Abstract
This paper proposes an extended linear fuzzy clustering algorithm for square-shape cluster extraction, in which the FCE algorithm is applied in conjunction with local coordinate rotation. The prototypical squares composed of four sides are handled as if it is a single linear sub-structure rotating data points around the centers of squares. In the extended data space constructed after the rotation phase, each linear sub-structure is extracted by estimating its normal vector of local minor component vector. In a similar way with FCE, the objective function is given by a linear combination of the FCM (point-prototype model) criterion and the FCL (line-prototype model) criterion so that the algorithm can perform prototype extraction in a local region. By changing the priority weight of two criteria, the proposed algorithm can estimate not only square-shape clusters but also grid-like clusters having long tails.
