Multiple candidate feature components of media content or projection matrices (or other hash functions, e.g., non-linear projections) are identified. Each of the candidate projection matrices (or other hash functions) includes an array of coefficients that relate to the candidate features. A subgroup of the candidate features or the projection matrices (or other hash functions) are selected based at least partially on an optimized combination of at least two characteristics of the candidate features or projection matrices (or other hash functions). Media fingerprints that uniquely identify the media content are derived from the selected optimized subgroup. Optimal projection matrices (or other hash functions) may be designed. Performance or sensitivity (e.g., search time) characteristics of the fingerprints are thus balanced with robustness characteristics thereof.