Words or concepts can be extracted as vectors using Google's word2vec algorithm: https://code.google.com/p/word2vec/
To express a complex thought composed of simpler concepts, a mathematically natural way is to multiply them together, for example "John loves Mary" = john x loves x mary. I'm wondering if forming the tensor products from word2vec vectors could be meaningful. The tensor product is a bi-linear form (the most universal such bi-linear mappings). So it may preserve the linearity of the original vector space (in other words, the scalar multiplication in the original vector space). If the scalar multiplication is meaningful in the word2vec space, then its meaning would be preserved by the tensor product. The dimension of the tensor product space is also much higher (as the product of the dimensions of the original spaces; this is even greater than the Cartesian product which is the sum of the dimensions of the original spaces.) Computationally, I wonder what is the advantage of using tensor products as opposed to Cartesian products...? Or perhaps the extra richness of tensor structure can be exploited differently... -- *YKY* *"The ultimate goal of mathematics is to eliminate any need for intelligent thought"* -- Alfred North Whitehead ------------------------------------------- AGI Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/21088071-f452e424 Modify Your Subscription: https://www.listbox.com/member/?member_id=21088071&id_secret=21088071-58d57657 Powered by Listbox: http://www.listbox.com
