Fuzzy clustering by Local Approximation of MEmberships (FLAME) is a data clustering algorithm that defines clusters in the dense parts of a dataset and performs cluster assignment solely based on the neighborhood relationships among objects.
The key feature of this algorithm is that the neighborhood relationships among neighboring objects in the feature space are used to constrain the memberships of neighboring objects in the fuzzy membership space.
The FLAME algorithm is mainly divided into three steps: The Local/Neighborhood Approximation of Fuzzy Memberships is a procedure to minimize the Local/Neighborhood Approximation Error (LAE/NAE) defined as the following: where
are the coefficients reflecting the relative proximities of the nearest neighbors.
The NAE can be minimized by solving the following linear equations with unique solution which is the unique global minimum of NAE with value zero: where
The following iterative procedure can be used to solve these linear equations: