I am following this paper: Measuring, Predicting and Visualizing Short-Term Change in Word Representation and Usage in VKontakte Social Network where in Differencing Statistics section they describe that they performed first-order differences of their trends.
More specifically, for word frequecy time series and tf-idf time series they have taken subtraction, and for word embeddings they have used cosine similarity.
My first question is why they have considered first-order difference without doing remaining tragectory clustering starightly using the original time-series data?
My second question is how first order difference is performed using substraction and cosine simialrity as it is not mentioned in the paper?
I am happy to provide more details if needed.