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significantly smaller » significantly lower (Expand Search), significantly greater (Expand Search), significantly better (Expand Search)
smaller decrease » small decrease (Expand Search), marked decrease (Expand Search), smaller areas (Expand Search)
higher decrease » higher degree (Expand Search), higher degrees (Expand Search), highest increase (Expand Search)
significantly smaller » significantly lower (Expand Search), significantly greater (Expand Search), significantly better (Expand Search)
smaller decrease » small decrease (Expand Search), marked decrease (Expand Search), smaller areas (Expand Search)
higher decrease » higher degree (Expand Search), higher degrees (Expand Search), highest increase (Expand Search)
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1144
Testing set error.
Published 2025“…Further integration of Spearman correlation analysis and PCA dimensionality reduction created multidimensional feature sets, revealing substantial accuracy improvements: The BiLSTM model achieved an 83.6% cumulative MAE reduction from 1.65 (raw data) to 0.27 (STL-PCA), while traditional models like Prophet showed an 82.2% MAE decrease after feature engineering optimization. Finally, the Beluga Whale Optimization (BWO)-tuned STL-PCA-BWO-BiLSTM hybrid model delivered optimal performance on test sets (RMSE = 0.22, MAE = 0.16, MAPE = 0.99%, ), exhibiting 40.7% higher accuracy than unoptimized BiLSTM (MAE = 0.27). …”
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1145
Internal structure of an LSTM cell.
Published 2025“…Further integration of Spearman correlation analysis and PCA dimensionality reduction created multidimensional feature sets, revealing substantial accuracy improvements: The BiLSTM model achieved an 83.6% cumulative MAE reduction from 1.65 (raw data) to 0.27 (STL-PCA), while traditional models like Prophet showed an 82.2% MAE decrease after feature engineering optimization. Finally, the Beluga Whale Optimization (BWO)-tuned STL-PCA-BWO-BiLSTM hybrid model delivered optimal performance on test sets (RMSE = 0.22, MAE = 0.16, MAPE = 0.99%, ), exhibiting 40.7% higher accuracy than unoptimized BiLSTM (MAE = 0.27). …”
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1146
Prediction effect of each model after STL.
Published 2025“…Further integration of Spearman correlation analysis and PCA dimensionality reduction created multidimensional feature sets, revealing substantial accuracy improvements: The BiLSTM model achieved an 83.6% cumulative MAE reduction from 1.65 (raw data) to 0.27 (STL-PCA), while traditional models like Prophet showed an 82.2% MAE decrease after feature engineering optimization. Finally, the Beluga Whale Optimization (BWO)-tuned STL-PCA-BWO-BiLSTM hybrid model delivered optimal performance on test sets (RMSE = 0.22, MAE = 0.16, MAPE = 0.99%, ), exhibiting 40.7% higher accuracy than unoptimized BiLSTM (MAE = 0.27). …”
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1147
The kernel density plot for data of each feature.
Published 2025“…Further integration of Spearman correlation analysis and PCA dimensionality reduction created multidimensional feature sets, revealing substantial accuracy improvements: The BiLSTM model achieved an 83.6% cumulative MAE reduction from 1.65 (raw data) to 0.27 (STL-PCA), while traditional models like Prophet showed an 82.2% MAE decrease after feature engineering optimization. Finally, the Beluga Whale Optimization (BWO)-tuned STL-PCA-BWO-BiLSTM hybrid model delivered optimal performance on test sets (RMSE = 0.22, MAE = 0.16, MAPE = 0.99%, ), exhibiting 40.7% higher accuracy than unoptimized BiLSTM (MAE = 0.27). …”
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1148
Analysis of raw data prediction results.
Published 2025“…Further integration of Spearman correlation analysis and PCA dimensionality reduction created multidimensional feature sets, revealing substantial accuracy improvements: The BiLSTM model achieved an 83.6% cumulative MAE reduction from 1.65 (raw data) to 0.27 (STL-PCA), while traditional models like Prophet showed an 82.2% MAE decrease after feature engineering optimization. Finally, the Beluga Whale Optimization (BWO)-tuned STL-PCA-BWO-BiLSTM hybrid model delivered optimal performance on test sets (RMSE = 0.22, MAE = 0.16, MAPE = 0.99%, ), exhibiting 40.7% higher accuracy than unoptimized BiLSTM (MAE = 0.27). …”
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1149
Flowchart of the STL.
Published 2025“…Further integration of Spearman correlation analysis and PCA dimensionality reduction created multidimensional feature sets, revealing substantial accuracy improvements: The BiLSTM model achieved an 83.6% cumulative MAE reduction from 1.65 (raw data) to 0.27 (STL-PCA), while traditional models like Prophet showed an 82.2% MAE decrease after feature engineering optimization. Finally, the Beluga Whale Optimization (BWO)-tuned STL-PCA-BWO-BiLSTM hybrid model delivered optimal performance on test sets (RMSE = 0.22, MAE = 0.16, MAPE = 0.99%, ), exhibiting 40.7% higher accuracy than unoptimized BiLSTM (MAE = 0.27). …”
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1150
SARIMA predicts season components.
Published 2025“…Further integration of Spearman correlation analysis and PCA dimensionality reduction created multidimensional feature sets, revealing substantial accuracy improvements: The BiLSTM model achieved an 83.6% cumulative MAE reduction from 1.65 (raw data) to 0.27 (STL-PCA), while traditional models like Prophet showed an 82.2% MAE decrease after feature engineering optimization. Finally, the Beluga Whale Optimization (BWO)-tuned STL-PCA-BWO-BiLSTM hybrid model delivered optimal performance on test sets (RMSE = 0.22, MAE = 0.16, MAPE = 0.99%, ), exhibiting 40.7% higher accuracy than unoptimized BiLSTM (MAE = 0.27). …”
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1151
BWO-BiLSTM model prediction results.
Published 2025“…Further integration of Spearman correlation analysis and PCA dimensionality reduction created multidimensional feature sets, revealing substantial accuracy improvements: The BiLSTM model achieved an 83.6% cumulative MAE reduction from 1.65 (raw data) to 0.27 (STL-PCA), while traditional models like Prophet showed an 82.2% MAE decrease after feature engineering optimization. Finally, the Beluga Whale Optimization (BWO)-tuned STL-PCA-BWO-BiLSTM hybrid model delivered optimal performance on test sets (RMSE = 0.22, MAE = 0.16, MAPE = 0.99%, ), exhibiting 40.7% higher accuracy than unoptimized BiLSTM (MAE = 0.27). …”
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1152
Bi-LSTM architecture diagram.
Published 2025“…Further integration of Spearman correlation analysis and PCA dimensionality reduction created multidimensional feature sets, revealing substantial accuracy improvements: The BiLSTM model achieved an 83.6% cumulative MAE reduction from 1.65 (raw data) to 0.27 (STL-PCA), while traditional models like Prophet showed an 82.2% MAE decrease after feature engineering optimization. Finally, the Beluga Whale Optimization (BWO)-tuned STL-PCA-BWO-BiLSTM hybrid model delivered optimal performance on test sets (RMSE = 0.22, MAE = 0.16, MAPE = 0.99%, ), exhibiting 40.7% higher accuracy than unoptimized BiLSTM (MAE = 0.27). …”
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1153
STL Linear Combination Forecast Graph.
Published 2025“…Further integration of Spearman correlation analysis and PCA dimensionality reduction created multidimensional feature sets, revealing substantial accuracy improvements: The BiLSTM model achieved an 83.6% cumulative MAE reduction from 1.65 (raw data) to 0.27 (STL-PCA), while traditional models like Prophet showed an 82.2% MAE decrease after feature engineering optimization. Finally, the Beluga Whale Optimization (BWO)-tuned STL-PCA-BWO-BiLSTM hybrid model delivered optimal performance on test sets (RMSE = 0.22, MAE = 0.16, MAPE = 0.99%, ), exhibiting 40.7% higher accuracy than unoptimized BiLSTM (MAE = 0.27). …”
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1154
LOSS curves for BWO-BiLSTM model training.
Published 2025“…Further integration of Spearman correlation analysis and PCA dimensionality reduction created multidimensional feature sets, revealing substantial accuracy improvements: The BiLSTM model achieved an 83.6% cumulative MAE reduction from 1.65 (raw data) to 0.27 (STL-PCA), while traditional models like Prophet showed an 82.2% MAE decrease after feature engineering optimization. Finally, the Beluga Whale Optimization (BWO)-tuned STL-PCA-BWO-BiLSTM hybrid model delivered optimal performance on test sets (RMSE = 0.22, MAE = 0.16, MAPE = 0.99%, ), exhibiting 40.7% higher accuracy than unoptimized BiLSTM (MAE = 0.27). …”
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1155
Analysis of STL-PCA prediction results.
Published 2025“…Further integration of Spearman correlation analysis and PCA dimensionality reduction created multidimensional feature sets, revealing substantial accuracy improvements: The BiLSTM model achieved an 83.6% cumulative MAE reduction from 1.65 (raw data) to 0.27 (STL-PCA), while traditional models like Prophet showed an 82.2% MAE decrease after feature engineering optimization. Finally, the Beluga Whale Optimization (BWO)-tuned STL-PCA-BWO-BiLSTM hybrid model delivered optimal performance on test sets (RMSE = 0.22, MAE = 0.16, MAPE = 0.99%, ), exhibiting 40.7% higher accuracy than unoptimized BiLSTM (MAE = 0.27). …”
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1156
Accumulated contribution rate of PCA.
Published 2025“…Further integration of Spearman correlation analysis and PCA dimensionality reduction created multidimensional feature sets, revealing substantial accuracy improvements: The BiLSTM model achieved an 83.6% cumulative MAE reduction from 1.65 (raw data) to 0.27 (STL-PCA), while traditional models like Prophet showed an 82.2% MAE decrease after feature engineering optimization. Finally, the Beluga Whale Optimization (BWO)-tuned STL-PCA-BWO-BiLSTM hybrid model delivered optimal performance on test sets (RMSE = 0.22, MAE = 0.16, MAPE = 0.99%, ), exhibiting 40.7% higher accuracy than unoptimized BiLSTM (MAE = 0.27). …”
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1157
Figure of ablation experiment.
Published 2025“…Further integration of Spearman correlation analysis and PCA dimensionality reduction created multidimensional feature sets, revealing substantial accuracy improvements: The BiLSTM model achieved an 83.6% cumulative MAE reduction from 1.65 (raw data) to 0.27 (STL-PCA), while traditional models like Prophet showed an 82.2% MAE decrease after feature engineering optimization. Finally, the Beluga Whale Optimization (BWO)-tuned STL-PCA-BWO-BiLSTM hybrid model delivered optimal performance on test sets (RMSE = 0.22, MAE = 0.16, MAPE = 0.99%, ), exhibiting 40.7% higher accuracy than unoptimized BiLSTM (MAE = 0.27). …”
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1158
Flowchart of the STL-PCA-BWO-BiLSTM model.
Published 2025“…Further integration of Spearman correlation analysis and PCA dimensionality reduction created multidimensional feature sets, revealing substantial accuracy improvements: The BiLSTM model achieved an 83.6% cumulative MAE reduction from 1.65 (raw data) to 0.27 (STL-PCA), while traditional models like Prophet showed an 82.2% MAE decrease after feature engineering optimization. Finally, the Beluga Whale Optimization (BWO)-tuned STL-PCA-BWO-BiLSTM hybrid model delivered optimal performance on test sets (RMSE = 0.22, MAE = 0.16, MAPE = 0.99%, ), exhibiting 40.7% higher accuracy than unoptimized BiLSTM (MAE = 0.27). …”
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1159
Parameter optimization results of BiLSTM.
Published 2025“…Further integration of Spearman correlation analysis and PCA dimensionality reduction created multidimensional feature sets, revealing substantial accuracy improvements: The BiLSTM model achieved an 83.6% cumulative MAE reduction from 1.65 (raw data) to 0.27 (STL-PCA), while traditional models like Prophet showed an 82.2% MAE decrease after feature engineering optimization. Finally, the Beluga Whale Optimization (BWO)-tuned STL-PCA-BWO-BiLSTM hybrid model delivered optimal performance on test sets (RMSE = 0.22, MAE = 0.16, MAPE = 0.99%, ), exhibiting 40.7% higher accuracy than unoptimized BiLSTM (MAE = 0.27). …”
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1160
Descriptive statistical analysis of data.
Published 2025“…Further integration of Spearman correlation analysis and PCA dimensionality reduction created multidimensional feature sets, revealing substantial accuracy improvements: The BiLSTM model achieved an 83.6% cumulative MAE reduction from 1.65 (raw data) to 0.27 (STL-PCA), while traditional models like Prophet showed an 82.2% MAE decrease after feature engineering optimization. Finally, the Beluga Whale Optimization (BWO)-tuned STL-PCA-BWO-BiLSTM hybrid model delivered optimal performance on test sets (RMSE = 0.22, MAE = 0.16, MAPE = 0.99%, ), exhibiting 40.7% higher accuracy than unoptimized BiLSTM (MAE = 0.27). …”