Have you ever wondered how to measure the similarity of a word’s neighborhood in a word embedding space? This is a problem that has puzzled many in the field of natural language processing. In essence, we want to determine how many other embedding vectors are very close to a query word’s vector. But how do we do this? One approach could be to measure the density of the query vector’s surrounding volume. Alternatively, we could calculate the mean or median of all the distances from all the vectors to the query vector. Another method might involve sorting the distances of all the vectors to the query vector and then measuring at what point the distances tail off, similar to the elbow method used in determining the optimal number of clusters. However, this might not be exactly the same as clustering all the vectors first and then measuring how dense the query vector’s cluster is, since the vector could be on the edge of its assigned cluster. So, what’s the best way to approach this problem? Let’s dive in and explore some possible solutions. We can start by looking at the different methods for measuring vector similarity, such as cosine similarity or Euclidean distance. We could also experiment with different clustering algorithms, such as k-means or hierarchical clustering, to see which one works best for our specific use case. By exploring these different approaches, we can gain a deeper understanding of how to measure vector similarity in word embedding spaces and improve our natural language processing models.