Nonnegative Matrix and Tensor Factorization for Discussion Tracking - Text Mining: Classification, Clustering, and Applications - page 103

1

California Energy
India
Downfall Newsfeeds
Education (Kaminski)
Fastow Companies

0.8

0.6

0.4

0.2

0

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Month

FIGURE 5.2 (SEE COLOR INSERT FOLLOWING PAGE 130.) :
Five discussion topics identified in the three-way analysis over months.

We also computed a 25-component ( r = 25) nonnegative decomposition of
the term-author-recipient-day array

Y

. One iteration required just under 16
seconds, and between 8 and 12 iterations would satisfy a tolerance of 10 − 4 in
the relative change of fit. We chose the smallest minimizer from among ten
runs from random starting points, and the relative norm of the difference was
0 . 9716.

5.5.2 Analysis of Three-Way Tensor
PARAFAC can be used to identify and track discussions over time in each
triad ,for j =1 ,...,r . A discussion or thread is associated with

the topic and primary participants identified in the columns of A and B ,re-
spectively, and the corresponding column of C provides a profile over time,
showing the relative activity of that discussion over 12 months or over 357
days. 3 As demonstrated in (5), discussions can be visualized as a histogram
(or Gantt chart) of the monthly activity for each discussion identified by the
classical and nonnegative PARAFAC models, respectively. Here, we com-
ment on both the monthly and daily discussions that were uncovered by both
models.
Qualitatively, the results of the nonnegative decomposition and the stan-
dard three-way PARAFAC were very similar. The major difference lies in
the ability to interpret the results. In the 25 discussion groups tracked by
PARAFAC, only six of the groups had any discernible meaning based on
known Enron activities (25). In comparison, the nonnegative PARAFAC
model revealed eight group discussions that could be interpreted. Figure 5.2
shows the temporal activity of some of these discussions.
The topics generated by the nonnegative PARAFAC model certainly re-
flected known events of the year 2001. In the first quarter of that year, Enron
was still dealing with the fallout of the 2000 California energy crisis. Discus-
sions about the Federal and California state governments' investigation of the
California situation were observed as well as Enron's attempted development

{ A j ,B j ,C j }

3 Eight days of the year 2001 involved no discussions for the 197 author subset used.