On Sat, Nov 10, 2012 at 3:44 AM, Aaron Hosford <[email protected]> wrote:
> My "matrix trick" may be able to map propositions to a high-dimensional >> vector space, but my assumption that concepts are matrices (that are also >> rotations in space) may be unjustified. I need to find a set of criteria >> for matrices to represent concepts faithfully. This direction is still >> hopeful. > > > I'm curious what your "matrix trick" is. Are you familiar with adjacency > matrices? They're the simplest and most common way of representing directed > graphs as matrices. http://en.wikipedia.org/wiki/Adjacency_matrix Semantic > nets typically have sparse adjacency matrices, and there are a lot of good > algorithms and libraries out there for efficiently representing and > manipulating sparse matrices. > Sorry, almost missed your post. My method is to *represent* logical atoms as square matrices with real entries. This allows me to convert the matrices to vectors (by simply flattening the matrices) and calculate the distances (ie similarities) between them via the Euclidean norm. My matrices are different from adjacency matrices which has integer entries. The continuous values potentially allow learning via propagation of errors similar to back-propagation for neural nets. My matrix representation is based on the observation that AB != BA in the composition of concepts, for example "john loves mary != mary loves john". I'm still trying to determine if the matrix representation is sound and consistent with our common-sense view of concepts, but it looks promising... YKY ------------------------------------------- AGI Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/21088071-c97d2393 Modify Your Subscription: https://www.listbox.com/member/?member_id=21088071&id_secret=21088071-2484a968 Powered by Listbox: http://www.listbox.com
