# Textual Data Science for Logistics and Supply Chain Management
## 3 Results
### Multidimensional Scaling  
The last method in our analysis is multidimensional scaling (MDS) [35; 36] and a subsequent hierarchical cluster analysis. MDS aims to represent input proximities (typically dissimilarities) between objects by means of fitted distances in a low-dimensional space. It therefore visualizes the level of (dis)similarity of cases in a dataset.  
For this analysis, we merged all the interviews into a single text corpus and strived to represent similarities between managers. The starting point is again a DTM with 19 rows (i.e., the total number of interviews) and 5059 columns reflecting all the words used in the interviews minus the ones eliminated through data preparation. The first step was to choose a proper dissimilarity measure, which was applied across columns since we are interested in scaling the managers. We picked the cosine distance, which is popular in text mining applications (see e.g. [37]) since it normalizes for document length. The resulting 19 \(\times\) 19 matrix acts as an input for the MDS computation.  
The MDS approach we used is called _SMACOF_, and it is implemented in the package of the same name [38; 39]. _SMACOF_ is a numerical algorithm that solves a target function called \"stress.\" In simple words, stress incorporates the observed dissimilarities and the fitted dissimilarities. The difference between the two should be as small as possible and hence the stress function is minimized. The smaller the resulting stress value, the better the  
Figure 2: Symmetric CA maps for companies A, B, and C.  
solution. In order to achieve a small stress value, _SMACOF_ provides the option to include an additional transformation step on the observed dissimilarities. For instance, in our application, we performed an ordinal transformation leading to a stress-1 value of 0.175. Stress-1 is a simple normalization of the raw stress value such that it becomes scale-free. Similar to CA, we aimed to fit a 2D or 3D solution as the configuration plot is the main output of MDS and is subject to interpretation. The configuration essentially represents a map of the objects that can be interpreted in a very intuitive way. The closer two points are in the configuration, the more similar they are. In our application, these points represent the interviews for all three companies. Figure 3 shows the resulting configuration plot, and we see that MDS neatly reveals three clusters of managers, according to the company they work for. This result indicates that the managers belonging to one company are more similar to each other when it comes to the topics they deal with (or their choice of words) as opposed to managers from other companies. This can potentially be traced back to the varying working areas, but could also be a strong indicator for differing organizational cultures that impact the choice of words and the respective way in which they see things. Interestingly, M2 from company C on the upper right seems to be an outlier, which might warrant further attention to clarify why his/her choice of words is so different from the other managers.  
This clear cluster separation based on the words used in the interviews is confirmed by a hierarchical cluster analysis based on the fitted MDS distance matrix. By cutting the dendrogram (see Figure 4), based on Ward clustering at a value corresponding to 3 clusters (since we have 3 companies), we see that the resulting clusters perfectly separate the managers from each other. In this example, the clusters represent the companies they are working for. This is also an indicator of the coherence of the respective topics within and between the companies.  
Figure 3: MDS configurations on full dataset.