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In large-scale fingerprinting localization systems, fine-grained location estimation and quick location determination are conflicting concerns. To achieve finer grained localization, we have to collect signal patterns at a larger number of training locations. However, this will incur higher computation cost during the pattern-matching process. In this paper, we propose a novel discriminant minimization search (DMS)-based localization methodology. Continuous and differentiable discriminant functions are designed to extract the spatial correlation of signal patterns at training locations. The advantages of the DMS-based methodology are threefold. First, with through slope of discriminant functions, the exhaustive pattern-matching process can be replaced by an optimization search process, which could be done by a few quick jumps. Second, the continuity of the discriminant functions helps predict signal patterns at untrained locations so as to achieve finer grained localization. Third, the large amount of training data can be compressed into some functions that can be represented by a few parameters. Therefore, the storage space required for localization can be significantly reduced. To realize this methodology, two algorithms, namely, Newton-PL and Newton-INT, are designed based on the concept of gradient descent search. Simulation and experiment studies show that our algorithms do provide finer grained localization and incur less computation cost.