SparsePZ uses sparse basis representation to fully represent individual photometric redshift probability density functions (PDFs). This approach requires approximately half the parameters for the same multi-Gaussian fitting accuracy, and has the additional advantage that an entire PDF can be stored by using a 4-byte integer per basis function. Only 10-20 points per galaxy are needed to reconstruct both the individual PDFs and the ensemble redshift distribution, N(z), to an accuracy of 99.9 per cent when compared to the one built using the original PDFs computed with a resolution of δz = 0.01, reducing the required storage of 200 original values by a factor of 10-20. This basis representation can be directly extended to a cosmological analysis, thereby increasing computational performance without losing resolution or accuracy.