Osteoporosis is still a worldwide problem, particularly due to associated fragility fractures. Patients at risk of fracture are currently detected using the X-Ray gold standard dual-energy X-ray absorptiometry (DXA), based on a calibrated 2-D image. Different alternatives, such as 3-D X-rays, magnetic resonance imaging (MRI) or ultrasound, have been proposed, the latter having advantages of being portable and sensitive to mechanical and geometrical properties. Bidirectional axial transmission (BDAT) has been used to classify between patients with or without nontraumatic fractures using "classical" ultrasonic parameters, such as velocities, as well as cortical thickness and porosity, obtained from an inverse problems. Recently, complementary parameters acquired with structural and textural analysis of guided wave spectrum images (GWSIs) have been introduced. These parameters are not limited by solution ambiguities, as for inverse problem. The aim of the study is to improve the patient classification using a feature selection strategy for all available ultrasound features completed by clinical parameters. To this end, three classical feature ranking methods were considered: analysis of variance (ANOVA), recursive feature elimination (RFE), and extreme gradient boosting importance feature (XGBI). In order to evaluate the performance of the feature selection techniques, three classical classification methods were used: logistic regression (LR), support vector machine (SVM), and extreme gradient boosting (XGB). The database was obtained from a previous clinical study [Minonzio et al., 2019]. Results indicate that the best accuracy of 71 [66-76]% was achieved by using RFE and SVM with 22 (out of 43) ultrasonic and clinical features. This value outperformed the accuracy of 68 [64-73]% reached with 2 (out of 6) DXA and clinical features. These values open promising perspectives toward improved and generalizable classification of patients at risk of fracture.