# Guided Semi-Supervised Non-Negative Matrix Factorization
## 4 Experiments
### Topic Modeling on the CIP Dataset
In Table 1, we provide an example of the outputs of topic modeling from Guided NMF using \(\lambda=0.4\) and from GSSNMF using \(\lambda=0.3\) and \(\mu=0.006\) for a rank of 7. Note that we output only the top 10 keywords under each identified topic group for ease of viewing, but our coherence scores are measured using the top 30 keywords. Thus, while the top 10 probable keywords of the generated topics may look similar across the two methods, and the coherence scores calculated from the top 30 probable keywords reveal that GSSNMF produces more coherent topics as a whole in comparison to Guided NMF. Specifically, GSSNMF demonstrates an ability to produce topics with similar levels of coherence (as seen from the small variance in individual coherence scores \(\mathcal{C}\) of each topic), while Guided NMF produces topics that may vary in level of coherence (as seen from the large variance in individual coherence scores \(\mathcal{C}\) for each topic). This further illustrates that GSSNMF is able to use the additional label information to execute topic modeling with better coherence. We also compare GSSNMF to two other NMF methods--classical NMF and TS-NMF--on the basis of topic modeling performance on the CIP dataset. Following our methodology for applying GSSNMF to this data, we ran 10 independent trials of classical NMF for each rank from 6 to 9 and computed the mean \(\mathcal{C}_{\text{avg}}\) for each rank. The results for classical NMF, Guided NMF, and GSS-NMF using ranks 6-9 are summarized in Table 2. For the rank 6-9 approximations, while classical NMF slightly outperforms GSSNMF on the basis of the topic coherence score \(\mathcal{C}_{\text{avg}}\), GSSNMF retains the advantage that the generated topics are guided by a priori information, whereas classical NMF has no such guarantee. As noted in Section 2.4, when TS-NMF is applied for topic modeling, the number of latent topics must be exactly equal to the number of different labels. In the case of the CIP data, the AOBs have 13 possible labels, so we ran TS-NMF on the CIP data with a rank of 13, computing \(\mathcal{C}_{\text{avg}}\) over 10 independent trials. TS-NMF (using rank 13) had \(\mathcal{C}_{\text{avg}}=1458.732\), which outperforms our recorded GSSNMF results for the same data. This could be a result of the structure of the CIP dataset, together with being constrained to use a rank of 13 when applying TS-NMF. As shown in Table 3, at least four of the topics generated by TS-NMF were all clearly related to gang activity, which is one of the labels used by TS-NMF. While the resulting topics are highly coherent, the abundance of closely related topics obscures the latent structure of the data. This arises from the fact that TS-NMF must use a rank exactly equal to the number of different labels, which may not accurately reflect the true low-rank structure of the data. In this case, we see that this splits larger topics into more specific subtopics that have several words in common. This increases \(\mathcal{C}_{\text{avg}}\), but the resulting topics do not correspond well to the original labels. Figure 4: Comparison of Guided NMF mean \(\mathcal{C}_{\text{avg}}\) score (over 10 independent trials) and highest GSSNMF mean \(\mathcal{C}_{\text{avg}}\) score (over 10 independent trials) for each \(\lambda\) tested.