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 substructure rotating data points around the centers of squares. In the extended data space constructed after the rotation phase, each linear substructure is extracted by estimating its normal vector of local minor

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... 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.