## 2 Materials and Methods
### Oxygen Forecasting Model for Flatfish  
In this forecasting model, there are three parts of this model for on-line calculation of forthcoming acquired data series, which are based feature clustering, training for different groups, and the forecasting method. Firstly, flatfish are statistically labeled and clustered by length and weight of their properties. By doing so, flatfish of similar characteristics will be clustered in the same group which may imply an identical requirement of oxygen when they are packaged for waterless transportation. Secondly, for objects in a reasonably clustered group, LSSVM for error correction can be used for GM (1, 1) oxygen prediction. Finally, the forecasting method will acquire on-line data and calculate the rectified forecasting data series by GM-PSO-LSSVM. The procedures are as demonstrated in Figure 3. The specific process of this forecasting model is discussed in the following segment.  
The specific procedure of the fuzzy clustered GM-PSO-LSSVM forecasting model that was processed as follows.  
1. Input a set of fish feature (W, L) representing fish weight W and length L. This is the process of clustering for flatfish properties. It is partitioned with classification coefficient \(m\) and obtains N groups by validity index numbering for fuzzy clustering.
2. As for every group, the model can utilize the GM model for ambient factor forecasting--carbon dioxide (CO\({}_{2}\)), and temperature (T) as well as humidity (H). These data were stepwise predictions of sequence parameters.
3. Take the ambient factors--CO\({}_{2}\), T, and H--as inputs of LSSVM, and the residual of actual and predicted oxygen series as outputs for training. At the same time, the model uses PSO to optimize the parameters \(\gamma\) and \(\delta^{2}\) to complete the best regression for error of oxygen prediction by GM (1, 1).
4. The GM-PSO-LSSVM forecasting model acquires the M segment data by utilizing the GM model to forecast the next M data of forthcoming oxygen concentration by residual compensation with full consideration of the influence of other ambient factors.
5. If the forecasting is not halted, the forecasting model can continuously obtain M segment data of ambient factors to perform the procedure of step 3, or to returns to step 5.
6. Evaluate the indices of this model by error analysis with mean absolute error (MAE), mean absolute percent error (MAPE), and root-mean-square error (RMSE).  
The modeling procedures are shown in below in Figure 4. Figure 4a shows the regression training by LSSVM with ambient changes (CO\({}_{2}\), humidity, temperature) in a series as input data and with the residual of actual and predicted data as output data. During this training process, the PSO algorithm would optimize the parameters in the regression process and move the LSSVM model closer to the optimal solution. In spite of this, the algorithm required a small sample for modeling, parallel computing, and adaptive strong ability to achieve higher precision in small sample circumstances, so as to improve the generalization ability of the model combination. In Figure 4b, the process of forecasting is to classify the given subjects which belong to a certain clustering center using its PSO-LSSVM model and the GM model for on-line prediction. The hybrid algorithm would forecast the forthcoming oxygen level of the GM (1, 1) method step by step and rectify the forecasted result by the PSO-LSSVM residual  
Figure 3: Oxygen concentration forecasting model of flatfish during waterless transportation. PSO: particle swarm optimization; LSSVM: least squares support vector machines; GM: gray model.  
regression value. Therefore, this method was more suitable for the changing of coming ambient factors, which was more advanced than the forecasting ability of utilizing a single prediction algorithm.