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In graph clustering, we want to cluster the nodes of a given graph, such that nodes in the same cluster are highly connected (by edges) and nodes in different clusters are poorly or not connected at all. A simple (hierarchical and divisive) algorithm to perform clustering on a graph is based on first finding the minimum spanning tree of the graph (using e....

Yes, the silhouette method (which is implemented in sklearn as silhouette_score) is commonly used to assess the quality of clusters produced by any clustering algorithm (including $k$-means or any hierarchical clustering algorithm). Roughly, you can compute the silhouette value for different $k$, then you would pick the $k$ with the highest silhouette value.

There is a problem with confining Artificial Intelligence to a single definition, because it has become an umbrella term encompassing many fields of science. It has come a long way from the "thinking machines" of the 50s. Actually, the term was coined in a summer workshop in 1956, whose proposal was: The study is to proceed on the basis of the conjecture ...

Its not required, you can have $m=1$, actually it can be any number $\geq 1$. Now the better question is why to have it? The answer is that it adds a smoothing effect. Lets look at it in each of the limits ($\lim m \rightarrow 1$ and $\lim m \rightarrow \infty$) Towards $\infty$, it makes $u_{ij}$ equal to $\frac{1}{c}$, making each point have equal ...

If you look at Kaufman & Rousseeuw (1990), Finding Groups in Data, they describe an algorithm to evaluate the quality of clusters in agglomerative clustering. You run the clustering algorithm with a specific value k for the number of clusters you want, and that routine then gives you a score to reflect the cohesion of the clustering. If you then cluster ...

This is the classic question of what structure is or can be. It relates directly to the concepts of generalization, pattern recognition, over-fitting in surface fitting strategies, and learning tabula rasa, Latin for blank slate. The underlying questions are these: How can it be determined whether the organization of data in a set, which appears to ...