED_WOM | Higher education women | Units/100 pop |

Search Method | Attribute Evaluator | Predictor | Acronym |
---|---|---|---|

MOES | Wrapper | Linear Regression | MOES-LR |

Random Forest | MOES-RF | ||

IBk | MOES-IBk | ||

Ranker | Wrapper (Classifier) | Linear Regression | Rnk-LR |

Random Forest | Rnk-RF | ||

Filter | Relief | Rnk-Rlf | |

PCA | Rnk-PCA |

Technique | Command |
---|---|

MOES | weka.attributeSelection.MultiObjectiveEvolutionarySearch -generations 20 -population-size 100 -seed 1 -algorithm 0 -report-frequency 20 -log-file “C:\\Program Files\\Weka-3-8” |

Ranker | weka.attributeSelection. Ranker -T -1. 8 -N -1 |

Wrapper LR | weka.attributeSelection.WrapperSubsetEval -B weka.classifiers.functions.LinearRegression -F 5 -T 0.01 -R 1 -E RMSE -- -S 0 -R 1.0E-8 -num-decimal-places 4 |

Wrapper RF | weka.attributeSelection.WrapperSubsetEval -B weka.classifiers.trees.RandomForest -F 5 -T 0.01 -R 1 -E RMSE -- -P 100 -I 100 -num-slots 1 -K 0 -M 1.0 -V 0.001 -S 1 -num-decimal-places 4 |

Wrapper IBk | weka.attributeSelection.WrapperSubsetEval -B weka.classifiers.lazy.IBk -F 5 -T 0.01 -R 1 -E RMSE -- -K 1 -W 0 -A “weka.core.neighboursearch.LinearNNSearch -A \”weka.core.EuclideanDistance -R first-last\”“ -num-decimal-places 4 |

Classifier LR | weka.attributeSelection.ClassifierAttributeEval -execution-slots 1 -B weka.classifiers.functions.LinearRegression -F 5 -T 0.01 -R 1 -E RMSE -- -S 0 -R 1.0E-8 -num-decimal-places 4 |

Classifier RF | weka.attributeSelection.ClassifierAttributeEval -execution-slots 1 -B weka.classifiers.trees.RandomForest -F 5 -T 0.01 -R 1 -E RMSE -- -P 100 -I 100 -num-slots 1 -K 0 -M 1.0 -V 0.001 -S 1 -num-decimal-places 4 |

Relief | weka.attributeSelection.ReliefFAttributeEval -M -1 -D 1 -K 10 |

PCA | weka.attributeSelection.PrincipalComponents -R 0.95 -A 5 |

Technique | Command |
---|---|

LR | weka.classifiers.functions.LinearRegression -S 0 -R 1.0E-8 -num-decimal-places 4 |

RF | weka.classifiers.trees.RandomForest -P 100 -I 100 -num-slots 1 -K 0 -M 1.0 -V 0.001 -S 1 |

SVM | weka.classifiers.functions.SMOreg -C 1.0 -N 0 -I “weka.classifiers.functions.supportVector.RegSMOImproved -T 0.001 -V -P 1.0E-12 -L 0.001 -W 1” -K “weka.classifiers.functions.supportVector.PolyKernel -E 1.0 -C 250007” |

GP | weka.classifiers.functions.GaussianProcesses -L 1.0 -N 0 -K “weka.classifiers.functions.supportVector.PolyKernel -E 1.0 -C 250007” -S 1 |

RMSE | ||||||||
---|---|---|---|---|---|---|---|---|

Subset FS | 1 Step | 2 Step | 3 Step | 4 Step | 5 Step | 6 Step | $\overline{\mathbf{RMSE}}$ | Standard Deviation |

Forecasting technique: LR | ||||||||

No F.S. | 0.2309 | 0.4502 | 0.6627 | 0.8719 | 1.0802 | 1.2785 | 0.7624 | 0.3922 |

MOES-LR | 0.2229 | 0.2784 | 0.2938 | 0.3059 | 0.3224 | 0.3418 | 0.2942 | 0.0413 |

MOES-RF | 0.1273 | 0.1784 | 0.1985 | 0.2015 | 0.2069 | 0.2093 | 0.1870 | 0.0312 |

MOES-IBk | 0.0914 | 0.1878 | 0.2853 | 0.3761 | 0.4576 | 0.5227 | 0.3202 | 0.1638 |

Rnk-LR | 0.1033 | 0.2034 | 0.2932 | 0.3589 | 0.4012 | 0.4039 | 0.2940 | 0.1203 |

Rnk-RF | 0.1198 | 0.2058 | 0.2632 | 0.3014 | 0.3292 | 0.3493 | 0.2615 | 0.0861 |

Rnk-Rlf | 0.3860 | 0.4017 | 0.4195 | 0.4362 | 0.4442 | 0.4253 | 0.4188 | 0.0217 |

Rnk-PCA | 0.2289 | 0.3227 | 0.3619 | 0.3859 | 0.4081 | 0.4315 | 0.3565 | 0.0729 |

$\overline{\overline{\mathbf{RMSE}}}$ | 0.3618 | |||||||

Forecasting technique: RF | ||||||||

No F.S. | 0.2083 | 0.2407 | 0.2513 | 0.2635 | 0.2748 | 0.2747 | 0.2522 | 0.0253 |

MOES-LR | 0.1680 | 0.1808 | 0.1867 | 0.1943 | 0.2047 | 0.2117 | 0.1910 | 0.0160 |

MOES-RF | 0.1489 | 0.1586 | 0.1646 | 0.1714 | 0.1806 | 0.1876 | 0.1686 | 0.0143 |

MOES-IBk | 0.1803 | 0.1941 | 0.2012 | 0.2104 | 0.2214 | 0.2275 | 0.2058 | 0.0176 |

Rnk-LR | 0.1824 | 0.1919 | 0.1978 | 0.2055 | 0.2166 | 0.2246 | 0.2031 | 0.0157 |

Rnk-RF | 0.1605 | 0.1801 | 0.1866 | 0.1930 | 0.2034 | 0.2125 | 0.1894 | 0.0183 |

Rnk-Rlf | 0.1919 | 0.2047 | 0.2121 | 0.2219 | 0.2333 | 0.2395 | 0.2172 | 0.0179 |

Rnk-PCA | 0.1820 | 0.1960 | 0.2047 | 0.2144 | 0.2258 | 0.2343 | 0.2095 | 0.0193 |

$\overline{\overline{\mathbf{RMSE}}}$ | 0.2046 | |||||||

Forecasting technique: SVM | ||||||||

No F.S. | 0.3825 | 0.4632 | 0.4879 | 0.5067 | 0.5307 | 0.5600 | 0.4885 | 0.0618 |

MOES-LR | 0.1706 | 0.2204 | 0.2372 | 0.2489 | 0.2621 | 0.2722 | 0.2352 | 0.0365 |

MOES-RF | 0.0987 | 0.1580 | 0.1913 | 0.1999 | 0.2082 | 0.2118 | 0.1780 | 0.0434 |

MOES-IBk | 0.1782 | 0.2765 | 0.3288 | 0.3603 | 0.3838 | 0.4056 | 0.3222 | 0.0837 |

Rnk-LR | 0.0759 | 0.1420 | 0.1929 | 0.2198 | 0.2314 | 0.2292 | 0.1819 | 0.0618 |

Rnk-RF | 0.1320 | 0.1648 | 0.1850 | 0.1922 | 0.1997 | 0.1997 | 0.1789 | 0.0264 |

Rnk-Rlf | 0.1292 | 0.2462 | 0.3460 | 0.4273 | 0.4974 | 0.5583 | 0.3674 | 0.1605 |

Rnk-PCA | 0.1321 | 0.2579 | 0.3762 | 0.4865 | 0.5869 | 0.6711 | 0.4185 | 0.2032 |

$\overline{\overline{\mathbf{RMSE}}}$ | 0.2963 | |||||||

Forecasting technique: GP | ||||||||

No F.S. | 0.3402 | 0.3823 | 0.3922 | 0.4005 | 0.4156 | 0.4383 | 0.3949 | 0.0332 |

MOES-LR | 0.1540 | 0.2160 | 0.2325 | 0.2344 | 0.2403 | 0.2531 | 0.2217 | 0.0353 |

MOES-RF | 0.1325 | 0.1648 | 0.1735 | 0.1813 | 0.1898 | 0.1913 | 0.1722 | 0.0219 |

MOES-IBk | 0.1694 | 0.2171 | 0.2325 | 0.2443 | 0.2560 | 0.2611 | 0.2301 | 0.0337 |

Rnk-LR | 0.1513 | 0.2118 | 0.2317 | 0.2373 | 0.2469 | 0.2603 | 0.2232 | 0.0388 |

Rnk-RF | 0.1720 | 0.2125 | 0.2220 | 0.2276 | 0.2374 | 0.2512 | 0.2205 | 0.0272 |

Rnk-Rlf | 0.3075 | 0.3525 | 0.3649 | 0.3758 | 0.3927 | 0.4161 | 0.3683 | 0.0371 |

Rnk-PCA | 0.2479 | 0.2989 | 0.3120 | 0.3229 | 0.3396 | 0.3592 | 0.3134 | 0.0384 |

$\overline{\overline{\mathbf{RMSE}}}$ | 0.2680 |

Subset FS | Spain | Madrid | Alicante | Segovia | ||||
---|---|---|---|---|---|---|---|---|

$(\overline{\mathbf{RMSE}}6-\mathbf{Steps})$ | Standard Deviation | $(\overline{\mathbf{RMSE}}6-\mathbf{Steps})$ | Standard Deviation | $(\overline{\mathbf{RMSE}}6-\mathbf{Steps})$ | Standard Deviation | $(\overline{\mathbf{RMSE}}6-\mathbf{Steps})$ | Standard Deviation | |

Forecasting technique: LR | ||||||||

No F.S. | 0.7624 | 0.3922 | 1.1144 | 0.5175 | 1.1849 | 0.2454 | 1.7304 | 0.5124 |

MOES-LR | 0.2942 | 0.0413 | 0.3430 | 0.1167 | 0.4724 | 0.1636 | 0.5129 | 0.1208 |

MOES-RF | 0.1870 | 0.0312 | 0.2709 | 0.0066 | 0.3974 | 0.0704 | 0.3104 | 0.1108 |

MOES-IBk | 0.3202 | 0.1638 | 0.5108 | 0.2423 | 0.9960 | 0.3369 | 0.8974 | 0.1692 |

Rnk-LR | 0.2940 | 0.1203 | 0.3519 | 0.1406 | 0.8525 | 0.0843 | 0.3370 | 0.0107 |

Rnk-RF | 0.2615 | 0.0861 | 0.3153 | 0.0493 | 0.4081 | 0.0047 | 0.2756 | 0.1074 |

Rnk-Rlf | 0.4188 | 0.0217 | 0.5127 | 0.1821 | 1.1618 | 0.3647 | 1.2120 | 0.1902 |

Rnk-PCA | 0.3565 | 0.0729 | 0.6136 | 0.0748 | 1.0383 | 0.3725 | 1.1588 | 0.7191 |

$\overline{\overline{\mathbf{RMSE}}}$ | 0.3618 | 0.5041 | 0.8139 | 0.8043 | ||||

Forecasting technique: RF | ||||||||

No F.S. | 0.2522 | 0.0253 | 0.3198 | 0.0208 | 0.4245 | 0.0384 | 0.7339 | 0.0178 |

MOES-LR | 0.1910 | 0.0160 | 0.3047 | 0.0224 | 0.3922 | 0.0360 | 0.6163 | 0.0118 |

MOES-RF | 0.1686 | 0.0143 | 0.2928 | 0.0258 | 0.3776 | 0.0297 | 0.5756 | 0.0127 |

MOES-IBk | 0.2058 | 0.0176 | 0.3051 | 0.0245 | 0.3978 | 0.0350 | 0.6592 | 0.0144 |

Rnk-LR | 0.2031 | 0.0157 | 0.2990 | 0.0171 | 0.3804 | 0.0418 | 0.6195 | 0.0160 |

Rnk-RF | 0.1894 | 0.0183 | 0.2921 | 0.0151 | 0.3704 | 0.0303 | 0.5798 | 0.0154 |

Rnk-Rlf | 0.2172 | 0.0179 | 0.3158 | 0.0155 | 0.4026 | 0.0348 | 0.7262 | 0.0288 |

Rnk-PCA | 0.2095 | 0.0193 | 0.3113 | 0.0218 | 0.4047 | 0.0324 | 0.6665 | 0.0231 |

$\overline{\overline{\mathbf{RMSE}}}$ | 0.2046 | 0.3051 | 0.3938 | 0.6471 | ||||

Forecasting technique: SVM | ||||||||

No F.S. | 0.4885 | 0.0618 | 0.8038 | 0.2394 | 1.4879 | 0.4664 | 1.7207 | 0.7698 |

MOES-LR | 0.2352 | 0.0365 | 0.3276 | 0.1057 | 0.4940 | 0.0888 | 0.4714 | 0.0987 |

MOES-RF | 0.1780 | 0.0434 | 0.2508 | 0.0329 | 0.3407 | 0.0620 | 0.3418 | 0.1222 |

MOES-IBk | 0.3222 | 0.0837 | 0.4588 | 0.1980 | 0.5229 | 0.1560 | 0.5738 | 0.1021 |

Rnk-LR | 0.1819 | 0.0618 | 0.4583 | 0.1478 | 0.4866 | 0.1523 | 0.5341 | 0.4749 |

Rnk-RF | 0.1789 | 0.0264 | 0.2620 | 0.0866 | 0.2975 | 0.0681 | 0.4103 | 0.2492 |

Rnk-Rlf | 0.3674 | 0.1605 | 0.5824 | 0.0747 | 0.8858 | 0.3994 | 1.0350 | 0.1614 |

Rnk-PCA | 0.4185 | 0.2032 | 0.4866 | 0.1357 | 0.7613 | 0.0778 | 0.6652 | 0.3641 |

$\overline{\overline{\mathbf{RMSE}}}$ | 0.2963 | 0.4538 | 0.6596 | 0.7190 | ||||

Forecasting technique: GP | ||||||||

No F.S. | 0.3949 | 0.0332 | 0.4966 | 0.0806 | 0.6799 | 0.0794 | 0.5454 | 0.0686 |

MOES-LR | 0.2217 | 0.0353 | 0.3650 | 0.0664 | 0.3271 | 0.0738 | 0.3644 | 0.0682 |

MOES-RF | 0.1722 | 0.0219 | 0.3013 | 0.0318 | 0.2602 | 0.0377 | 0.3033 | 0.0376 |

MOES-IBk | 0.2301 | 0.0337 | 0.3709 | 0.0353 | 0.5322 | 0.0766 | 0.3788 | 0.0513 |

Rnk-LR | 0.2232 | 0.0388 | 0.3136 | 0.0378 | 0.3299 | 0.0442 | 0.3116 | 0.0321 |

Rnk-RF | 0.2205 | 0.0272 | 0.2762 | 0.0541 | 0.3192 | 0.0493 | 0.2899 | 0.0384 |

Rnk-Rlf | 0.3683 | 0.0371 | 0.4226 | 0.0426 | 0.6502 | 0.1130 | 0.4225 | 0.0826 |

Rnk-PCA | 0.3134 | 0.0384 | 0.3945 | 0.0716 | 0.6471 | 0.0606 | 0.4656 | 0.0939 |

$\overline{\overline{\mathbf{RMSE}}}$ | 0.2680 | 0.3676 | 0.4682 | 0.3852 | ||||

Average among techniques$\overline{\overline{\overline{\mathbf{RMSE}}}}$ | 0.2826 | 0.4076 | 0.5839 | 0.6389 |

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## Share and Cite

**MDPI and ACS Style**

Rodríguez-Rodríguez, I.; Rodríguez, J.-V.; Pardo-Quiles, D.-J.; Heras-González, P.; Chatzigiannakis, I.
Modeling and Forecasting Gender-Based Violence through Machine Learning Techniques. *Appl. Sci.* **2020**, *10*, 8244.
https://doi.org/10.3390/app10228244

**AMA Style**

Rodríguez-Rodríguez I, Rodríguez J-V, Pardo-Quiles D-J, Heras-González P, Chatzigiannakis I.
Modeling and Forecasting Gender-Based Violence through Machine Learning Techniques. *Applied Sciences*. 2020; 10(22):8244.
https://doi.org/10.3390/app10228244

**Chicago/Turabian Style**

Rodríguez-Rodríguez, Ignacio, José-Víctor Rodríguez, Domingo-Javier Pardo-Quiles, Purificación Heras-González, and Ioannis Chatzigiannakis.
2020. "Modeling and Forecasting Gender-Based Violence through Machine Learning Techniques" *Applied Sciences* 10, no. 22: 8244.
https://doi.org/10.3390/app10228244