Nonnegative Matrix and Tensor Factorization for Discussion Tracking - Text Mining: Classification, Clustering, and Applications - page 105

Aug. 22 (California Campaign Closeout)

0.8

0.6

0.4

0.2

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

Month

Nov. 19 (College Football/Nebraska/Sooners)

0.8

0.6

0.4

0.2

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

Month

Oct. 25 (Enron implodes/news wires)

0.8

0.6

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

Month

FIGURE 5.3 : Three discussion topics identified in the three-way analysis
over days.

with subject line California Campaign Closeout . In essence, Richard Shapiro
praised a subset of employees who worked on California-related projects and
many responded to his acknowledgement. A second discussion group iden-
tified by terms such as college football , Nebraska , Sooners , bowl , Cougars ,
and Tennessee was initiated by M. Motley on November 20. Finally, a third
group (involving many news wire stories) described Enron's pending implo-
sion around October 25 and 26. PARAFAC also found this topic but two days
earlier—we speculate that the difference is due to the random initialization of
both the PARAFAC and nonnegative PARAFAC models. Figure 5.3 shows
the temporal activity of these discussions.

5.5.3 Analysis of Four-Way Tensor
When analyzing the four-way term-author-recipient-day array

,weob-
served four types of profiles over time: ( i ) discussions centered largely on one
or a few days, resulting in a single spike, ( ii ) continual activity, represented
as multiple weekly spikes throughout the year, ( iii ) continual activity with
lulls, where a period of calm separates bursts of discussion, and ( iv )aseries
of weekly spikes usually spanning three or more months.
In the analysis of the three-way

Y

data, NTF identified temporal patterns
that include these four cases. Roughly one third are single spikes patterns,
and just two discussions are of the bimodal type with a lull. Of the 25 groups
found in the four-way analysis of

X

, roughly half were single spikes. Four were
double spikes in time, and nine had sustained activity over many weeks.
Previous research in (5) showed results containing a single spike in time

Y