Matrix memories

Many times since the 1950s it has been noted that methods from linear algebra suggest ways to construct associative memories in which data can potentially be retrieved on the basis of some form of similarity. Typically one starts from some list of vectors to be stored, then forms a matrix such as m=PseudoInverse[list]. Given a new piece of data corresponding to a vector v, its decomposition in terms of stored vectors can be found by computing v . m. And by applying various forms of thresholding one can often pick out at least approximately the stored vector closest to the piece of data given. But such schemes tend to be inefficient in practice, as well as presumably being unrealistic as actual models of the brain.