Error Correction Based Deep Neural Networks for Modeling and Predicting South African Wildlife–Vehicle Collision Data
The seasonal autoregressive integrated moving average with exogenous factors (SARIMAX) has shown promising results in modeling small and sparse observed time-series data by capturing linear features using independent and dependent variables. Long short-term memory (LSTM) is a promising neural networ...
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| Format: | Article |
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MDPI AG
2022-10-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/21/3988 |
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| author | Irene Nandutu Marcellin Atemkeng Nokubonga Mgqatsa Sakayo Toadoum Sari Patrice Okouma Rockefeller Rockefeller Theophilus Ansah-Narh Jean Louis Ebongue Kedieng Fendji Franklin Tchakounte |
| author_facet | Irene Nandutu Marcellin Atemkeng Nokubonga Mgqatsa Sakayo Toadoum Sari Patrice Okouma Rockefeller Rockefeller Theophilus Ansah-Narh Jean Louis Ebongue Kedieng Fendji Franklin Tchakounte |
| author_sort | Irene Nandutu |
| collection | DOAJ |
| description | The seasonal autoregressive integrated moving average with exogenous factors (SARIMAX) has shown promising results in modeling small and sparse observed time-series data by capturing linear features using independent and dependent variables. Long short-term memory (LSTM) is a promising neural network for learning nonlinear dependence features from data. With the increase in wildlife roadkill patterns, the SARIMAX-only and LSTM-only models would likely fail to learn the precise endogenous and/or exogenous variables driven by this wildlife roadkill data. In this paper, we design and implement an error correction mathematical framework based on LSTM-only. The framework extracts features from the residual error generated by a SARIMAX-only model. The learned residual features correct the output time-series prediction of the SARIMAX-only model. The process combines SARIMAX-only predictions and LSTM-only residual predictions to obtain a hybrid SARIMAX-LSTM. The models are evaluated using South African wildlife–vehicle collision datasets, and the experiments show that compared to single models, SARIMAX-LSTM increases the accuracy of a taxon whose linear components outweigh the nonlinear ones. In addition, the hybrid model fails to outperform LSTM-only when a taxon contains more nonlinear components rather than linear components. Our assumption of the results is that the collected exogenous and endogenous data are insufficient, which limits the hybrid model’s performance since it cannot accurately detect seasonality on residuals from SARIMAX-only and minimize the SARIMAX-LSTM error. We conclude that the error correction framework should be preferred over single models in wildlife time-series modeling and predictions when a dataset contains more linear components. Adding more related data may improve the prediction performance of SARIMAX-LSTM. |
| first_indexed | 2024-03-09T18:53:22Z |
| format | Article |
| id | doaj.art-eb7afcaaa1794bffb9cf18ed77df95df |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T18:53:22Z |
| publishDate | 2022-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-eb7afcaaa1794bffb9cf18ed77df95df2023-11-24T05:43:09ZengMDPI AGMathematics2227-73902022-10-011021398810.3390/math10213988Error Correction Based Deep Neural Networks for Modeling and Predicting South African Wildlife–Vehicle Collision DataIrene Nandutu0Marcellin Atemkeng1Nokubonga Mgqatsa2Sakayo Toadoum Sari3Patrice Okouma4Rockefeller Rockefeller5Theophilus Ansah-Narh6Jean Louis Ebongue Kedieng Fendji7Franklin Tchakounte8Department of Mathematics, Rhodes University, Grahamstown 6139, South AfricaDepartment of Mathematics, Rhodes University, Grahamstown 6139, South AfricaDepartment of Zoology and Entomology, Rhodes University, Grahamstown 6139, South AfricaAfrican Institute of Mathematical Sciences, Limbe P.O. Box 608, CameroonDepartment of Mathematics, Rhodes University, Grahamstown 6139, South AfricaAfrican Institute of Mathematical Sciences, Limbe P.O. Box 608, CameroonRadio Astronomy and Astrophysics Centre, Ghana Space Science and Technology Institute, GAEC, Accra P.O. Box LG 80 233, GhanaDepartment of Computer Engineering, University Institute of Technology, University of Ngaoundéré, Ngaoundéré P.O. Box 454, CameroonDepartment of Mathematics, Rhodes University, Grahamstown 6139, South AfricaThe seasonal autoregressive integrated moving average with exogenous factors (SARIMAX) has shown promising results in modeling small and sparse observed time-series data by capturing linear features using independent and dependent variables. Long short-term memory (LSTM) is a promising neural network for learning nonlinear dependence features from data. With the increase in wildlife roadkill patterns, the SARIMAX-only and LSTM-only models would likely fail to learn the precise endogenous and/or exogenous variables driven by this wildlife roadkill data. In this paper, we design and implement an error correction mathematical framework based on LSTM-only. The framework extracts features from the residual error generated by a SARIMAX-only model. The learned residual features correct the output time-series prediction of the SARIMAX-only model. The process combines SARIMAX-only predictions and LSTM-only residual predictions to obtain a hybrid SARIMAX-LSTM. The models are evaluated using South African wildlife–vehicle collision datasets, and the experiments show that compared to single models, SARIMAX-LSTM increases the accuracy of a taxon whose linear components outweigh the nonlinear ones. In addition, the hybrid model fails to outperform LSTM-only when a taxon contains more nonlinear components rather than linear components. Our assumption of the results is that the collected exogenous and endogenous data are insufficient, which limits the hybrid model’s performance since it cannot accurately detect seasonality on residuals from SARIMAX-only and minimize the SARIMAX-LSTM error. We conclude that the error correction framework should be preferred over single models in wildlife time-series modeling and predictions when a dataset contains more linear components. Adding more related data may improve the prediction performance of SARIMAX-LSTM.https://www.mdpi.com/2227-7390/10/21/3988SARIMAXSARIMAX-LSTMmodelingLSTMneural networkswildlife |
| spellingShingle | Irene Nandutu Marcellin Atemkeng Nokubonga Mgqatsa Sakayo Toadoum Sari Patrice Okouma Rockefeller Rockefeller Theophilus Ansah-Narh Jean Louis Ebongue Kedieng Fendji Franklin Tchakounte Error Correction Based Deep Neural Networks for Modeling and Predicting South African Wildlife–Vehicle Collision Data Mathematics SARIMAX SARIMAX-LSTM modeling LSTM neural networks wildlife |
| title | Error Correction Based Deep Neural Networks for Modeling and Predicting South African Wildlife–Vehicle Collision Data |
| title_full | Error Correction Based Deep Neural Networks for Modeling and Predicting South African Wildlife–Vehicle Collision Data |
| title_fullStr | Error Correction Based Deep Neural Networks for Modeling and Predicting South African Wildlife–Vehicle Collision Data |
| title_full_unstemmed | Error Correction Based Deep Neural Networks for Modeling and Predicting South African Wildlife–Vehicle Collision Data |
| title_short | Error Correction Based Deep Neural Networks for Modeling and Predicting South African Wildlife–Vehicle Collision Data |
| title_sort | error correction based deep neural networks for modeling and predicting south african wildlife vehicle collision data |
| topic | SARIMAX SARIMAX-LSTM modeling LSTM neural networks wildlife |
| url | https://www.mdpi.com/2227-7390/10/21/3988 |
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