Indexing methods are described that may be used by databases, search engines, query and retrieval systems, context sensitive data mining, context mapping, language identification, image recognition, and robotic systems. Raw baseline features from an input signal are aggregated, abstracted and indexed for later retrieval or manipulation. The feature index is the quantization number for the underlying features that are represented by an abstraction. Trajectories are used to signify how the features evolve over time. Features indexes are linked in an ordered sequence indicative of time quanta, where the sequence represents the underlying input signal. An example indexing system based on the described processes is an inverted index that creates a mapping from features or atoms to the underlying documents, files, or data. A highly optimized set of operations can be used to manipulate the quantized feature indexes, where the operations can be fine tuned independent from the base feature set.