The risk of falling is high among different groups of people, such as older people, individuals with Parkinson's disease or patients in neuro-rehabilitation units. Developing robust fall detectors is important for acting promptly in case of a fall. Therefore, in this study we propose to personalize smartphone-based detectors to boost their performance as compared to a non-personalized system. Four algorithms were investigated using a public dataset: three novelty detection algorithms--Nearest Neighbor (NN), Local Outlier Factor (LOF) and One-Class Support Vector Machine (OneClass-SVM)--and a traditional supervised algorithm, Support Vector Machine (SVM). The effect of personalization was studied for each subject by considering two different training conditions: data coming only from that subject or data coming from the remaining subjects. The area under the receiver operating characteristic curve (AUC) was selected as the primary figure of merit. The results show that there is a general trend towards the increase in performance by personalizing the detector, but the effect depends on the individual being considered. A personalized NN can reach the performance of a non-personalized SVM (average AUC of 0.9861 and 0.9795, respectively), which is remarkable since NN only uses activities of daily living for training.