# Committee Machine Learning for Electrofacies-Guided Well Placement and Oil Recovery Optimization
## 2 Data and Methodology
### Electrofacies Prediction
\begin{table}
\begin{tabular}{l l l l l l l} \hline \hline
**Method** & **K-Means Clustering** & **K-Medians Clustering** & **Hierarchical Clustering** & **GMM Clustering** & **Spectral Clustering** \\ \hline \multirow{4}{*}{Key Characteristics} & Divides data into K & Similar to K-Means but & Builds a hierarchy of & Probabilistic model & Based on graph theory \\  & clusters. Uses centroids to & of the mean to find the & agglomerative & assuming each cluster is & and eigenvalues of a \\  & represent clusters. & center of clusters. & (bottom-up) or divisive & a Gaussian distribution. & similarity matrix. \\ \hline \multirow{4}{*}{Cluster Membership} & Hard (each data point & Hard (each data point & \multirow{2}{*}{Harden (each data point & \multirow{2}{*}{a probability of } \\  & belongs to one cluster) & & & & \\  & & belongs to one cluster) & & hierarchical structure) & be belonging to \\  & & & & & & \\ \hline \multirow{4}{*}{Scalability} & High (efficient for & \multirow{2}{*}{Moderate} & \multirow{2}{*}{Low to Moderate} & \multirow{2}{*}{Low to Moderate} & \multirow{2}{*}{Low (computationally \\  & large datasets)} & & & & \\ \hline \multirow{4}{*}{Advantages} & Simple and efficient. & Less sensitive to outliers & \multirow{2}{*}{No need to specify} & Can model & \multirow{2}{*}{Can handle non-linearly} \\  & Well-suited for spherical & & than K-Means. More & number of clusters in & non-spherical clusters & separable clusters. \\  & clusters. Scalable to & robust for & robust for & & and varied cluster & Effective for clustering \\  & large datasets. & Gaussian data & dendrogram for visualizing cluster relationships. & shapes. Provides a probability of membership. & & complex shapes \\ \hline \multirow{4}{*}{Disadvantages} & Sensitive to initialization. & Computationally & \multirow{2}{*}{Computationally } & Computationally & \multirow{2}{*}{Repeures computing } \\  & Assumes clusters are & expensive for large & & & & \\ \cline{1-1}  & spherical and equally sized. & datasets. Sensitive to & \multirow{2}{*}{Antistisals. Can struggle} & \multirow{2}{*}{which may not always fit} & \multirow{2}{*}{expensive. Sensitive to } \\ \cline{1-1}  & Not ideal for & & initial conditions. Assumes spherical clusters. & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: A comparison of the properties of the different machine learning methods. specific electrofacies. The distribution of the three predicted electrofacies using five different machine learning methods--k-means, k-median, hierarchical clustering, Gaussian mixture model, and spectral clustering--for the upper formation, the lower formation, and the middle formation are shown in Figures 5-7, respectively. Facies 2 is the target electrofacies of interest; hence, its vertical and lateral distribution is obtained using the committee machine in Figures 5, 6 and 7f for the upper, lower, and middle formations, respectively. Figure 3: Well logs (gamma-ray, density, and resistivity shown on tabs 1 to 3 respectively) and predicted electrofacies using different clustering methods shown on tabs 4 to 8, respectively, for k-means, k-median, hierarchical, Gaussian mixture model, and spectral clustering for (**a**) Well 1 and (**b**) Well 3. Shale facies (Facies 1), Sand facies (Facies 2), and Mixed Facies (Facies 3) are shown as red, green, and blue, respectively. Figure 4: Silhouette plots for the different methods and the committee machine, demonstrating significantly better separation of the clusters for the committee machine prediction (last panel) as compared to the individual methods. Figure 5: 3D distributed electrofacies for the top formation generated using (**a**) k-means, (**b**) k-median, (**c**) hierarchical, (**d**) Gaussian mixture model, and (**e**) spectral clustering. (**f**) shows the committee machine results where all methods agree on the distribution of Facies 2 in the top formation.