Estimating the Mass of Galactic Components Using Machine Learning Algorithms
Abstract
:1. Introduction
2. The Data
Features Importance
3. Implementation of the ML Algorithms
- KN-Neighbours (KNN). This algorithm relies on the idea that the set of k nearest data points , where have similar values among them; here, D is defined in Equation (3). To consider two points as neighbours, they should fulfillThis distance is defined in the hyperspace of features using the Euclidian metric, and the final value is the average of their outputs. In this case, the number of neighbours is a free parameter, and we found that the highest accuracy is achieved when the number of neighbours is close to 18; the error starts to increase beyond that value.
- Linear regression (LR). The traditional linear regression minimises the sum of the squared differences between the predicted and actual values. We are considering this method to compare it with more sophisticated techniques.
- Random forest (RF). This algorithm is subject to the number of trees and their depth. Each tree contains decision nodes that split the data (in the parent node) into smaller (left and right) subsets in new child nodes and until the branch finds a homogeneous group according to the set of hyperparameters. Splitting each node in regression is conducted following the minimisation of the residual as
- Neural network (NN). NN is an interconnected group of nodes stored in a layer and is connected to other nodes in the network by unidirectional connections of different weights. Patterns learned in a layer are transferred to the next activated nodes. We implement the early stopping-based method as a regularisation technique to avoid overfitting, stopping the training once the performance no longer improves. This is measured by the loss function, which quantifies the discrepancy between the predicted error and true values. For a regression, it can be taken as the squared loss function
4. Testing the Algorithms Performance
Relative Percentage Difference
5. Predictions for Observational Data
5.1. Mass–Magnitude Relation
5.2. Bulge–Disk Components
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
1 | In fact, when using a mock catalogue to train the algorithms, we set dark matter in a CDM prescription and make inferences about mass components holding such a hypothesis. |
2 | Notice that the gas component has been neglected, as the primary light contributions in massive galaxies come from stars. |
3 | Further information such as the metallicity, age, or other complex processes of baryons have not been included, as obtaining such features from observed galaxies is not straightforward. |
4 | The NASA/IPAC Extragalactic Database (NED) is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. |
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Input | u | r | g | i | z | |
---|---|---|---|---|---|---|
Set I () | ✓ | ✓ | ✓ | ✓ | ✓ | |
Set II () | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ |
Output (y) | ) |
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López-Sánchez, J.N.; Munive-Villa, E.; Avilez-López, A.A.; Martínez-Bravo, O.M. Estimating the Mass of Galactic Components Using Machine Learning Algorithms. Universe 2024, 10, 220. https://doi.org/10.3390/universe10050220
López-Sánchez JN, Munive-Villa E, Avilez-López AA, Martínez-Bravo OM. Estimating the Mass of Galactic Components Using Machine Learning Algorithms. Universe. 2024; 10(5):220. https://doi.org/10.3390/universe10050220
Chicago/Turabian StyleLópez-Sánchez, Jessica N., Erick Munive-Villa, Ana A. Avilez-López, and Oscar M. Martínez-Bravo. 2024. "Estimating the Mass of Galactic Components Using Machine Learning Algorithms" Universe 10, no. 5: 220. https://doi.org/10.3390/universe10050220