I would not use any mathematical tool unless it perfectly fits the problem to solve. I doubt tensor products can solve NLP. But I can be wrong. I would rather use analogical correspondences via Markov models for NLP. But I can be wrong too. :)
On Wed, Jun 18, 2014 at 2:16 PM, Jim Bromer via AGI <[email protected]> wrote: > If all active words (verbs) had only one or two directions then a directed > vector could be used. However, part of the value of words is that you can > assign a variety of possible relations to them and a single standard will > not work. Suddenly the space and the mathematics has to be warped to cover > the variations. Vector Space and Semantics is just not a good match. > Jim Bromer > > *If you can solve a problem by avoiding it then your attitude may be part > of the problem.* > > > On Wed, Jun 18, 2014 at 10:23 AM, Matt Mahoney via AGI <[email protected]> > wrote: > >> The semantic vector of a sentence is approximately the sum of the word >> vectors, not the product. It is not exact because it does not account >> for word order. John + loves + Mary = Mary + loves + John. >> >> On Wed, Jun 18, 2014 at 8:47 AM, YKY (Yan King Yin, 甄景贤) >> <[email protected]> wrote: >> > >> > 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 >> > >> > -- >> > You received this message because you are subscribed to the Google >> Groups >> > "Genifer" group. >> > To unsubscribe from this group and stop receiving emails from it, send >> an >> > email to [email protected]. >> > For more options, visit https://groups.google.com/d/optout. >> >> >> >> -- >> -- Matt Mahoney, [email protected] >> >> >> ------------------------------------------- >> AGI >> Archives: https://www.listbox.com/member/archive/303/=now >> RSS Feed: >> https://www.listbox.com/member/archive/rss/303/24379807-f5817f28 >> Modify Your Subscription: https://www.listbox.com/member/?&; >> >> Powered by Listbox: http://www.listbox.com >> > > *AGI* | Archives <https://www.listbox.com/member/archive/303/=now> > <https://www.listbox.com/member/archive/rss/303/23601136-e0982844> | > Modify > <https://www.listbox.com/member/?&;> > Your Subscription <http://www.listbox.com> > ------------------------------------------- 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
