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, Understanding Collaborative Filtering with Galois Connections

I. Dmitry and . Ignatov,

. Abstract, We compare the properties of these operators and their applicability in simple collaborative user-to-user and item-to-item setting. Moreover, we propose a new neighbourhood-forming operator based on pair-wise similarity ranking of users, which takes intermediate place between the studied closure operators and its relaxations in terms of neighbourhood size and demonstrates comparatively good Precision-Recall trade-off. In addition, we compare the studied neighbourhood-forming operators in the collaborative filtering setting against simple but strong benchmark, the SlopeOne algorithm, over bimodal cross-validation on MovieLens dataset, this paper, we explain how Galois connection and related operators between sets of users and items naturally arise in user-item data for forming neighbourhoods of a target user or item for Collaborative Filtering

X. ,

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A. Op, 2 U is called a kernel operator iff for X ? U : op(X) ? X (intensity). us discuss the meaning of several important properties of the introduced Galois operators in terms of Collaborative Filtering domain

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, ·) is not idempotent

, Operator (·) is a kernel operator (antitone, extensive, and idempotent), Corollary, vol.1

, N k \ {u}) \ {u}

, Make a prediction of the rating for each items found in the previous step. Choose top n of them

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