Visible light communications (VLC) based indoor positioning is a promising approach to serve an increasing need for location-aware services. Received signal strength (RSS) fingerprints based visible light positioning (VLP) was shown to achieve highly accurate, yet simple, VLP systems. It needs, however, large training datasets; whose collection is labor intensive. In this work, an artificial dataset generation methodology based on a modified pathloss model is proposed, where the pathloss exponent is assumed to be variable. Four interpolation techniques were investigated for the estimation of the variable pathloss exponent, where bicubic interpolation showed the best results in the simulation using a uniform sparse grid. The method is specially conceived to address the site surveying demand while attaining high positioning accuracy under non-line-of-sight (NLOS) conditions with sparse offline measurements. The technique is not limited to Visible light applications since it depends only on the RSS and the pathloss model. Moreover, by using the weighted k-nearest-neighbor (k-NN) machine learning technique, this work designs an accurate VLP system based on sparse fingerprints. Simulation results show an average positioning error of 2.48 cm using weighted k-NN (Wk-NN) with only 53 offline measurements in a 25 m2 area. Furthermore, experimental results show an average positioning error of 3.04 cm with only 18 offline measurements in an area of approximately 9 m2, and an average positioning error of 1.92 cm using only 16 offline measurements in an area of 6 m2.