Position-sensitive positron cameras using silicon pixel detectors have been applied for some preclinical and intraoperative clinical applications. However, the spatial resolution of a positron camera is limited by positron multiple scattering in the detector. An incident positron may fire a number of successive pixels on the imaging plane. It is still impossible to capture the primary fired pixel along a particle trajectory by hardware or to perceive the pixel firing sequence by direct observation. Here, we propose a novel data-driven method to improve the spatial resolution by classifying the primary pixels within the detector using support vector machine. A classification model is constructed by learning the features of positron trajectories based on Monte-Carlo simulations using Geant4. Topological and energy features of pixels fired by (18)F positrons were considered for the training and classification. After applying the classification model on measurements, the primary fired pixels of the positron tracks in the silicon detector were estimated. The method was tested and assessed for [(18)F]FDG imaging of an absorbing edge protocol and a leaf sample. The proposed method improved the spatial resolution from 154.6 ± 4.2 µm (energy weighted centroid approximation) to 132.3 ± 3.5 µm in the absorbing edge measurements. For the positron imaging of a leaf sample, the proposed method achieved lower root mean square error relative to phosphor plate imaging, and higher similarity with the reference optical image. The improvements of the preliminary results support further investigation of the proposed algorithm for the enhancement of positron imaging in clinical and preclinical applications.