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The uniaxial compressive strength (UCS) and elasticity modulus (E) of intact rock are two fundamental requirements in engineering applications. These parameters can be measured either directly from the uniaxial compressive strength test or indirectly by using soft computing predictive models. In the present research, the UCS and E of intact carbonate rocks have been predicted by introducing two stacking ensemble learning models from non-destructive simple laboratory test results. For this purpose, dry unit weight, porosity, P‐wave velocity, Brinell surface harnesses, UCS, and static E were measured for 70 carbonate rock samples. Then, two stacking ensemble learning models were developed for estimating the UCS and E of the rocks. The applied stacking ensemble learning method integrates the advantages of two base models in the first level, where base models are multi-layer perceptron (MLP) and random forest (RF) for predicting UCS, and support vector regressor (SVR) and extreme gradient boosting (XGBoost) for predicting E. Grid search integrating k-fold cross validation is applied to tune the parameters of both base models and meta-learner. The results demonstrate the generalization ability of the stacking ensemble method in the comparison of base models in the terms of common performance measures. The values of coefficient of determination (R2) obtained from the stacking ensemble are 0.909 and 0.831 for predicting UCS and E, respectively. Similarly, the stacking ensemble yielded Root Mean Squared Error (RMSE) values of 1.967 and 0.621 for the prediction of UCS and E, respectively. Accordingly, the proposed models have superiority in the comparison of SVR and MLP as single models and RF and XGBoost as two representative ensemble models. Furthermore, sensitivity analysis is carried out to investigate the impact of input parameters. [ABSTRACT FROM AUTHOR]

Considerable research efforts have been done in learning semi-supervised distance metric learning based on both manifold and cluster assumptions in the past few years. However, there is a major problem with them once they are applied to data lying on stratified space. The problem is that label smoothness assumption on manifold and cluster may be violated in the intersecting regions of manifolds. This problem is caused by overlearning of locality that misleads the metric learning process in the absence of enough labeled data. In this paper, we will propose a novel semi-supervised metric learning for stratified spaces (S2MLS2) which removes unsuitable local constraints in the manifold based methods for adapting to the smoothness assumption on multi manifolds. We will also impose some non-local constraints to detect the shared structures at different positions in the absence of enough supervised information. Besides, a novel bootstrapping method based on smoothness assumption on multi manifolds will be proposed to enlarge the labeled data. The proposed algorithm is based on different behavior of Laplacian of piecewise-smooth function on multi manifolds in the neighborhood of non-interior points of the manifolds as compared with interior points of the manifolds. Experiments on artificial and real benchmark data sets demonstrate that the proposed metric learning method outperforms many state-of-the-art metric learning methods. [ABSTRACT FROM AUTHOR]

Manifold-based semi-supervised classifiers have attracted increasing interest in recent years. However, they suffer from over learning of locality and cannot be applied to the point cloud sampled from a stratified space. This problem is resolved in this paper by using the fact that the smoothness assumption must be satisfied with the interior points of the manifolds and may be violated in the non-interior points. Distinction of interior and non-interior points is based on the behavior of graph Laplacian in the ϵ -neighborhood of the intersection points. First, this property was generalized to K NN graph representing the stratified space and then a new algorithm was proposed that penalizes the smoothness on the non-interior points of the manifolds by modifying the edge weights of the graph. Compared to some recent multi-manifold semi-supervised classifiers, the proposed method does not require neither knowing the dimensions of the manifolds nor large amount of unlabeled points to estimate the underling manifolds and does not assume similar properties for neighbors of all data points. Some experiments have been conducted in order to show that it improves the classification accuracy on a number of artificial and real benchmark data sets. [ABSTRACT FROM AUTHOR]