A DenseAlert: Incremental Dense-Subtensor Detection in Tensor Streams - Supplementary Document
نویسندگان
چکیده
In this section, we show that the density measure (Definition 1) used in the main paper satisfies properties that a reasonable “anomalousness” measure should meet. These properties were proposed in [Jiang et al. 2015]. Here, we consider two N -way tensors, T of size I1 × I2 × ...× IN and T′ of size I ′ 1 × I ′ 2 × ...× I ′ N . We denote the sum of the entries in each tensor by sum(T) and sum(T′), and define their average entry value as t̄ = sum(T) ∏N n=1 IN and t̄′ = sum(T ′) ∏N n=1 I ′ N . We first list three basic axioms that any anomalousness measure f should
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