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I have $1000$ scenarios, each of which is composed of $5$ users' coordinates $(x_i,y_i), \forall i \in \{1,\dots,5\}$. Now, based on users' coordinates, I want to cluster these $1000$ scenarios into 100 clusters. Specifically, if users in two scenarios keep proximal or same coordinates, such two scenarios should be grouped into the same cluster.

My idea is to create a matrix with $1000$ scenarios as rows and $5$ users' coordinates (i.e., $5$ x-coordinates and $5$ y-coordinates) as columns. The matrix will hence have $1000$ rows and $10$ columns. Then, I apply a clustering algorithm such as k-means to cluster these $1000$ scenarios into $100$ clusters.

My concern is how to define a distance or similarity metric based only on these coordinates. Can anyone help me with this? Any comments would be appreciated!

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