In this paper, we present a novel approach for mining opinions from product reviews, where it converts opinion mining task to identify product features, expressions of opinions and relations between them. By taking advantage of the observation that a lot of product features are phrases, a concept of phrase dependency parsing is introduced, which extends traditional dependency parsing to phrase level. This concept is then implemented for extracting relations between product features and expressions of opinions. Experimental evaluations show that the mining task can benefit from phrase dependency parsing.
Abstract. We revisit the diffusive limit of a steady neutron transport equation in a 2-D unit disk Ω = { x = (x 1 , x 2 ) : | x| ≤ 1} with one-speed velocity Σ = { w = (w 1 , w 2 ) : w ∈ S 1 } asand n is the outward normal vector on ∂Ω, with the Knudsen number 0 < ǫ << 1. A classical result in [4] states thatwhere U 0 is the Knudsen layer solution to the Milne problem (1.28) while U 0 is the corresponding interior solution to the Laplace equation (1.29). We observe that the construction of the first order Knudsen layer fails in [4], due to the intrinsic singularity in the Milne problem. Instead, we are able to establishwhere U ǫ 0 is the solution to the ǫ-Milne problem (1.53) while U ǫ 0 is the corresponding interior solution to the Laplace equation (1.54). Consequently, we deduce thatfor some data, and the classical Knudsen layer theory (3) is invalid in L ∞ .
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