## 3 Modeling Methodology  
The data mining techniques used in this research are comprised of methods with numeric continuous biodegradability, and methods with discrete biodegradability. The former type includes Multiple Regression Models using a number K of most similar base oils referred, to here as K-Nearest Neighbors Multiple Linear Regression (KNN-MLR) models, Artificial Neural Networks (ANN), and a continuous type of Decision Trees known as Classification and Regression Trees (CART). The discrete approaches include the unsupervised classification techniques of K-means and Two-step clustering methods, and the supervised classification techniques of Logistic Regression, and Decision Trees.  
In order to use the largest data set available for the estimation/training phase, the \"Leave-One-Out-Cross-Validation (LOOCV)\" approach is used. Each of the oils considered is in turn left out of the training /model building phase, and then its biodegradability is predicted using the resulting model. Except for trained (traditional) MLR, and clustering, LOOCV with a number K of most similar oils is used in model building and prediction. The problem of the optimal number N of nearest neighbors is addressed by estimating biodegradability models for a number M of different values of K and taking the median of the K predictions as the final prediction. The median serves as a shield against \"extreme\" predictions. With the ANN technique, the M predictions are derived using M different two-hidden-layer networks, where the starting weights are selected randomly in each of the M runs.  
The performance and testing of each technique in terms of prediction accuracy is analyzed using the predicted median values for all the oils considered following the methodology above. All the tested techniques are evaluated for their performance at three different partitions of the biodegradability spectrum in an attempt to uncover any significant differences in their predictive accuracy between these biodegradability partitions. In addition to the whole data set, two biodegradability classes are considered -low biodegradable (less than 50%), and high biodegradable (over 50%) for model evaluation. This two-class partitioning is supported by the Two-step automatic cluster detection technique which uncovered only two clusters in the available data. This classification was also adopted by some of the previous research practice under the umbrellas of readily or highly biodegradable class and not readily or slowly biodegradable class [11,4].  
Model accuracy is measured by the Mean Absolute Percent Error (MAPE) for the continuous models, and by the percent of misclassified cases for the discrete models. As mentioned earlier, we use the base oils data reported by [PERSON] _et al._[1] and the properties they found to have the most significant impact on biodegradability, namely PC, Log(KV), and Log(NV). The available data is deemed to be representative of the base oil biodegradability process since it includes a wide range of biodegradability as well as a wide range of KV and NV values. The results and findings of the various modeling techniques using this data set are discussed in the following section.