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Author: Admin | 2025-04-28
F ∪ M – ≥ min _ prev . As the size of the C-LP increases, its PI is monotonically nonincreasing. In addition, M ⊆ M ′ ; therefore , PI F ∪ M ′ ≤ min _ prev . Because M ′ is a prevalent C-LP, PI M ′ ≥ min _ prev . Therefore, PI M ′ ≥ min _ prev , PI F ≥ min _ prev , PI F ∪ M ′ ≤ min _ prev . Because PI F ∪ M – ≥ min_prev , M ⊆ M ′ . It can be obtained from Lemma 1 that PI F ∪ M ′ – ≥ PI F ∪ M – ≥ min _ prev . It is thus proved that T = F ∪ M ′ – is a prevalent negative C-LP. □Definition 4 (Candidate negative co-location).According to the definition of prevalent negative C-LP in Jiang et al. [49], to better calculate the prevalent negative C-LP, the negative C-LP that meets the following conditions is called the candidate negative C-LP:“ P I X ≥ m i n _ p r e v , P I Y ≥ m i n _ p r e v a n d P I X ∪ Y m i n _ p r e v ”.Lemma 4.For any size n candidate negative C-LP, it must be composed of an SZ n − 1 candidate negative C-LP or prevalent C-LP connected to an SZ 2 prevalent C-LP.Proof.Assume an SZ n candidate negative C-LP, T = F ∪ M – . T h e r e f o r e P I F ≥ min _ p r e v , P I M ≥ min _ prev . (1) For any spatial feature in F = F 1 , F 2 , F 3 , … , F n , if one of them is removed, P I F ≥ min _ p r e v will still be true. The C-LP composed of any two spatial features in F = F 1 , F 2 , F 3 , … , F n must be the SZ 2 prevalent C-LP. In addition, if F ′ = F 1 , F 2 , F 3 , … , F n − 1 ∪ M , P I F ′ ≥ min _ p r e v , P I M ≥ min _ p r e v . If PI F ′ ∪ M ≥ min _ prev , then it is prevalent C-LP. If PI F ∪ M min _ prev , it is a candidate negative C-LP. T h e r e f o r e , P
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