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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....

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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.

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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 ...

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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 ...

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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 ...

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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 ...

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