Efficient dictionary learning for constructing quasi-local transformation models

This paper develops four innovative dictionary learning (DL) approaches for constructing quasi-local transformation models. Quasi-local transformation models are useful in geotechnical design at a target site to infer design parameters from site-specific measurements containing other soil/rock properties. Typically, a quasi-local transformation model is trained using a subset of database sites from a geotechnical database, selected based on their “similarity” to the target site. In previous approaches for constructing quasi-local transformation models, such as the recently developed tailored clustering enabled regionalization (TCER), uniform weights are usually assigned to the selected database sites (i.e., they are equally important to inference). Conversely, the proposed DLs allocate different weights to different database sites. In the proposed DLs, each database site is used to train a Bayesian model for drawing an atom that contains several posterior design parameter samples conditioning on the known soil/rock property data at the target site. Then several atoms are selected as the non-trivial atoms, and the quasi-local inference result is obtained by linearly superposing these non-trivial atoms with different weights. The four proposed DLs are OMP-DL, Lasso-DL, CC-DL, and TC-DL. They correspond to distinct atom selection solutions: orthogonal matching pursuit (OMP; a traditional solution for DL), the least absolute shrinkage and selection operator (Lasso), classical clustering (CC), and tailored clustering (TC). OMP and Lasso are sparsity solutions, while CC and TC are clustering solutions. Notably, clustering has not previously been applied in DL for non-trivial atom selection. TCER is utilized as the baseline solution in this study. Illustrative examples utilizing four databases indicate that TC-DL generally exhibits superior inference performance. Compared with the baseline solution, OMP-DL achieves a reduction in the root mean square error (RMSE) of inference results by 4.7% to 49.4% (averaging 19.4%), while TC-DL reduces the RMSE by 19.4% to 52.0% (averaging 34.8%).