SVD (A) = U*S*VT
In the current scenario matrix A is a term-document matrix (m terms * n documents). Visually SVD looks like this:
In my previous post I had used 1.7 million sentences and 44 million words for training word2vec, i.e. if we run SVD on this large matrix, it might end up taking centuries on my machine. However SVD calculations on large matrices can be done using a large cluster of Spark. [3] [4]
I kept the document size constant at 2500 and let the term size vary. In order to rank the terms in relation to query term I used cosine distance. This time along with named entities I also added the noun phrases. The data is the news articles from yesterday (4th May, 2015). Here is the vector for the first query "delhi":
Query for "chief_minister":
What if we want to find out a relationship, instead of querying? Query for india and narendra_modi:
Word vectors obtained from LSA can be useful in expanding the search queries, guessing the relationships (as shown above), generating similarity based recommendations and many other tasks related to text.
I wrote a one file implementation of LSA in Java (its buggy and design patterns free!), it uses jBLAS for SVD and other matrix operations, code can be found at github.
A couple of more links to understand LSA through examples:
Results
I kept the document size constant at 2500 and let the term size vary. In order to rank the terms in relation to query term I used cosine distance. This time along with named entities I also added the noun phrases. The data is the news articles from yesterday (4th May, 2015). Here is the vector for the first query "delhi":
[law_minister=0.34, jitender_singh_tomar=0.23, chief_minister=0.22, fake=0.21, arvind_kejriwal=0.21, degree=0.18, protest=0.16, law_degree=0.16, win=0.15, congress=0.15, aam_aadmi_party=0.14, incident=0.14]Notice that the vector contains terms like chief_minister and law_degree which are not named entities.
Query for "chief_minister":
[arvind_kejriwal=0.34, parkash_singh_badal=0.29, today=0.28, delhi=0.28, mamata_banerjee=0.27, office=0.26, state=0.26, people=0.26, act=0.25, mufti_mohammad_sayeed=0.25, bjp=0.25, jammu_and_kashmir=0.25, governor=0.24]The vector gives the name of all the chief ministers which were in the news recently. Same goes for the query "prime_minster":
[shinzo_abe=0.37, japanese=0.33, sushil_koirala=0.27, david_cameron=0.27, tony_abbott=0.26, 2015=0.24, benjamin_netanyahu=0.24, president=0.23, country=0.23, government=0.22, washington=0.22]Lets look up for a person now, "rohit_sharma":
[mumbai_indians=0.45, skipper=0.4, ritika_sajdeh=0.37, captain=0.36, batsman=0.35, indian=0.34, lendl_simmons=0.34, kieron_pollard=0.33, parthiv_patel=0.31, ipl=0.29, runs=0.29, good=0.29, ambati_rayudu=0.29, mitchell_mcclenaghan=0.27, unmukt_chand=0.27]
Finding relations
What if I query for chief_minister and west_bengal and add both the vectors?
[mamata_banerjee=0.69, bjp=0.67, state=0.6]It gives the correct result, Mamata Banerjee is the current Chief Minister of West Bengal. Note that now numbers don't represent the cosine distance.
What if we want to find out a relationship, instead of querying? Query for india and narendra_modi:
[prime_minister=0.5, make=0.42, government=0.4, country=0.4]Querying mumbai_attack with charged gives a list of a few names of those who were involved/charged:
[people=1.14, left=1.08, november=1.05, dead=1.05, 166=1.05, executing=1.04, planning=1.04, 2008=1.02, hamad_amin_sadiq=1.0, shahid_jameel_riaz=1.0, mazhar_iqbal=1.0, jamil_ahmed=1.0, younis_anjum=0.94, abdul_wajid=0.94, zaki-ur_rehman_lakhvi=0.62]Although above results look good, they are not always accurate, for example, query for captain and royal_challengers_bangalore does not return virat_kohli as the first result:
[ipl=0.67, rcb=0.66, match=0.64, kolkata_knight_riders=0.6, virat_kohli=0.57]I guess more data from different time periods can help in establishing concrete relationships.
Word vectors obtained from LSA can be useful in expanding the search queries, guessing the relationships (as shown above), generating similarity based recommendations and many other tasks related to text.
I wrote a one file implementation of LSA in Java (its buggy and design patterns free!), it uses jBLAS for SVD and other matrix operations, code can be found at github.
A couple of more links to understand LSA through examples:
