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Note: The following are write-ups written by me critiquing and analysing some of the papers that I have read. I claim no rights to the ideas that were shared in the paper.

The impossibility theorem for clustering Advances in Neural Information Processing Systems - Kleinberg J

The paper discusses about how formalizing clustering can be difficult in most situations. In most situation when there are a heterogeneous collection of objects the need for clustering arises. When processing the heterogeneous set of objects it is obvious that the user would tend to fall back to the technique of clustering. Clustering mostly falls under a persuasive destination. Even though the goal of clustering is clear and persuasive goal it has become very hard to construct a unified framework when we are looking for cognition at a technical level. The numerous approaches towards clustering also hasn't helped this cause. The paper proves that with the help of a certain impossibility theorem as a medium. A set of three simple properties have been taken into consideration and we show that there is no clustering function satisfying all three of the properties. The observation has been that some relaxation in the operation of these properties exposed some trade-offs in well-known clustering techniques.

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Measures of clustering quality: a working set of axioms for Clustering - Ackerman M, Ben-David S

This is an interesting paper that has a counter statement to Klienberg's paper. This paper argues that it is not inherent that a clustering technique may always satisfy the theory of impossibility. The clustering quality measures are axiomatized in this approach. A cluster quality measure function is considered as the medium to measure the quality of the clusters. The cluster quality measures are then analyzed a set of axioms are introduced for the output measures. The axioms are nothing but a medium that retains the principles expressed by Klienberg's axioms while ensuring consistency. By this way the quality measures are considered as the technique to measure the quality of a set of clustering techniques without giving way to any off the tradeoffs as seen in Klienberg's method.

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