 Hi, I'm back! Hierarchical clustering, the topic of our previous videos, is a simple and cool method of finding clusters in our data. Remember, we use the data on course grades with 16 students and 7 school subjects. We measured the Euclidean distance between each pair of students and clustered the data accordingly. Here I will use the word minimum variance method for linkage. This will join clusters so that the points in the resulting cluster are nearest the center. It's a bit more complicated than that, but the idea of word linkage is that the points in the resulting clusters are as close together as possible. My problem here, however, is not a clustering algorithm, but how to interpret the resulting clustering structure. Why are Phil, Bill and Leah in the same cluster? What do they have in common? The hierarchical clustering widget emits two signals. Selected data, as well as the entire data set with an additional column that indicates the selection. Let me first show this in the data table widget. I have to rewire the connection between hierarchical clustering and data table to communicate the entire data set. See the selected column in the data table. We would now like to find the features that is school subjects, which can differentiate between selected students and students outside the selection. But wait a second, this is something we have already done. Remember our video on data distribution where we constructed a workflow that told us which socioeconomic features are related to extended life expectancy? Maybe not, but you can always check that out on our channel. The critical part to remember is that we used boxplot. Let me add one to the output of hierarchical clustering and rewire the signal to transfer all the data instead of just a selection. In boxplot, I have to set selected as a subgrouping feature, and I also check order by relevance to subgroups. I find history, English and French at the top of the list of variables. Taking a closer look at history, for example, we can see that Phil, George and company perform quite well, their average score being 73. Compare that to the mediocre 19 of everyone else. In English, the cluster's average score is even higher at 91 compared to 31 of everyone else. And the scores in French tell a similar story. The cluster of students we have selected is particularly good in subjects from social sciences. How about a cluster that includes Fred, Nash and Catherine? Ouch, their scores in history are terrible at 16. However, with a score of 83, they do well in algebra and are better than the other students in physics. It looks like we have a group of natural science enthusiasts on our hands. The only remaining cluster is the one with Anna and Henry. They love sports. With the hierarchical clustering boxplot combination, we can explore any cluster or subcluster in our data. Clicking on any branch will update the boxplot which, with its ordered list of variables, can help us characterize the cluster. Boxplot uses the student's t-statistic to rank the features according to the difference between their distribution within the cluster and distribution of feature values outside the cluster. For instance, the feature that best distinguishes students in my current cluster is biology, with a student's t-statistic of 5.2. Explaining clusters with Orange's boxplot is simple. I find it surprising that it was so easy to characterize groups of students in our data sets. I could use the same workflow for other data sets and hierarchical clusters. For instance, I could characterize different groups of countries we found from the socio-economic data sets in our previous videos. But I will leave that up to you. It is time to move on to other exciting topics in data sets.