# Local and Global Algorithms for Disambiguation to Wikipedia

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2 Document text with mentions m1 = Taiwan... m2 = China... m3 = Jiangsu Province φ(m1, t1) φ(m1, t3) φ(m1, t2) t1 = Taiwan t2 = Chinese Taipei t3 =Republic of China t4 = China t5 =People's Republic of China t6 = History of China t7 = Jiangsu ψ(t1, t7) ψ(t3, t7) ψ(t5, t7) Figure 1: Sample Disambiguation to Wikipedia problem with three mentions. The mention Jiangsu is unambiguous. The correct mapping from mentions to titles is marked by heavy edges would expect a mention of Monte Carlo in the same document to refer to the statistical technique rather than the location. Global approaches utilize the Wikipedia link graph to estimate coherence. In this paper, we analyze global and local approaches to the D2W task. Our contributions are as follows: (1) We present a formulation of the D2W task as an optimization problem with local and global variants, and identify the strengths and the weaknesses of each, (2) Using this formulation, we present a new global D2W system, called GLOW. In experiments on existing and novel D2W data sets, GLOW is shown to outperform the previous stateof-the-art system of (Milne and Witten, 2008b), (3) We present an error analysis and identify the key remaining challenge: determining when mentions refer to concepts not captured in Wikipedia. 2 Problem Definition and Approach We formalize our Disambiguation to Wikipedia (D2W) task as follows. We are given a document d with a set of mentions M = {m 1,...,m N }, and our goal is to produce a mapping from the set of mentions to the set of Wikipedia titles W = {t 1,...,t W }. Often, mentions correspond to a concept without a Wikipedia page; we treat this case by adding a special null title to the set W. The D2W task can be visualized as finding a many-to-one matching on a bipartite graph, with mentions forming one partition and Wikipedia titles the other (see Figure 1). We denote the output matching as an N-tuple Γ = (t 1,...,t N ) where t i is the output disambiguation for mention m i. 2.1 Local and Global Disambiguation A local D2W approach disambiguates each mention m i separately. Specifically, let φ(m i,t j ) be a score function reflecting the likelihood that the candidate title t j W is the correct disambiguation for m i M. A local approach solves the following optimization problem: Γ local = arg max Γ N φ(m i,t i ) (1) i=1 Local D2W approaches, exemplified by (Bunescu and Pasca, 2006) and (Mihalcea and Csomai, 2007), utilize φ functions that assign higher scores to titles with content similar to that of the input document. We expect, all else being equal, that the correct disambiguations will form a coherent set of related concepts. Global approaches define a coherence function ψ, and attempt to solve the following disambiguation problem: Γ = arg max [ N φ(m i,t i ) + ψ(γ)] (2) Γ i=1 The global optimization problem in Eq. 2 is NPhard, and approximations are required (Cucerzan, 2007). The common approach is to utilize the Wikipedia link graph to obtain an estimate pairwise relatedness between titles ψ(t i,t j ) and to efficiently generate a disambiguation context Γ, a rough approximation to the optimal Γ. We then solve the easier problem: Γ arg max Γ N [φ(m i,t i ) + i=1 t j Γ ψ(t i,t j )] (3)

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