example 3: two less clear features (revisited)

let's move onto an example, similiar to the last, but with some more 'noise'

again let's work with a contrived corpus

d1: a a a a a a  b b b b b b b b  c c c c c c  e e  f f 
d2: a a a a a a a  b b b b b b  c c c c c c c c c  d
d3: a  c c c c c c c c  d d d d d d d d  e e e e e e e e e  f f f f f f f
d4: b  c c c c c  d d d d d d d d  e e e e e e e  f f f f f f f

which is represented as the 6x4 document term matrix

	d1	d2	d3	d4
a	6	7	1	0
b	8	6	0	1
c	6	9	8	5
d	0	1	8	8
e	2	0	9	7
f	2	0	7	7

singular value decomposition

here is a decomposition of A performed again using SVDLIBC

recall:
S describes the relative strengths of the features
U describes the relationship between terms (rows) and features (columns)
Vt describes the relationshop between features (rows) and documents (columns)

interpretation of S

similiarly to our last example we've got two dominant features but the additional non zero term frequencies have meant we've got variance for all possible 4 features.
(this is representive of the general non contrived case where if we were dealing with a large number of documents we'd only be interested in the first dominant features)
like last time since the first two values are much higher than the second two we can derive that there are two main dominant features in the corpus.

interpretation of VS

the matrix product VS describes the relation between documents (VS's rows) and the features (VS's columns)