# Guided Semi-Supervised Non-Negative Matrix Factorization
## 5 Conclusions and Future Works  
In this paper, we analyze the characteristics of SSNMF (Section 2.2), Guided NMF (Section 2.3), and TS-NMF (Section 2.4) concerning the tasks of classification and topic modeling. From these methods, we propose a novel NMF model, namely the GSSNMF, which combines characteristics of SSNMF, Guided NMF, and TS-NMF. SSNMF utilizes label information for classification, Guided NMF leverages user-specific seed words to guided topic content, and TS-NMF uses selected label information to inform topic modeling. To carry out classification and topic modeling simultaneously, ourGSSNMF uses additional label information to improve the coherence of topic modeling results while incorporating seed words for more accurate classification. Taking advantage of multiplicative updates, we provide a solver for GSSNMF and then evaluate its performance on real-life data. In general, GSSNMF is able to out-perform SSNMF on the task of classification. The extra information from the seed words contributes to a more accurate classification result. Specifically, SSNMF tends to focus on the most prevalent class label and classifies all documents into that class label. Unlike SSNMF, the additional information from choosing seed words as the class labels can help GSSNMF treat each class label equally and avoid the trivial solution of classifying every single document into the most prevalent class label. Additionally, GSSNMF is able to generate more coherent topics when compared to Guided NMF on the task of topic modeling. The extra information from the known label matrix can help GSSNMF better identify which documents belong to the same class. As a result, GSSNMF generates topics with higher and less variable coherence scores. When compared with TS-NMF, GSSNMF also reveals its flexibility in choosing the latent topic number, \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Rank** & **6** & **7** & **8** & **9** \\ \hline \multirow{4}{*}{\(\mathcal{C}_{\text{avg}}\)} & Classical NMF & 980.860 & 940.967 & 874.404 & 832.409 \\ \cline{2-6}  & Guided NMF & 858.361 & 798.737 & 741.057 & 714.796 \\ \cline{2-6}  & TS-NMF & - & - & - & 856.786 \\ \cline{2-6}  & GSSNMF & 984.443 & 942.678 & 881.626 & 843.399 \\ \hline \multirow{2}{*}{Best GSSNMF Parameters} & \(\mu=0.0085\) & \(\mu=0.012\) & \(\mu=0.012\) & \(\mu=0.0001\) \\  & \(\lambda=0.1\) & \(\lambda=0.3\) & \(\lambda=0.3\) & \(\lambda=0.5\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Coherence of topics generated by Classical NMF, Guided NMF, TS-NMF, and GSSNMF for 20 Newsgroups data. which potentially helps it to generate a set of more coherent topics and meanwhile a higher classification accuracy. While there are other variants of SSNMF according to [14], we developed GSSNMF only based on the standard Frobenius norm. In the future, we plan to make use of other comparable measures like the _information divergence_, and derive a corresponding multiplicative updates solver. In addition, across all the experiments, we selected the parameters \(\lambda\) and \(\mu\), which put weight on the seed word matrix and label matrix, respectively, based on the experimental results. In our continued work, we plan to conduct error analysis to determine how each parameter affects the other parameter and the overall approximation results. Particularly, for a given parameter \(\lambda\) or \(\mu\), we hope to identify an underlying, hidden relationship that allows us to quickly pick a matching \(\mu\) or \(\lambda\), respectively, that maximizes GSSNMF performance. Conceptualization, P.L., C.T. and Y.Z. ; Data curation, P.L., C.T. and Y.Z. ; Formal analysis, P.L., C.T. and Y.Z. ; Funding acquisition, D.N. ; Investigation, P.L., C.T. and Y.Z. ; Project administration, D.N. ; Software, J.A.C. ; Supervision, J.A.C., L.H., B.J. and D.N. ; Visualization, P.L., C.T. and Y.Z. ; Writing--original draft, P.L., C.T. and Y.Z. ; Writing--review and editing, J.A.C., L.H., B.J. and D.N. All authors have read and agreed to the published version of the manuscript.